{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,3]],"date-time":"2026-05-03T02:31:28Z","timestamp":1777775488406,"version":"3.51.4"},"reference-count":1199,"publisher":"Emerald","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,7,21]]},"abstract":"<jats:p>Advances in artificial intelligence (AI) are fueling a new paradigm of discoveries in natural sciences. Today, AI has started to advance natural sciences by improving, accelerating, and enabling our understanding of natural phenomena at a wide range of spatial and temporal scales, giving rise to a new area of research known as AI for science (AI4Science). Being an emerging research paradigm, AI4Science is unique in that it is an enormous and highly interdisciplinary area. Thus, a unified and technical treatment of this field is needed, yet challenging. This work aims to provide a technically thorough account of a subarea of AI4Science; namely, AI for quantum, atomistic, and continuum systems. These areas aim at understanding the physical world from the subatomic (wavefunctions and electron density), atomic (molecules, proteins, materials, and interactions), to macro (fluids, climate, and subsurface) scales and form an important subarea of AI4Science. A unique advantage of focusing on these areas is that they largely share a common set of challenges, thereby allowing a unified and foundational treatment. A key common challenge is how to capture physics first principles, especially symmetries, in natural systems by deep learning methods. We provide an in-depth yet intuitive account of techniques to achieve equivariance to symmetry transformations. We also discuss other common technical challenges, including explainability, out-of-distribution generalization, knowledge transfer with foundation and large language models, and uncertainty quantification. To facilitate learning and education, we provide categorized lists of resources that we found to be useful. We strive to be thorough and unified and hope this initial effort may trigger more community interests and efforts to further advance AI4Science.<\/jats:p>","DOI":"10.1561\/2200000115","type":"journal-article","created":{"date-parts":[[2025,7,23]],"date-time":"2025-07-23T10:25:42Z","timestamp":1753266342000},"page":"385-849","source":"Crossref","is-referenced-by-count":11,"title":["Artificial intelligence for science in quantum, atomistic, and continuum systems"],"prefix":"10.1108","volume":"18","author":[{"given":"Xuan","family":"Zhang","sequence":"first","affiliation":[{"name":"Texas A&M University Department of Computer Science and Engineering, , College Station, ,","place":["Texas, USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Limei","family":"Wang","sequence":"additional","affiliation":[{"name":"Texas A&M University Department of Computer Science and Engineering, , College Station, ,","place":["Texas, 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(2022), \u201cChemberta-2: towards chemical foundation models\u201d, arXiv preprint arXiv:2209.01712."},{"key":"2026041607113563400_ref007","first-page":"3438","article-title":"Invariance principle meets information bottleneck for out-of-distribution generalization","volume":"34","author":"Ahuja","year":"2021","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026041607113563400_ref008","unstructured":"Ajakan, H., Germain, P., Larochelle, H., Laviolette, F. and Marc-Hand, M. (2014), \u201cDomain-adversarial neural networks\u201d, arXiv preprint arXiv:1412.4446."},{"key":"2026041607113563400_ref009","article-title":"Lie point symmetry and physics in-formed networks","author":"Akhound-Sadegh","year":"2023"},{"key":"2026041607113563400_ref010","doi-asserted-by":"crossref","unstructured":"Alayrac, J.-B., Donahue, J., Luc, P., Miech, A., Barr, I., Hasson, Y., Lenc, K., Mensch, A., Millican, K., Reynolds, M., Ring, R., Rutherford, E., Cabi, S., Han, T., Gong, Z., Samangooei, S., Monteiro, M., Menick, J., Borgeaud, S., Brock, A., Nematzadeh, A., Sharifzadeh, S., Binkowski, M., Barreira, R., Vinyals, O., Zisserman, A. and Simonyan, K. (2022), \u201cFlamingo: a visual language model for few-shot learning\u201d, arXiv preprint arXiv:2204.14198.","DOI":"10.52202\/068431-1723"},{"issue":"2","key":"2026041607113563400_ref011","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1063\/1.1730376","article-title":"Studies in molecular dynamics. I. General method","volume":"31","author":"Alder","year":"1959","journal-title":"The Journal of Chemical Physics"},{"issue":"1","key":"2026041607113563400_ref012","doi-asserted-by":"publisher","first-page":"e27005","DOI":"10.1002\/qua.27005","article-title":"Constraint-based analysis of a physics-guided kinetic energy density expansion","volume":"123","author":"Aldossari","year":"2023","journal-title":"International Journal of Quantum Chemistry"},{"key":"2026041607113563400_ref013","volume-title":"Advances in Neural Information Processing Systems","author":"Allen","year":"2022"},{"key":"2026041607113563400_ref014","volume-title":"ICLR.","author":"Alon","year":"2021"},{"issue":"7","key":"2026041607113563400_ref015","doi-asserted-by":"crossref","first-page":"1324","DOI":"10.1109\/TPS.2009.2021476","article-title":"Design of the plasma position and shape control in the ITER tokamak using in-vessel coils","volume":"37","author":"Ambrosino","year":"2009","journal-title":"IEEE Transactions on Plasma Science"},{"key":"2026041607113563400_ref016","first-page":"14927","article-title":"Deep evidential regression","volume":"33","author":"Amini","year":"2020","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"9","key":"2026041607113563400_ref017","doi-asserted-by":"crossref","first-page":"787","DOI":"10.1016\/j.chembiol.2003.09.002","article-title":"The process of structure-based drug design","volume":"10","author":"Anderson","year":"2003","journal-title":"Chemistry & Biology"},{"key":"2026041607113563400_ref018","article-title":"Cormorant: covariant molecular neural networks","volume":"32","author":"Anderson","year":"2019","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026041607113563400_ref019","volume-title":"Fundamentals of Aerodynamics","author":"Anderson","year":"2017"},{"issue":"4047","key":"2026041607113563400_ref020","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1126\/science.177.4047.393","article-title":"More is different","volume":"177","author":"Anderson","year":"1972","journal-title":"Science"},{"key":"2026041607113563400_ref021","first-page":"15","article-title":"Exploring local rotation invariance in 3D CNNs with steerable filters","author":"Andrearczyk","year":"2019"},{"issue":"3","key":"2026041607113563400_ref022","doi-asserted-by":"crossref","first-page":"738","DOI":"10.1016\/j.chempr.2020.12.009","article-title":"Active learning accelerates ab initio molecular dynamics on reactive energy surfaces","volume":"7","author":"Ang","year":"2021","journal-title":"Chem"},{"key":"2026041607113563400_ref023","unstructured":"Angelopoulos, A.N. and Bates, S. (2021), \u201cA gentle introduction to con-formal prediction and distribution-free uncertainty quantification\u201d, arXiv preprint arXiv:2107.07511."},{"issue":"1","key":"2026041607113563400_ref024","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41467-024-54639-7","article-title":"Crystal structure generation with autoregressive large language modeling","volume":"15","author":"Antunes","year":"2024","journal-title":"Nature Communications"},{"key":"2026041607113563400_ref025","first-page":"266","article-title":"Adaptive activity monitoring with uncertainty quantification in switching Gaussian process models","author":"Ardywibowo","year":"2019"},{"key":"2026041607113563400_ref026","unstructured":"Arjovsky, M., Bottou, L., Gulrajani, I. and Lopez-Paz, D. (2019), \u201cIn-variant risk minimization\u201d, arXiv preprint arXiv:1907.02893."},{"issue":"1","key":"2026041607113563400_ref027","doi-asserted-by":"crossref","first-page":"014112","DOI":"10.1103\/PhysRevB.96.014112","article-title":"Efficient and accurate machine-learning interpolation of atomic energies in compositions with many species","volume":"96","author":"Artrith","year":"2017","journal-title":"Physical Review B"},{"issue":"1","key":"2026041607113563400_ref028","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1038\/75556","article-title":"Gene ontology: tool for the unification of biology","volume":"25","author":"Ashburner","year":"2000","journal-title":"Nature Genetics"},{"issue":"9","key":"2026041607113563400_ref029","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1038\/nrg.2016.86","article-title":"Towards precision medicine","volume":"17","author":"Ashley","year":"2016","journal-title":"Nature Reviews Genetics"},{"issue":"7","key":"2026041607113563400_ref030","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1016\/j.advengsoft.2008.08.001","article-title":"Parametric design of aircraft geometry using partial differential equations","volume":"40","author":"Athanasopoulos","year":"2009","journal-title":"Advances in Engineering Software"},{"issue":"7795","key":"2026041607113563400_ref031","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1038\/s41586-020-1994-5","article-title":"Closed-loop optimization of fast-charging protocols for batteries with machine learning","volume":"578","author":"Attia","year":"2020","journal-title":"Nature"},{"key":"2026041607113563400_ref032","unstructured":"Axelrod, S. and Gomez-Bombarelli, R. (2020), \u201cMolecular machine learning with conformer ensembles\u201d, arXiv preprint arXiv:2012.08452."},{"issue":"1","key":"2026041607113563400_ref033","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1038\/s41597-022-01288-4","article-title":"GEOM, energy-annotated molecular conformations for property prediction and molecular generation","volume":"9","author":"Axelrod","year":"2022","journal-title":"Scientific Data"},{"key":"2026041607113563400_ref034","first-page":"4","article-title":"GBPNet: universal geometric representation learning on protein structures","author":"Aykent","year":"2022"},{"key":"2026041607113563400_ref035","article-title":"GotenNet: rethinking efficient 3D equivariant graph neural networks","author":"Aykent","year":"2025"},{"key":"2026041607113563400_ref036","article-title":"Predicting properties of amorphous solids with graph network potentials","author":"Aykol","year":"2023"},{"issue":"6557","key":"2026041607113563400_ref037","doi-asserted-by":"crossref","first-page":"871","DOI":"10.1126\/science.abj8754","article-title":"Accurate prediction of protein structures and interactions using a three-track neural network","volume":"373","author":"Baek","year":"2021","journal-title":"Science"},{"key":"2026041607113563400_ref038","doi-asserted-by":"crossref","first-page":"4625","DOI":"10.1007\/s00521-021-06616-0","article-title":"Graph neural network for Hamiltonian-based material property prediction","volume":"34","author":"Bai","year":"2022","journal-title":"Neural Computing and Applications"},{"key":"2026041607113563400_ref039","doi-asserted-by":"crossref","first-page":"111608","DOI":"10.1016\/j.jcp.2022.111608","article-title":"Uncertainty quantification of the 4th kind; optimal posterior accuracy-uncertainty tradeoff with the minimum enclosing ball","volume":"471","author":"Bajgiran","year":"2022","journal-title":"Journal of Computational Physics"},{"issue":"51","key":"2026041607113563400_ref040","doi-asserted-by":"crossref","first-page":"21484","DOI":"10.1073\/pnas.0906910106","article-title":"Multiscale mobility networks and the spatial spreading of infectious diseases","volume":"106","author":"Balcan","year":"2009","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"2026041607113563400_ref041","article-title":"Explainability techniques for graph convolutional networks","author":"Baldassarre","year":"2019"},{"issue":"1","key":"2026041607113563400_ref042","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41524-021-00575-9","article-title":"Deep learning for visualization and novelty detection in large X-ray diffraction datasets","volume":"7","author":"Banko","year":"2021","journal-title":"NPJ Computational Materials"},{"issue":"4","key":"2026041607113563400_ref043","doi-asserted-by":"crossref","first-page":"448","DOI":"10.1038\/s41567-020-0842-8","article-title":"Unveiling the predictive power of static structure in glassy systems","volume":"16","author":"Bapst","year":"2020","journal-title":"Nature Physics"},{"issue":"2","key":"2026041607113563400_ref044","doi-asserted-by":"crossref","first-page":"020603","DOI":"10.1103\/PhysRevLett.100.020603","article-title":"Well-tempered meta-dynamics: a smoothly converging and tunable free-energy method","volume":"100","author":"Barducci","year":"2008","journal-title":"Physical Review Letters"},{"issue":"2","key":"2026041607113563400_ref045","doi-asserted-by":"publisher","first-page":"515","DOI":"10.1103\/RevModPhys.73.515","article-title":"Phonons and related crystal properties from density-functional perturbation theory","volume":"73","author":"Baroni","year":"2001","journal-title":"Reviews of Modern Physics"},{"issue":"4","key":"2026041607113563400_ref046","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1038\/s42256-022-00461-z","article-title":"Autoregressive neural-network wavefunctions for ab initio quantum chemistry","volume":"4","author":"Barrett","year":"2022","journal-title":"Nature Machine Intelligence"},{"key":"2026041607113563400_ref047","first-page":"3","volume-title":"Finite Difference Method","author":"Bartels","year":"2016"},{"key":"2026041607113563400_ref048","unstructured":"Batatia, I., Batzner, S., Kov\u00e1cs, D.P., Musaelian, A., Simm, G.N.C., Drautz, R., Ortner, C., Kozinsky, B. and Cs\u00e1nyi, G. (2022a), \u201cThe design space of E(3)-equivariant atom-centered interatomic potentials\u201d, arXiv preprint arXiv:2205.06643."},{"key":"2026041607113563400_ref049","doi-asserted-by":"crossref","unstructured":"Batatia, I., Geiger, M., Munoz, J., Smidt, T., Silberman, L. and Ortner, C. (2023), \u201cA general framework for equivariant neural networks on reductive Lie groups\u201d, arXiv preprint arXiv:2306.00091.","DOI":"10.52202\/075280-2412"},{"key":"2026041607113563400_ref050","doi-asserted-by":"crossref","DOI":"10.52202\/068431-0830","article-title":"MACE: Higher order equivariant message passing neural networks for fast and accurate force fields","author":"Batatia","year":"2022","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026041607113563400_ref051","first-page":"524","article-title":"Noise2self: Blind denoising by self-supervision","author":"Batson","year":"2019"},{"issue":"1","key":"2026041607113563400_ref052","doi-asserted-by":"crossref","first-page":"2453","DOI":"10.1038\/s41467-022-29939-5","article-title":"E (3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials","volume":"13","author":"Batzner","year":"2022","journal-title":"Nature Communications"},{"issue":"6","key":"2026041607113563400_ref053","doi-asserted-by":"publisher","first-page":"3098","DOI":"10.1103\/PhysRevA.38.3098","article-title":"Density-functional exchange-energy approximation with correct asymptotic behavior","volume":"38","author":"Becke","year":"1988","journal-title":"Physical Review A"},{"issue":"7","key":"2026041607113563400_ref054","doi-asserted-by":"publisher","first-page":"5648","DOI":"10.1063\/1.464913","article-title":"Density-functional thermochemistry. 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(2022), \u201cPangu-weather: a 3D high-resolution model for fast and accurate global weather forecast\u201d, arXiv preprint arXiv:2211.02556."},{"key":"2026041607113563400_ref071","doi-asserted-by":"crossref","unstructured":"Bian, N., Han, X., Sun, L., Lin, H., Lu, Y. and He, B. (2023), \u201cChatGPT is a knowledgeable but inexperienced solver: An investigation of commonsense problem in large language models\u201d, arXiv preprint arXiv:2303.16421.","DOI":"10.63317\/32y85i5g9gso"},{"issue":"2","key":"2026041607113563400_ref072","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1038\/nchem.1243","article-title":"Quantifying the chemical beauty of drugs","volume":"4","author":"Bickerton","year":"2012","journal-title":"Nature Chemistry"},{"key":"2026041607113563400_ref073","doi-asserted-by":"crossref","unstructured":"Bigi, F., Pozdnyakov, S.N. and Ceriotti, M. (2023), \u201cWigner kernels: body-ordered equivariant machine learning without a basis\u201d, arXiv preprint arXiv:2303.04124.","DOI":"10.1063\/5.0208746"},{"key":"2026041607113563400_ref074","volume-title":"Pattern Recognition and Machine Learning","author":"Bishop","year":"2006"},{"issue":"518","key":"2026041607113563400_ref075","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1080\/01621459.2017.1285773","article-title":"Variational inference: a review for statisticians","volume":"112","author":"Blei","year":"2017","journal-title":"Journal of the American statistical Association"},{"key":"2026041607113563400_ref076","first-page":"1613","article-title":"Weight uncertainty in neural network","author":"Blundell","year":"2015"},{"issue":"1","key":"2026041607113563400_ref077","doi-asserted-by":"crossref","first-page":"5479","DOI":"10.1038\/s41467-020-19286-8","article-title":"Autonomously revealing hidden local structures in supercooled liquids","volume":"11","author":"Boattini","year":"2020","journal-title":"Nature Communications"},{"key":"2026041607113563400_ref078","unstructured":"Bogatskiy, A., Ganguly, S., Kipf, T., Kondor, R., Miller, D.W., Murnane, D., Offermann, J.T., Pettee, M., Shanahan, P., Shimmin, C., et al. (2022), \u201cSymmetry group equivariant architectures for physics\u201d, arXiv preprint arXiv:2203.06153."},{"issue":"1","key":"2026041607113563400_ref079","doi-asserted-by":"publisher","first-page":"5223","DOI":"10.1038\/s41467-020-19093-1","article-title":"Quantum chemical accuracy from density functional approximations via machine learning","volume":"11","author":"Bogojeski","year":"2020","journal-title":"Nature Communications"},{"key":"2026041607113563400_ref080","unstructured":"Boiko, D.A., MacKnight, R. and Gomes, G. (2023), \u201cEmergent autonomous scientific research capabilities of large language models\u201d, arXiv preprint arXiv:2304.05332."},{"key":"2026041607113563400_ref081","article-title":"BioMedLM","author":"Bolton","year":"2022"},{"key":"2026041607113563400_ref082","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/1758-2946-3-32","article-title":"PubChem3D: a new resource for scientists","volume":"3","author":"Bolton","year":"2011","journal-title":"Journal of Cheminformatics"},{"key":"2026041607113563400_ref083","first-page":"3905","article-title":"Learnable Bernoulli dropout for Bayesian deep learning","author":"Boluki","year":"2020"},{"key":"2026041607113563400_ref084","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/TAI.2023.3268609","article-title":"Bayesian proper orthogonal decomposition for learnable reduced-order models with uncertainty quantification","author":"Boluki","year":"2023","journal-title":"IEEE Transactions on Artificial Intelligence"},{"key":"2026041607113563400_ref085","unstructured":"Bommasani, R.\n          \n          et al. (2021), \u201cOn the opportunities and risks of foundation models\u201d, ArXiv, available at:https:\/\/crfm.stanford.edu\/assets\/report.pdf"},{"key":"2026041607113563400_ref086","article-title":"Spherical Fourier neural operators: learning stable dynamics on the sphere","author":"Bonev","year":"2023"},{"key":"2026041607113563400_ref087","article-title":"AirfRANS: high fidelity computational fluid dynamics dataset for approximating Reynolds-averaged Navier-Stokes solutions","author":"Bonnet","year":"2022","journal-title":"36th Conference on Neural Information Processing Systems (NeurIPS 2022) Track on Datasets and Benchmarks."},{"issue":"20","key":"2026041607113563400_ref088","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1002\/andp.19273892002","article-title":"Zur quantentheorie der molekeln","volume":"389","author":"Born","year":"1927","journal-title":"Annalen der Physik"},{"key":"2026041607113563400_ref089","article-title":"SE(3)-stochastic flow matching for protein backbone generation","author":"Bose","year":"2023"},{"issue":"16","key":"2026041607113563400_ref090","doi-asserted-by":"crossref","first-page":"1074","DOI":"10.1002\/qua.24836","article-title":"Adaptive machine learning frame-work to accelerate ab initio molecular dynamics","volume":"115","author":"Botu","year":"2015","journal-title":"International Journal of Quantum Chemistry"},{"key":"2026041607113563400_ref091","first-page":"31972","article-title":"MAgnet: mesh agnostic neural PDE solver","volume":"35","author":"Boussif","year":"2022","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026041607113563400_ref092","doi-asserted-by":"crossref","DOI":"10.1002\/0470072768","volume-title":"Response Surfaces, Mixtures, and Ridge Analyses","author":"Box","year":"2007"},{"key":"2026041607113563400_ref093","volume-title":"Bayesian Inference in Statistical Analysis","author":"Box","year":"2011"},{"issue":"1063","key":"2026041607113563400_ref094","doi-asserted-by":"publisher","first-page":"542","DOI":"10.1098\/rspa.1950.0036","article-title":"Electronic wave functions - I. 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(2023), \u201cChemCrow: augmenting large-language models with chemistry tools\u201d, arXiv preprint arXiv:2304.05376."},{"key":"2026041607113563400_ref098","article-title":"Geometric and physical quantities improve E(3) equivariant message passing","author":"Brandstetter","year":"2022"},{"key":"2026041607113563400_ref099","unstructured":"Brandstetter, J., van den Berg, R., Welling, M. and Gupta, J.K. (2023), \u201cClifford neural layers for PDE modeling\u201d, in The Eleventh International Conference on Learning Representations, available at:https:\/\/openreview.net\/forum?id=okwxL_c4x84"},{"key":"2026041607113563400_ref100","first-page":"2241","article-title":"Lie point symmetry data augmentation for neural PDE solvers","author":"Brandstetter","year":"2022"},{"key":"2026041607113563400_ref101","article-title":"Message passing neural PDE solvers","author":"Brandstetter","year":"2022"},{"issue":"1","key":"2026041607113563400_ref102","doi-asserted-by":"publisher","first-page":"872","DOI":"10.1038\/s41467","article-title":"Bypassing the Kohn-Sham equations with machine learning","volume":"8","author":"Brockherde","year":"2017","journal-title":"Nature Communications"},{"key":"2026041607113563400_ref103","unstructured":"Bronstein, M.M., Bruna, J., Cohen, T. and Veli\u010dkovi\u0107, P. (2021), \u201cGeometric deep learning: grids, groups, graphs, geodesics, and gauges\u201d, arXiv preprint arXiv:2104.13478."},{"key":"2026041607113563400_ref104","unstructured":"Brosse, N., Riquelme, C., Martin, A., Gelly, S. and Moulines, \u00c9. (2020), \u201cOn last-layer algorithms for classification: Decoupling representation from uncertainty estimation\u201d, arXiv preprint arXiv:2001.08049."},{"issue":"9","key":"2026041607113563400_ref105","doi-asserted-by":"crossref","first-page":"4105","DOI":"10.1063\/1.1775767","article-title":"Quantum and classical studies of vibrational motion of CH 5+ on a global potential energy surface obtained from a novel ab initio direct dynamics approach","volume":"121","author":"Brown","year":"2004","journal-title":"The Journal of Chemical Physics"},{"issue":"28","key":"2026041607113563400_ref106","doi-asserted-by":"crossref","first-page":"2004","DOI":"10.1002\/jcc.26732","article-title":"MCML: Combining physical constraints with experimental data for a multi-purpose meta-generalized gradient approximation","volume":"42","author":"Brown","year":"2021","journal-title":"Journal of Computational Chemistry"},{"key":"2026041607113563400_ref107","first-page":"1877","article-title":"Language models are few-shot learners","volume":"33","author":"Brown","year":"2020","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026041607113563400_ref108","doi-asserted-by":"crossref","DOI":"10.1017\/9781009089517","volume-title":"Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control","author":"Brunton","year":"2022"},{"key":"2026041607113563400_ref109","article-title":"Machine learning for partial differential equations","author":"Brunton","year":"2023"},{"key":"2026041607113563400_ref110","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1146\/annurev-fluid-010719-060214","article-title":"Machine learning for fluid mechanics","volume":"52","author":"Brunton","year":"2020","journal-title":"Annual Review of Fluid Mechanics"},{"issue":"15","key":"2026041607113563400_ref111","doi-asserted-by":"crossref","first-page":"3932","DOI":"10.1073\/pnas.1517384113","article-title":"Discovering governing equations from data by sparse identification of nonlinear dynamical systems","volume":"113","author":"Brunton","year":"2016","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"2","key":"2026041607113563400_ref112","first-page":"e1631","article-title":"Delocalization error: the greatest outstanding challenge in density-functional theory","volume":"13","author":"Bryenton","year":"2023","journal-title":"Wiley Interdisciplinary Reviews: Computational Molecular Science"},{"issue":"15","key":"2026041607113563400_ref113","doi-asserted-by":"publisher","first-page":"150901","DOI":"10.1063\/1.4704546","article-title":"Perspective on density functional theory","volume":"136","author":"Burke","year":"2012","journal-title":"The Journal of Chemical Physics"},{"issue":"7715","key":"2026041607113563400_ref114","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1038\/s41586-018-0337-2","article-title":"Machine learning for molecular and materials science","volume":"559","author":"Butler","year":"2018","journal-title":"Nature"},{"issue":"4","key":"2026041607113563400_ref115","doi-asserted-by":"crossref","first-page":"2180","DOI":"10.1021\/acs.jctc.1c00904","article-title":"CIDER: an expressive, nonlocal feature set for machine learning density functionals with exact constraints","volume":"18","author":"Bystrom","year":"2022","journal-title":"Journal of Chemical Theory and Computation"},{"key":"2026041607113563400_ref116","unstructured":"Bystrom, K. and Kozinsky, B. (2023), \u201cNonlocal machine-learned ex-change functional for molecules and solids\u201d, arXiv preprint arXiv: 2303.00682."},{"issue":"4","key":"2026041607113563400_ref117","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1002\/anie.196603851","article-title":"Specification of molecular chirality","volume":"5","author":"Cahn","year":"1966","journal-title":"Angewandte Chemie International Edition in English"},{"issue":"9","key":"2026041607113563400_ref118","doi-asserted-by":"crossref","first-page":"2561","DOI":"10.1093\/bioinformatics\/btac154","article-title":"DeepREAL: a deep learning powered multi-scale modeling framework for predicting out-of-distribution ligand-induced GPCR activity","volume":"38","author":"Cai","year":"2022","journal-title":"Bioinformatics"},{"key":"2026041607113563400_ref119","first-page":"11","article-title":"Binding site-enhanced sequence pretraining and out-of-cluster meta-learning predict genome-wide chemical-protein interactions for dark proteins","author":"Cai","year":"2022"},{"issue":"1","key":"2026041607113563400_ref120","doi-asserted-by":"crossref","first-page":"e1010851","DOI":"10.1371\/journal.pcbi.1010851","article-title":"End-to-end sequence-structure-function meta-learning predicts genome-wide chemical-protein interactions for dark proteins","volume":"19","author":"Cai","year":"2023","journal-title":"PLoS Computational Biology"},{"issue":"3","key":"2026041607113563400_ref121","doi-asserted-by":"crossref","first-page":"035116","DOI":"10.1103\/PhysRevB.97.035116","article-title":"Approximating quantum many-body wave functions using artificial neural networks","volume":"97","author":"Cai","year":"2018","journal-title":"Physical Review B"},{"issue":"4","key":"2026041607113563400_ref122","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1051\/m2an:2000102","article-title":"On the convergence of SCF algorithms for the Hartree-Fock equations","volume":"34","author":"Cances","year":"2000","journal-title":"ESAIM: Mathematical Modelling and Numerical Analysis"},{"key":"2026041607113563400_ref123","first-page":"24924","article-title":"Choose a transformer: Fourier or Galerkin","volume":"34","author":"Cao","year":"2021","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"6325","key":"2026041607113563400_ref124","doi-asserted-by":"crossref","first-page":"602","DOI":"10.1126\/science.aag2302","article-title":"Solving the quantum many-body problem with artificial neural networks","volume":"355","author":"Carleo","year":"2017","journal-title":"Science"},{"key":"2026041607113563400_ref125","doi-asserted-by":"crossref","unstructured":"Caro, M.C., Huang, H.-Y., Ezzell, N., Gibbs, J., Sornborger, A.T., Cincio, L., Coles, P.J. and Holmes, Z. (2022), \u201cOut-of-distribution generalization for learning quantum dynamics\u201d, arXiv preprint arXiv:2204.10268.","DOI":"10.2172\/2377336"},{"key":"2026041607113563400_ref126","article-title":"La th\u00e9orie des groupes fnis et continus et la g\u00e9om\u00e9trie dif\u00e9rentielle trait\u00e9es par la m\u00e9thode du rep\u00e8re mobile","author":"Cartan","year":"1937"},{"issue":"3","key":"2026041607113563400_ref127","doi-asserted-by":"crossref","first-page":"036401","DOI":"10.1103\/PhysRevLett.130.036401","article-title":"Discovering quantum phase transitions with fermionic neural networks","volume":"130","author":"Cassella","year":"2023","journal-title":"Physical Review Letters"},{"issue":"10","key":"2026041607113563400_ref128","doi-asserted-by":"crossref","first-page":"9034","DOI":"10.1039\/c2ee22341d","article-title":"New cubic perovskites for one-and two-photon water splitting using the computational materials repository","volume":"5","author":"Castelli","year":"2012","journal-title":"Energy & Environmental Science"},{"issue":"2","key":"2026041607113563400_ref129","doi-asserted-by":"crossref","first-page":"5814","DOI":"10.1039\/C1EE02717D","article-title":"Computational screening of perovskite metal oxides for optimal solar light capture","volume":"5","author":"Castelli","year":"2012","journal-title":"Energy & Environmental Science"},{"issue":"6","key":"2026041607113563400_ref130","doi-asserted-by":"crossref","first-page":"1649","DOI":"10.1021\/acs.jcim.3c00285","article-title":"Do large language models understand chemistry? A conversation with ChatGPT","volume":"63","author":"Castro Nascimento","year":"2023","journal-title":"Journal of Chemical Information and Modeling"},{"key":"2026041607113563400_ref131","doi-asserted-by":"crossref","unstructured":"Cen, J., Li, A., Lin, N., Ren, Y., Wang, Z. and Huang, W. (2024), \u201cAre high-degree representations really unnecessary in equivariant graph neural networks?\u201d arXiv preprint arXiv:2410.11443.","DOI":"10.52202\/079017-0826"},{"issue":"7","key":"2026041607113563400_ref132","doi-asserted-by":"crossref","first-page":"3081","DOI":"10.1103\/PhysRevB.16.3081","article-title":"Monte Carlo simulation of a many-fermion study","volume":"16","author":"Ceperley","year":"1977","journal-title":"Physical Review B"},{"key":"2026041607113563400_ref133","doi-asserted-by":"crossref","first-page":"1237","DOI":"10.1007\/BF01030009","article-title":"Fermion nodes","volume":"63","author":"Ceperley","year":"1991","journal-title":"Journal of Statistical Physics"},{"issue":"7","key":"2026041607113563400_ref134","doi-asserted-by":"crossref","first-page":"566","DOI":"10.1103\/PhysRevLett.45.566","article-title":"Ground state of the electron gas by a stochastic method","volume":"45","author":"Ceperley","year":"1980","journal-title":"Physical Review Letters"},{"key":"2026041607113563400_ref135","article-title":"A program to build E(N)-equivariant steerable CNNs","volume-title":"International Conference on Learning Representations (ICLR)","author":"Cesa","year":"2022"},{"key":"2026041607113563400_ref136","unstructured":"Cesa, G., Lang, L. and Weiler, M. (2022b), \u201cESCNN PyTorch extension for E(d)-steerable CNNs\u201d, available at:https:\/\/github.com\/QUVA-Lab\/escnn"},{"key":"2026041607113563400_ref137","doi-asserted-by":"publisher","DOI":"10.1021\/acscatal.0c04525","article-title":"Open catalyst 2020 (OC20) dataset and community challenges","author":"Chanussot","year":"2021","journal-title":"ACS Catalysis"},{"issue":"10","key":"2026041607113563400_ref138","doi-asserted-by":"crossref","first-page":"4113","DOI":"10.1039\/C5DT04392A","article-title":"Defects and disorder in metal organic frameworks","volume":"45","author":"Cheetham","year":"2016","journal-title":"Dalton Transactions"},{"key":"2026041607113563400_ref139","unstructured":"Chen, A. and Heyl, M. (2023), \u201cEfficient optimization of deep neural quantum states toward machine precision\u201d, arXiv preprint arXiv: 2302.01941."},{"issue":"11","key":"2026041607113563400_ref140","doi-asserted-by":"crossref","first-page":"718","DOI":"10.1038\/s43588-022-00349-3","article-title":"A universal graph deep learning interatomic potential for the periodic table","volume":"2","author":"Chen","year":"2022","journal-title":"Nature Computational Science"},{"issue":"9","key":"2026041607113563400_ref141","doi-asserted-by":"crossref","first-page":"3564","DOI":"10.1021\/acs.chemmater.9b01294","article-title":"Graph networks as a universal machine learning framework for molecules and crystals","volume":"31","author":"Chen","year":"2019","journal-title":"Chemistry of Materials"},{"issue":"6","key":"2026041607113563400_ref142","doi-asserted-by":"crossref","first-page":"1241","DOI":"10.1016\/j.drudis.2018.01.039","article-title":"The rise of deep learning in drug discovery","volume":"23","author":"Chen","year":"2018","journal-title":"Drug Discovery Today"},{"key":"2026041607113563400_ref143","article-title":"Systematic improvement of neural network quantum states using Lanczos","author":"Chen","year":"2023","journal-title":"Advances in Neural Information Processing Systems."},{"issue":"8","key":"2026041607113563400_ref144","doi-asserted-by":"crossref","first-page":"085104","DOI":"10.1103\/PhysRevB.97.085104","article-title":"Equivalence of restricted Boltzmann machines and tensor network states","volume":"97","author":"Chen","year":"2018","journal-title":"Physical Review B"},{"key":"2026041607113563400_ref145","article-title":"Projected Stein variational gradient descent","author":"Chen","year":"2020","journal-title":"Advances in Neural Information Processing Systems."},{"key":"2026041607113563400_ref146","unstructured":"Chen, R.T.Q., Rubanova, Y., Bettencourt, J. and Duvenaud, D. (2019b), \u201cNeural ordinary differential equations\u201d, arXiv preprint arXiv:1806.07366."},{"issue":"4","key":"2026041607113563400_ref147","doi-asserted-by":"crossref","first-page":"911","DOI":"10.1109\/72.392253","article-title":"Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems","volume":"6","author":"Chen","year":"1995","journal-title":"IEEE Transactions on Neural Networks"},{"key":"2026041607113563400_ref148","article-title":"A simple framework for contrastive learning of visual representations","author":"Chen","year":"2020"},{"issue":"5","key":"2026041607113563400_ref149","first-page":"3035","article-title":"Calculation of cyclodextrin binding affinities: energy, entropy, and implications for drug design","volume":"87","author":"Chen","year":"2004"},{"issue":"8","key":"2026041607113563400_ref150","doi-asserted-by":"crossref","first-page":"084101","DOI":"10.1063\/5.0059915","article-title":"Machine learning implicit solvation for molecular dynamics","volume":"155","author":"Chen","year":"2021","journal-title":"The Journal of Chemical Physics"},{"key":"2026041607113563400_ref151","doi-asserted-by":"crossref","first-page":"7038","DOI":"10.52202\/068431-0510","article-title":"When does group invariant learning survive spurious correlations?","volume":"35","author":"Chen","year":"2022","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026041607113563400_ref152","article-title":"Learning causally invariant representations for out-of-distribution generalization on graphs","author":"Chen","year":"2022","journal-title":"Advances in Neural Information Processing Systems."},{"issue":"12","key":"2026041607113563400_ref153","doi-asserted-by":"publisher","first-page":"2004214","DOI":"10.1002\/advs.202004214","article-title":"Direct prediction of phonon density of states with Euclidean neural networks","volume":"8","author":"Chen","year":"2021","journal-title":"Advanced Science"},{"key":"2026041607113563400_ref154","unstructured":"Chen, Z., Luo, D., Hu, K. and Clark, B.K. (2022c), \u201cSimulating 2+ 1d lattice quantum electrodynamics at finite density with neural flow wavefunctions\u201d, arXiv preprint arXiv:2212.06835."},{"key":"2026041607113563400_ref155","article-title":"Symplectic recurrent neural networks","volume-title":"International Conference on Learning Representations","author":"Chen","year":"2020"},{"key":"2026041607113563400_ref156","doi-asserted-by":"crossref","DOI":"10.1039\/D3DD00012E","article-title":"Group SELFIES: a robust fragment-based molecular string representation","author":"Cheng","year":"2023","journal-title":"Digital Discovery."},{"issue":"1","key":"2026041607113563400_ref157","doi-asserted-by":"publisher","first-page":"015010","DOI":"10.1088\/2632-2153\/acb315","article-title":"Direct prediction of inelastic neutron scattering spectra from the crystal structure*","volume":"4","author":"Cheng","year":"2023","journal-title":"Machine Learning: Science and Technology"},{"issue":"1","key":"2026041607113563400_ref158","doi-asserted-by":"crossref","first-page":"16","DOI":"10.4103\/2229-516X.112233","article-title":"A review of drug isomerism and its significance","volume":"3","author":"Chhabra","year":"2013","journal-title":"International Journal of Applied and Basic Medical Research"},{"key":"2026041607113563400_ref159","unstructured":"Chithrananda, S., Grand, G. and Ramsundar, B. (2020), \u201cChemBERTa: large-scale self-supervised pretraining for molecular property prediction\u201d, arXiv preprint arXiv:2010.09885."},{"issue":"5","key":"2026041607113563400_ref160","doi-asserted-by":"crossref","first-page":"e1603015","DOI":"10.1126\/sciadv.1603015","article-title":"Machine learning of accurate energy-conserving molecular force fields","volume":"3","author":"Chmiela","year":"2017","journal-title":"Science Advances"},{"issue":"1","key":"2026041607113563400_ref161","doi-asserted-by":"crossref","first-page":"3887","DOI":"10.1038\/s41467-018-06169-2","article-title":"Towards exact molecular dynamics simulations with machine-learned force fields","volume":"9","author":"Chmiela","year":"2018","journal-title":"Nature Communications"},{"issue":"2","key":"2026041607113563400_ref162","doi-asserted-by":"crossref","first-page":"eadf0873","DOI":"10.1126\/sciadv.adf0873","article-title":"Accurate global machine learning force fields for molecules with hundreds of atoms","volume":"9","author":"Chmiela","year":"2023","journal-title":"Science Advances"},{"key":"2026041607113563400_ref163","article-title":"Hypernetwork-based meta-learning for low-rank physics-informed neural networks","volume":"36","author":"Cho","year":"2024","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"1","key":"2026041607113563400_ref164","doi-asserted-by":"crossref","first-page":"1168","DOI":"10.1038\/s41467-023-36823-3","article-title":"Prediction of transition state structures of gas-phase chemical reactions via machine learning","volume":"14","author":"Choi","year":"2023","journal-title":"Nature Communications"},{"key":"2026041607113563400_ref165","doi-asserted-by":"crossref","unstructured":"Chong, S., Grasselli, F., Mahmoud, C.B., Morrow, J.D., Deringer, V.L. and Ceriotti, M. (2023), \u201cRobustness of local predictions in atomistic machine learning models\u201d, arXiv preprint arXiv:2306.15638.","DOI":"10.1021\/acs.jctc.3c00704"},{"issue":"16","key":"2026041607113563400_ref166","doi-asserted-by":"crossref","first-page":"167204","DOI":"10.1103\/PhysRevLett.121.167204","article-title":"Symmetries and many-body excitations with neural-network quantum states","volume":"121","author":"Choo","year":"2018","journal-title":"Physical Review Letters"},{"issue":"1","key":"2026041607113563400_ref167","doi-asserted-by":"crossref","first-page":"2368","DOI":"10.1038\/s41467-020-15724-9","article-title":"Fermionic neural-network states for ab-initio electronic structure","volume":"11","author":"Choo","year":"2020","journal-title":"Nature Communications"},{"issue":"12","key":"2026041607113563400_ref168","doi-asserted-by":"publisher","first-page":"125124","DOI":"10.1103\/PhysRevB.100.12","article-title":"Two-dimensional frustrated J1-J2 model studied with neural network quantum states","volume":"100","author":"Choo","year":"2019","journal-title":"Physical Review B"},{"issue":"1","key":"2026041607113563400_ref169","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1038\/s41524-021-00650-1","article-title":"Atomistic line graph neural network for improved materials property predictions","volume":"7","author":"Choudhary","year":"2021","journal-title":"npj Computational Materials"},{"key":"2026041607113563400_ref170","doi-asserted-by":"crossref","unstructured":"Choudhary, K., Wines, D., Li, K., Garrity, K.F., Gupta, V., Romero, A.H., Krogel, J.T., Saritas, K., Fuhr, A., Ganesh, P., Kent, P.R.C., Yan, K., Lin, Y., Ji, S., Blaiszik, B., Reiser, P., Friederich, P., Agrawal, A., Tiwary, P., Beyerle, E., Minch, P., Rhone, T.D., Takeuchi, I., Wexler, R.B., Mannodi-Kanakkithodi, A., Ertekin, E., Mishra, A. (2023), \u201cLarge scale benchmark of materials design methods\u201d, arXiv preprint arXiv:2306.11688.","DOI":"10.1038\/s41524-024-01259-w"},{"key":"2026041607113563400_ref171","unstructured":"Chowdhery, A., Narang, S., Devlin, J., Bosma, M., Mishra, G., Roberts, A., Barham, P., Chung, H.W., Sutton, C., Gehrmann, S.\n          et al. (2022), \u201cPalm: Scaling language modeling with pathways\u201d, arXiv preprint arXiv:2204.02311."},{"issue":"4","key":"2026041607113563400_ref172","first-page":"045018","article-title":"On the role of gradients for machine learning of molecular energies and forces","volume":"1","author":"Christensen","year":"2020","journal-title":"Machine Learning: Science and Technology"},{"key":"2026041607113563400_ref173","unstructured":"Christofdellis, D., Giannone, G., Born, J., Winther, O., Laino, T. and Manica, M. (2023), \u201cUnifying molecular and textual representations via multi-task language modelling\u201d, arXiv preprint arXiv:2301.12586."},{"issue":"6","key":"2026041607113563400_ref174","doi-asserted-by":"publisher","first-page":"1799","DOI":"10.1107\/S1600576721010840","article-title":"Automated prediction of lattice parameters from X-ray powder diffraction patterns","volume":"54","author":"Chitturi","year":"2021","journal-title":"Journal of Applied Crystallography"},{"key":"2026041607113563400_ref175","unstructured":"Chuang, K.V. and Keiser, M.J. (2020), \u201cAttention-based learning on molecular ensembles\u201d, arXiv preprint arXiv:2011.12820."},{"issue":"4","key":"2026041607113563400_ref176","first-page":"1","article-title":"The best of the 20th century: Editors name top 10 algorithms","volume":"33","author":"Cipra","year":"2000","journal-title":"SIAM News"},{"key":"2026041607113563400_ref177","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139031783","volume-title":"Fundamentals of Condensed Matter Physics","author":"Cohen","year":"2016"},{"key":"2026041607113563400_ref178","first-page":"2990","article-title":"Group equivariant convolutional networks","author":"Cohen","year":"2016"},{"key":"2026041607113563400_ref179","article-title":"Steerable CNNs","author":"Cohen","year":"2017"},{"key":"2026041607113563400_ref180","article-title":"A general theory of equivariant CNNs on homogeneous spaces","author":"Cohen","year":"2019"},{"key":"2026041607113563400_ref181","article-title":"Spherical CNNs","author":"Cohen","year":"2018"},{"key":"2026041607113563400_ref182","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1613\/jair.295","article-title":"Active learning with statistical models","volume":"4","author":"Cohn","year":"1996","journal-title":"Journal of Artificial Intelligence Research"},{"key":"2026041607113563400_ref183","first-page":"3843","article-title":"MEDNERF: Medical neural radiance fields for reconstructing 3D-aware CT-projections from a single X-ray","author":"Corona-Figueroa","year":"2022"},{"issue":"2","key":"2026041607113563400_ref184","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1107\/S1600576723000596","article-title":"CrystalMELA: A new crystallographic machine learning platform for crystal system determination","volume":"56","author":"Corriero","year":"2023","journal-title":"Journal of Applied Crystallography"},{"key":"2026041607113563400_ref185","unstructured":"Corso, G., St\u00e4rk, H., Jing, B., Barzilay, R. and Jaakkola, T. (2022), \u201cDiffDock: Diffusion steps, twists, and turns for molecular docking\u201d, arXiv preprint arXiv:2210.01776."},{"key":"2026041607113563400_ref186","unstructured":"Corso, G., Xu, Y., de Bortoli, V., Barzilay, R. and Jaakkola, T. (2023), \u201cParticle guidance: non-IID diverse sampling with diffusion models\u201d, arXiv preprint arXiv:2310.13102."},{"issue":"1","key":"2026041607113563400_ref187","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1007\/BF01448839","article-title":"\u00dcber die partiellen differenzengleichungen der mathematischen physik","volume":"100","author":"Courant","year":"1928","journal-title":"Mathematische Annalen"},{"issue":"10","key":"2026041607113563400_ref188","doi-asserted-by":"crossref","first-page":"4518","DOI":"10.1021\/acs.jcim.0c00464","article-title":"3-D inorganic crystal structure generation and property prediction via representation learning","volume":"60","author":"Court","year":"2020","journal-title":"Journal of Chemical Information and Modeling"},{"key":"2026041607113563400_ref189","doi-asserted-by":"crossref","DOI":"10.52202\/075280-3127","article-title":"Evaluating the robustness of interpretability methods through explanation invariance and equivariance","author":"Crabb\u00e9","year":"2023"},{"key":"2026041607113563400_ref190","article-title":"Lagrangian neural networks","author":"Cranmer","year":"2020"},{"issue":"2","key":"2026041607113563400_ref191","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1007\/s11005-023-01665-z","article-title":"Seven useful questions in density functional theory","volume":"113","author":"Crisostomo","year":"2023","journal-title":"Letters in Mathematical Physics"},{"key":"2026041607113563400_ref192","first-page":"540","article-title":"Pairwise supervised hashing with Bernoulli variational auto-encoder and self-control gradient estimator","author":"Dadaneh","year":"2020"},{"key":"2026041607113563400_ref193","article-title":"Learning integrable dynamics with action-angle networks","author":"Daigavane","year":"2022"},{"issue":"D1","key":"2026041607113563400_ref194","doi-asserted-by":"crossref","first-page":"D482","DOI":"10.1093\/nar\/gky1114","article-title":"SIFTS: Updated structure integration with function, taxonomy and sequences resource allows 40-fold increase in coverage of structure-based annotations for proteins","volume":"47","author":"Dana","year":"2019","journal-title":"Nucleic Acids Research"},{"issue":"6615","key":"2026041607113563400_ref195","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1126\/science.add2187","article-title":"Robust deep learning-based protein sequence design using ProteinMPNN","volume":"378","author":"Dauparas","year":"2022","journal-title":"Science"},{"key":"2026041607113563400_ref196","unstructured":"Dawid, A., Arnold, J., Requena, B., Gresch, A., P\u0142odzie, M., Donatella, K., Nicoli, K.A., Stornati, P., Koch, R., B\u00fcttner, M.\n          et al. (2022), \u201cModern applications of machine learning in quantum sciences\u201d, arXiv preprint arXiv:2204.04198."},{"issue":"6825","key":"2026041607113563400_ref197","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1038\/35065704","article-title":"Supercooled liquids and the glass transition","volume":"410","author":"Debenedetti","year":"2001","journal-title":"Nature"},{"issue":"7897","key":"2026041607113563400_ref198","doi-asserted-by":"crossref","first-page":"414","DOI":"10.1038\/s41586-021-04301-9","article-title":"Magnetic control of tokamak plasmas through deep reinforcement learning","volume":"602","author":"Degrave","year":"2022","journal-title":"Nature"},{"issue":"18","key":"2026041607113563400_ref199","doi-asserted-by":"publisher","first-page":"184302","DOI":"10.1103\/PhysRevB.80.184302","article-title":"Phonon density of states and heat capacity of La3\u2212xTe4","volume":"80","author":"Delaire","year":"2009","journal-title":"Physical Review B"},{"key":"2026041607113563400_ref200","first-page":"1","article-title":"CHGNet as a pretrained universal neural network potential for charge-informed atomistic modelling","author":"Deng","year":"2023","journal-title":"Nature Machine Intelligence"},{"key":"2026041607113563400_ref201","first-page":"6007","article-title":"OpenFWI: large-scale multi-structural benchmark datasets for full waveform inversion","volume":"35","author":"Deng","year":"2022","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026041607113563400_ref202","first-page":"12200","article-title":"Vector neurons: a general framework for SO(3)-equivariant networks","author":"Deng","year":"2021"},{"issue":"2","key":"2026041607113563400_ref203","doi-asserted-by":"crossref","first-page":"021021","DOI":"10.1103\/PhysRevX.7.021021","article-title":"Quantum entanglement in neural network states","volume":"7","author":"Deng","year":"2017","journal-title":"Physical Review X"},{"issue":"9","key":"2026041607113563400_ref204","doi-asserted-by":"publisher","first-page":"094203","DOI":"10.1103\/PhysRevB.95.094203","article-title":"Machine learning based inter-atomic potential for amorphous carbon","volume":"95","author":"Deringer","year":"2017","journal-title":"Physical Review B"},{"issue":"11","key":"2026041607113563400_ref205","doi-asserted-by":"publisher","first-page":"2879","DOI":"10.1021\/acs.jpclett.8b00902","article-title":"Realistic atomistic structure of amorphous silicon from machine-learning-driven molecular dynamics","volume":"9","author":"Deringer","year":"2018","journal-title":"The Journal of Physical Chemistry Letters"},{"key":"2026041607113563400_ref206","unstructured":"Deshmukh, A.A., Lei, Y., Sharma, S., Dogan, U., Cutler, J.W. and Scott, C. (2019), \u201cA generalization error bound for multi-class domain generalization\u201d, arXiv preprint arXiv:1905.10392."},{"key":"2026041607113563400_ref207","first-page":"4171","article-title":"BERT: pre-training of deep bidirectional transformers for language understanding","author":"Devlin","year":"2019"},{"key":"2026041607113563400_ref208","article-title":"Graph neural networks as gradient flows: understanding graph convolutions via energy","author":"Di Giovanni","year":"2023"},{"issue":"14","key":"2026041607113563400_ref209","doi-asserted-by":"publisher","DOI":"10.1063\/1.5114618","article-title":"Learning from the density to correct total energy and forces in first principle simulations","volume":"151","author":"Dick","year":"2019","journal-title":"The Journal of Chemical Physics"},{"issue":"1","key":"2026041607113563400_ref210","doi-asserted-by":"publisher","first-page":"3509","DOI":"10.1038\/s41467-020-17265-7","article-title":"Machine learning accurate ex-change and correlation functionals of the electronic density","volume":"11","author":"Dick","year":"2020","journal-title":"Nature Communications"},{"issue":"16","key":"2026041607113563400_ref211","doi-asserted-by":"crossref","first-page":"L161109","DOI":"10.1103\/PhysRevB.104.L161109","article-title":"Highly accurate and con-strained density functional obtained with differentiable program-ming","volume":"104","author":"Dick","year":"2021","journal-title":"Physical Review B"},{"issue":"1-2","key":"2026041607113563400_ref212","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/S0004-3702(96)00034-3","article-title":"Solving the multiple instance problem with axis-parallel rectangles","volume":"89","author":"Dietterich","year":"1997","journal-title":"Artificial intelligence"},{"issue":"792","key":"2026041607113563400_ref213","first-page":"714","article-title":"Quantum mechanics of many-electron systems","volume":"123","author":"Dirac","year":"1929","journal-title":"Proceedings of the Royal Society of London. 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(2023a), \u201cAccurate transition state generation with an object-aware equivariant elementary reaction diffusion model\u201d, arXiv preprint arXiv:2304.06174.","DOI":"10.1038\/s43588-023-00563-7"},{"issue":"1","key":"2026041607113563400_ref226","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1038\/s43588-022-00384-0","article-title":"A transferable recommender approach for selecting the best density functional approximations in chemical discovery","volume":"3","author":"Duan","year":"2023","journal-title":"Nature Computational Science"},{"issue":"1","key":"2026041607113563400_ref227","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1038\/s41524-020-00406-3","article-title":"Bench-marking materials property prediction methods: the Matbench test set and Automatminer reference algorithm","volume":"6","author":"Dunn","year":"2020","journal-title":"npj Computational Materials"},{"key":"2026041607113563400_ref228","article-title":"Efficient and scalable Bayesian neural nets with rank-1 factors","author":"Dusenberry","year":"2020"},{"key":"2026041607113563400_ref229","doi-asserted-by":"crossref","first-page":"110946","DOI":"10.1016\/j.jcp.2022.110946","article-title":"Atomic cluster expansion: completeness, efficiency and stability","volume":"454","author":"Dusson","year":"2022","journal-title":"Journal of Computational Physics"},{"key":"2026041607113563400_ref230","unstructured":"Duval, A., Schmidt, V., Garcia, A.H., Miret, S., Malliaros, F.D., Bengio, Y. and Rolnick, D. (2023), \u201cFAENet: Frame averaging equivariant GNN for materials modeling\u201d, arXiv preprint arXiv:2305.05577."},{"key":"2026041607113563400_ref231","unstructured":"Dym, N. and Maron, H. (2021), \u201cOn the universality of rotation equivariant point cloud networks\u201d, arXiv preprint arXiv:2010.02449."},{"key":"2026041607113563400_ref232","article-title":"On the universality of rotation equivariant point cloud networks","author":"Dym","year":"2025"},{"key":"2026041607113563400_ref233","unstructured":"Dym, N., Lawrence, H. and Siegel, J.W. (2024), \u201cEquivariant frames and the impossibility of continuous canonicalization\u201d, arXiv preprint arXiv:2402.16077."},{"issue":"1","key":"2026041607113563400_ref234","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1038\/s41597-022-01882-6","article-title":"SPICE, A dataset of drug-like molecules and peptides for training machine learning potentials","volume":"10","author":"Eastman","year":"2023","journal-title":"Scientific Data"},{"key":"2026041607113563400_ref235","doi-asserted-by":"crossref","DOI":"10.1112\/blms\/4.2.236","article-title":"Optimal control of systems governed by partial differential equations","author":"Edmunds","year":"1972"},{"key":"2026041607113563400_ref236","first-page":"375","article-title":"Translation between molecules and natural language","author":"Edwards","year":"2022"},{"key":"2026041607113563400_ref237","first-page":"595","article-title":"Text2Mol: cross-modal molecule retrieval with natural language queries","author":"Edwards","year":"2021"},{"key":"2026041607113563400_ref238","doi-asserted-by":"publisher","DOI":"10.1101\/2023.07.06.547759","article-title":"SynerGPT: in-context learning for personalized drug synergy prediction and drug design","author":"Edwards","year":"2023","journal-title":"bioRxiv"},{"key":"2026041607113563400_ref239","unstructured":"Elesedy, B. and Zaidi, S. (2021), \u201cProvably strict generalisation benefit for equivariant models\u201d, arXiv preprint arXiv:2102.10333."},{"key":"2026041607113563400_ref240","unstructured":"Elfein, S.\n           (2023), \u201cOut-of-distribution detection with energy-based models\u201d, arXiv preprint arXiv:2302.12002."},{"key":"2026041607113563400_ref241","volume-title":"Stereochemistry of Organic Com-pounds","author":"Eliel","year":"1994"},{"key":"2026041607113563400_ref242","first-page":"18648","article-title":"Variational inference for graph convolutional networks in the absence of graph data and adversarial settings","volume":"33","author":"Elinas","year":"2020","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026041607113563400_ref243","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-14090-7","volume-title":"Density Functional Theory: An Advanced Course. 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(2020), \u201cMolecular representation learning with language models and domain-relevant auxiliary tasks\u201d, arXiv preprint arXiv:2011.13230."},{"key":"2026041607113563400_ref251","article-title":"Continuous-discrete convolution for geometry-sequence modeling in proteins","author":"Fan","year":"2023"},{"key":"2026041607113563400_ref252","first-page":"16362","article-title":"Bayesian attention modules","volume":"33","author":"Fan","year":"2020","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026041607113563400_ref253","first-page":"353","article-title":"Gaussian process with graph convolutional Kernel for relational learning","author":"Fang","year":"2021"},{"key":"2026041607113563400_ref254","unstructured":"Fang, Y., Liang, X., Zhang, N., Liu, K., Huang, R., Chen, Z., Fan, X. and Chen, H. (2023), \u201cMol-instructions: a large-scale biomolecular instruction dataset for large language models\u201d, arXiv preprint arXiv:2306.08018."},{"issue":"11","key":"2026041607113563400_ref255","doi-asserted-by":"crossref","first-page":"1520","DOI":"10.1021\/acscentsci.8b00507","article-title":"PotentialNet for molecular property prediction","volume":"4","author":"Feinberg","year":"2018","journal-title":"ACS Central Science"},{"key":"2026041607113563400_ref256","first-page":"247","article-title":"Excited-state calculations with quantum Monte Carlo","author":"Feldt","year":"2020"},{"issue":"12","key":"2026041607113563400_ref257","doi-asserted-by":"crossref","first-page":"125131","DOI":"10.1103\/PhysRevB.100.125131","article-title":"Neural Gutzwiller-projected variational wave functions","volume":"100","author":"Ferrari","year":"2019","journal-title":"Physical Review B"},{"key":"2026041607113563400_ref258","volume-title":"The Feynman Lectures on Physics: The New Millennium Edition","author":"Feynman","year":"2011"},{"issue":"9","key":"2026041607113563400_ref259","doi-asserted-by":"publisher","first-page":"750","DOI":"10.1119\/1.1972241","article-title":"The Feynman lectures on physics; Volume I","volume":"33","author":"Feynman","year":"1965","journal-title":"American Journal of Physics"},{"issue":"4","key":"2026041607113563400_ref260","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevMaterials.6.040301","article-title":"Deep dive into machine learning density functional theory for materials science and chemistry","volume":"6","author":"Fiedler","year":"2022","journal-title":"Physical Review Materials"},{"key":"2026041607113563400_ref261","unstructured":"Fifty, C., Paggi, J.M., Amid, E., Leskovec, J. and Dror, R. (2023), \u201cHarnessing simulation for molecular embeddings\u201d, arXiv preprint arXiv:2302.02055."},{"key":"2026041607113563400_ref262","article-title":"Residual pathway priors for soft equivariance constraints","volume":"34","author":"Finzi","year":"2021","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026041607113563400_ref263","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-37072-2","volume-title":"A Primer in Density Functional Theory","author":"Fiolhais","year":"2003"},{"issue":"3","key":"2026041607113563400_ref264","doi-asserted-by":"crossref","first-page":"2985","DOI":"10.1002\/cber.18940270364","article-title":"Einfuss der confguration auf die wirkung der enzyme","volume":"27","author":"Fischer","year":"1894","journal-title":"Berichte der deutschen chemischen Gesellschaft"},{"key":"2026041607113563400_ref265","unstructured":"Flam-Shepherd, D. and Aspuru-Guzik, A. (2023), \u201cLanguage models can generate molecules, materials, and protein binding sites directly in three dimensions as XYZ, CIF, and PDB fles\u201d, arXiv preprint arXiv:2305.05708."},{"key":"2026041607113563400_ref266","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-78650-6","volume-title":"The Uncertainty in Physical Measurements: An Introduction to Data Analysis in the Physics Laboratory","author":"Fornasini","year":"2008"},{"issue":"1","key":"2026041607113563400_ref267","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1103\/RevModPhys.73.33","article-title":"Quantum Monte Carlo simulations of solids","volume":"73","author":"Foulkes","year":"2001","journal-title":"Reviews of Modern Physics"},{"issue":"3","key":"2026041607113563400_ref268","first-page":"034001","article-title":"Managing uncertainty in data-derived densities to accelerate density functional theory","volume":"2","author":"Fowler","year":"2019","journal-title":"Journal of Physics: Materials"},{"issue":"9","key":"2026041607113563400_ref269","doi-asserted-by":"crossref","first-page":"4200","DOI":"10.1021\/acs.jcim.0c00411","article-title":"Three-dimensional convolutional neural networks and a cross-docked data set for structure-based drug design","volume":"60","author":"Francoeur","year":"2020","journal-title":"Journal of Chemical Information and Modeling"},{"issue":"1","key":"2026041607113563400_ref270","doi-asserted-by":"crossref","first-page":"6539","DOI":"10.1038\/s41467-024-50620-6","article-title":"A Euclidean transformer for fast and stable machine learned force fields","volume":"15","author":"Frank","year":"2024","journal-title":"Nature Communications"},{"key":"2026041607113563400_ref271","volume-title":"Understanding Molecular Simulation: From Algorithms to Applications","author":"Frenkel","year":"2001"},{"key":"2026041607113563400_ref272","doi-asserted-by":"publisher","DOI":"10.26434\/chemrxiv-2022-3s512","article-title":"Neural scaling of deep chemical models","author":"Frey","year":"2022"},{"issue":"1","key":"2026041607113563400_ref273","doi-asserted-by":"crossref","first-page":"145","DOI":"10.5195\/jmla.2018.280","article-title":"Semantic scholar","volume":"106","author":"Fricke","year":"2018","journal-title":"Journal of the Medical Library Association: JMLA"},{"issue":"6","key":"2026041607113563400_ref274","doi-asserted-by":"crossref","first-page":"750","DOI":"10.1038\/s41563-020-0777-6","article-title":"Machine-learned potentials for next-generation matter simulations","volume":"20","author":"Friederich","year":"2021","journal-title":"Nature Materials"},{"key":"2026041607113563400_ref275","article-title":"Gaussian, Vol. 09 (Revision D.01)","author":"Frisch","year":"2009"},{"key":"2026041607113563400_ref276","unstructured":"Fu, C., Yan, K., Wang, L., Au, W.Y., McThrow, M., Komikado, T., Maruhashi, K., Uchino, K., Qian, X. and Ji, S. (2023a), \u201cA latent diffusion model for protein structure generation\u201d, arXiv preprint arXiv:2305.04120."},{"key":"2026041607113563400_ref277","unstructured":"Fu, C., Zhang, X., Zhang, H., Ling, H., Xu, S. and Ji, S. (2022a), \u201cLattice convolutional networks for learning ground states of quantum many-body systems\u201d, arXiv preprint arXiv:2206.07370."},{"key":"2026041607113563400_ref278","first-page":"12325","article-title":"Reinforced genetic algorithm for structure-based drug design","volume":"35","author":"Fu","year":"2022","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"1","key":"2026041607113563400_ref279","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1609\/aaai.v35i1.16085","article-title":"Mimosa: multi-constraint molecule sampling for molecule optimization","volume":"35","author":"Fu","year":"2021","journal-title":"Proceedings of the AAAI Conference on Artificial Intelligence"},{"key":"2026041607113563400_ref280","unstructured":"Fu, X., Wu, Z., Wang, W., Xie, T., Keten, S., Gomez-Bombarelli, R. and Jaakkola, T.S. (2023b), \u201cForces are not enough: benchmark and critical evaluation for machine learning force fields with molecular simulations\u201d, Transactions on Machine Learning Research. Survey Certification, available at:https:\/\/openreview.net\/forum?id=A8pqQipwkt"},{"key":"2026041607113563400_ref281","unstructured":"Fu, X., Xie, T., Rebello, N.J., Olsen, B.D. and Jaakkola, T. (2022c), \u201cSimulate time-integrated coarse-grained molecular dynamics with geometric machine learning\u201d, arXiv preprint arXiv:2204.10348."},{"key":"2026041607113563400_ref282","first-page":"1970","article-title":"SE(3)-transformers: 3D roto-translation equivariant attention networks","volume":"33","author":"Fuchs","year":"2020","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"19","key":"2026041607113563400_ref283","doi-asserted-by":"publisher","first-page":"8208","DOI":"10.1021\/acs.jpclett.0c02405","article-title":"Accurate and numerically efficient r2SCAN meta-generalized gradient approximation","volume":"11","author":"Furness","year":"2020","journal-title":"The Journal of Physical Chemistry Letters"},{"issue":"2","key":"2026041607113563400_ref284","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1038\/s41592-019-0666-6","article-title":"Deciphering interaction fingerprints from protein molecular surfaces using geometric deep learning","volume":"17","author":"Gainza","year":"2020","journal-title":"Nature Methods"},{"key":"2026041607113563400_ref285","first-page":"1","article-title":"De novo design of protein interactions with learned surface fingerprints","author":"Gainza","year":"2023","journal-title":"Nature"},{"key":"2026041607113563400_ref286","first-page":"1050","article-title":"Dropout as a Bayesian approximation: representing model uncertainty in deep learning","author":"Gal","year":"2016"},{"key":"2026041607113563400_ref287","article-title":"Concrete dropout","volume":"30","author":"Gal","year":"2017","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026041607113563400_ref288","first-page":"1183","article-title":"Deep Bayesian active learning with image data","author":"Gal","year":"2017"},{"key":"2026041607113563400_ref289","article-title":"Protnlm: Model-based natural language protein annotation","author":"Gane","year":"2022"},{"key":"2026041607113563400_ref290","first-page":"13757","article-title":"GeoMol: torsional geometric generation of molecular 3d conformer ensembles","volume":"34","author":"Ganea","year":"2021","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026041607113563400_ref291","first-page":"1180","article-title":"Unsupervised domain adaptation by backpropagation","author":"Ganin","year":"2015"},{"issue":"1","key":"2026041607113563400_ref292","first-page":"2096","article-title":"Domain-adversarial training of neural networks","volume":"17","author":"Ganin","year":"2016","journal-title":"The Journal of Machine Learning Research"},{"key":"2026041607113563400_ref293","doi-asserted-by":"publisher","first-page":"741","DOI":"10.1145\/3292500.3330897","article-title":"Graph representation learning via Hard and channel-wise attention networks","author":"Gao","year":"2019"},{"key":"2026041607113563400_ref294","article-title":"Ab-Initio potential energy surfaces by pairing GNNs with neural wave functions","author":"Gao","year":"2021"},{"key":"2026041607113563400_ref295","article-title":"Generalizing neural wave functions","author":"Gao","year":"2023"},{"key":"2026041607113563400_ref296","unstructured":"Gao, N. and G\u00fcnnemann, S. (2023b), \u201cSampling-free inference for ab-initio potential energy surface networks\u201d, in The Eleventh Inter-national Conference on Learning Representations, available at:https:\/\/openreview.net\/forum?id=Tuk3Pqaizx"},{"key":"2026041607113563400_ref297","first-page":"21342","article-title":"Sample efficiency matters: a benchmark for practical molecular optimization","volume":"35","author":"Gao","year":"2022","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"1","key":"2026041607113563400_ref298","doi-asserted-by":"crossref","first-page":"662","DOI":"10.1038\/s41467-017-00705-2","article-title":"Efficient representation of quantum many-body states with deep neural networks","volume":"8","author":"Gao","year":"2017","journal-title":"Nature Communications"},{"key":"2026041607113563400_ref299","article-title":"PiFold: Toward effective and efficient protein inverse folding","author":"Gao","year":"2023"},{"key":"2026041607113563400_ref300","article-title":"Proteininvbench: benchmarking protein inverse folding on diverse tasks, models, and metrics","volume":"36","author":"Gao","year":"2024","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026041607113563400_ref301","doi-asserted-by":"publisher","first-page":"4490","DOI":"10.1109\/BigData47090.2019.9005968","article-title":"Learning to predict material structure from neutron scattering data","author":"Garcia-Cardona","year":"2019"},{"key":"2026041607113563400_ref302","first-page":"6790","article-title":"GemNet: universal directional graph neural networks for molecules","volume":"34","author":"Gasteiger","year":"2021","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026041607113563400_ref303","article-title":"Directional message passing for molecular graphs","author":"Gasteiger","year":"2020"},{"key":"2026041607113563400_ref304","unstructured":"Gasteiger, J., Shuaibi, M., Sriram, A., G\u00fcnnemann, S., Ulissi, Z.W., Zitnick, C.L. and Das, A. (2022), \u201cGemNet-OC: developing graph neural networks for large and diverse molecular simulation datasets\u201d, Transactions on Machine Learning Research, available at:https:\/\/openreview.net\/forum?id=u8tvSxm4Bs"},{"key":"2026041607113563400_ref305","article-title":"Symmetry-adapted generation of 3d point sets for the targeted discovery of molecules","volume":"32","author":"Gebauer","year":"2019","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"1","key":"2026041607113563400_ref306","doi-asserted-by":"publisher","first-page":"015011","DOI":"10.1088\/2632-2153\/ac3149","article-title":"Machine learning the derivative discontinuity of density-functional theory","volume":"3","author":"Gedeon","year":"2021","journal-title":"Machine Learning: Science and Technology"},{"key":"2026041607113563400_ref307","article-title":"e3nn: Euclidean neural networks","author":"Geiger","year":"2022"},{"key":"2026041607113563400_ref308","volume-title":"Advances in Neural Information Processing Systems","author":"Gerard","year":"2022"},{"issue":"6606","key":"2026041607113563400_ref309","doi-asserted-by":"crossref","first-page":"eabq3385","DOI":"10.1126\/science.abq3385","article-title":"Comment on \u2018Pushing the frontiers of density functionals by solving the fractional electron problem\u2019","volume":"377","author":"Gerasimov","year":"2022","journal-title":"Science"},{"issue":"10","key":"2026041607113563400_ref310","doi-asserted-by":"crossref","first-page":"105503","DOI":"10.1103\/PhysRevLett.114.105503","article-title":"Big data of materials science: critical role of the descriptor","volume":"114","author":"Ghiringhelli","year":"2015","journal-title":"Physical Review Letters"},{"key":"2026041607113563400_ref311","first-page":"1263","article-title":"Neural message passing for quantum chemistry","author":"Gilmer","year":"2017"},{"key":"2026041607113563400_ref312","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1146\/annurev.biophys.36.040306.132550","article-title":"Calculation of protein-ligand binding affinities","volume":"36","author":"Gilson","year":"2007","journal-title":"Annual Review of Biophysics and Biomolecular Structure"},{"issue":"3","key":"2026041607113563400_ref313","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1093\/mnras\/181.3.375","article-title":"Smoothed particle hydro-dynamics: theory and application to non-spherical stars","volume":"181","author":"Gingold","year":"1977","journal-title":"Monthly Notices of the Royal Astronomical Society"},{"key":"2026041607113563400_ref314","volume-title":"Materials Modelling using Density Functional Theory: Properties and Predictions","author":"Giustino","year":"2014"},{"issue":"1","key":"2026041607113563400_ref315","doi-asserted-by":"crossref","first-page":"3168","DOI":"10.1038\/s41467-021-23303-9","article-title":"Structure-based protein function prediction using graph convolutional networks","volume":"12","author":"Gligorijevi\u0107","year":"2021","journal-title":"Nature Communications"},{"key":"2026041607113563400_ref316","first-page":"45","article-title":"Bayesian neural networks: an introduction and survey","author":"Goan","year":"2020"},{"key":"2026041607113563400_ref317","article-title":"Simple GNN regularisation for 3D molecular property prediction and beyond","author":"Godwin","year":"2022"},{"issue":"48","key":"2026041607113563400_ref318","doi-asserted-by":"crossref","first-page":"32184","DOI":"10.1039\/C7CP04913G","article-title":"A look at the density functional theory zoo with the advanced GMTKN55 database for general main group thermochemistry, kinetics and noncovalent interactions","volume":"19","author":"Goerigk","year":"2017","journal-title":"Physical Chemistry Chemical Physics"},{"issue":"2","key":"2026041607113563400_ref319","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1016\/j.molcel.2016.06.012","article-title":"Automated structure-and sequence-based design of proteins for high bacterial expression and stability","volume":"63","author":"Goldenzweig","year":"2016","journal-title":"Molecular Cell"},{"issue":"1","key":"2026041607113563400_ref320","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1039\/C8CP06433D","article-title":"Kinetic energy densities based on the fourth order gradient expansion: performance in different classes of materials and improvement via machine learning","volume":"21","author":"Golub","year":"2019","journal-title":"Physical Chemistry Chemical 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stoichiometry","volume":"11","author":"Goodall","year":"2020","journal-title":"Nature Communications"},{"issue":"30","key":"2026041607113563400_ref324","doi-asserted-by":"crossref","first-page":"eabn4117","DOI":"10.1126\/sciadv.abn4117","article-title":"Rapid discovery of stable materials by coordinate-free coarse graining","volume":"8","author":"Goodall","year":"2022","journal-title":"Science Advances"},{"key":"2026041607113563400_ref325","volume-title":"Deep Learning","author":"Goodfellow","year":"2016"},{"key":"2026041607113563400_ref326","first-page":"2672","article-title":"Generative adversarial nets","volume":"27","author":"Goodfellow","year":"2014","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026041607113563400_ref327","unstructured":"Goodfellow, I.J., Shlens, J. and Szegedy, C. (2014a), \u201cExplaining and harnessing adversarial examples\u201d, arXiv preprint arXiv:1412.6572."},{"key":"2026041607113563400_ref328","unstructured":"Google\n           (2004), \u201cGoogle Scholar\u201d, available at:https:\/\/scholar.google.com\/"},{"key":"2026041607113563400_ref329","article-title":"Performance and structural coverage of the latest, in-development AlphaFold model","author":"Google-DeepMind-AlphaFold-Team and Isomorphic-Labs-Team","year":"2023","journal-title":"Technical Report."},{"issue":"44","key":"2026041607113563400_ref330","doi-asserted-by":"crossref","first-page":"27735","DOI":"10.1039\/C8CP05554H","article-title":"\u2018Diet GMTKN55\u2019 offers accelerated benchmarking through a representative subset approach","volume":"20","author":"Gould","year":"2018","journal-title":"Physical Chemistry Chemical Physics"},{"issue":"1","key":"2026041607113563400_ref331","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1038\/s41524-019-021","article-title":"Ab initio vibrational free energies including anharmonicity for multicomponent alloys","volume":"5","author":"Grabowski","year":"2019","journal-title":"npj Computational Materials"},{"key":"2026041607113563400_ref332","doi-asserted-by":"crossref","unstructured":"Grambow, C.A., Weir, H., Cunningham, C.N., Biancalani, T. and Chuang, K.V. (2023), \u201cCREMP: Conformer-rotamer ensembles of macro-cyclic peptides for machine learning\u201d, arXiv preprint arXiv:2305. 08057.","DOI":"10.1038\/s41597-024-03698-y"},{"key":"2026041607113563400_ref333","first-page":"24","article-title":"Practical variational inference for neural networks","author":"Graves","year":"2011","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"12","key":"2026041607113563400_ref334","doi-asserted-by":"publisher","first-page":"5334","DOI":"10.1007\/s10853-023-08343-4","article-title":"Exploring supervised machine learning for multi-phase identification and quantification from powder X-ray diffraction spectra","volume":"58","author":"Greasley","year":"2023","journal-title":"Journal of Materials Science"},{"issue":"9","key":"2026041607113563400_ref335","doi-asserted-by":"crossref","first-page":"e0256990","DOI":"10.1371\/journal.pone.0256990","article-title":"Differentiable molecular simulation can learn all the parameters in a coarse-grained force field for proteins","volume":"16","author":"Greener","year":"2021","journal-title":"PLoS One"},{"issue":"2","key":"2026041607113563400_ref336","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1016\/0021-9991(87)90140-9","article-title":"A fast algorithm for particle simulations","volume":"73","author":"Greengard","year":"1987","journal-title":"Journal of Computational Physics"},{"key":"2026041607113563400_ref337","doi-asserted-by":"crossref","DOI":"10.1101\/2023.04.17.536962","article-title":"Benchmarking uncertainty quantification for protein engineering","author":"Greenman","year":"2023"},{"key":"2026041607113563400_ref338","article-title":"Hamiltonian neural networks","author":"Greydanus","year":"2019"},{"key":"2026041607113563400_ref339","doi-asserted-by":"crossref","DOI":"10.1017\/9781316995433","volume-title":"Introduction to Quantum Mechanics","author":"Griffiths","year":"2018"},{"key":"2026041607113563400_ref340","unstructured":"Griffiths, R.-R.\n           (2023), \u201cApplications of Gaussian processes at extreme length scales: from molecules to black holes\u201d, arXiv preprint arXiv:2303.14291."},{"key":"2026041607113563400_ref341","unstructured":"Griffiths, R.-R., Klarner, L., Moss, H.B., Ravuri, A., Truong, S., Rankovic, B., Du, Y., Jamasb, A., Schwartz, J., Tripp, A., et al. (2022), \u201cGAUCHE: a library for Gaussian processes in chemistry\u201d, arXiv preprint arXiv:2212.04450."},{"issue":"24","key":"2026041607113563400_ref342","doi-asserted-by":"crossref","first-page":"244104","DOI":"10.1063\/1.4811331","article-title":"A simplified Tamm-Dancoff density functional approach for the electronic excitation spectra of very large molecules","volume":"138","author":"Grimme","year":"2013","journal-title":"The Journal of Chemical Physics"},{"issue":"5","key":"2026041607113563400_ref343","doi-asserted-by":"crossref","first-page":"2847","DOI":"10.1021\/acs.jctc.9b00143","article-title":"Exploration of chemical compound, conformer, and reaction space with meta-dynamics simulations based on tight-binding quantum chemical calculations","volume":"15","author":"Grimme","year":"2019","journal-title":"Journal of Chemical Theory and Computation"},{"issue":"5","key":"2026041607113563400_ref344","doi-asserted-by":"crossref","first-page":"054103","DOI":"10.1063\/1.4959605","article-title":"Ultra-fast computation of electronic spectra for large systems by tight-binding based simplified Tamm-Dancoff approximation (sTDA-xTB)","volume":"145","author":"Grimme","year":"2016","journal-title":"The Journal of Chemical Physics"},{"key":"2026041607113563400_ref345","doi-asserted-by":"crossref","first-page":"102527","DOI":"10.1016\/j.sbi.2023.102527","article-title":"Chemical language models for de novo drug design: challenges and opportunities","volume":"79","author":"Grisoni","year":"2023","journal-title":"Current Opinion in Structural Biology"},{"issue":"2","key":"2026041607113563400_ref346","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1107\/S2052520616003954","article-title":"The Cambridge Structural Database","volume":"72","author":"Groom","year":"2016","journal-title":"Acta Crystallographica Section B: Structural Science, Crystal Engineering and Materials"},{"key":"2026041607113563400_ref347","article-title":"Effective surrogate models for protein design with Bayesian optimization","author":"Gruver","year":"2021"},{"issue":"1","key":"2026041607113563400_ref348","first-page":"1","article-title":"Domain-specific language model pretraining for biomedical natural language processing","volume":"3","author":"Gu","year":"2021","journal-title":"ACM Trans-actions on Computing for Healthcare (HEALTH)"},{"key":"2026041607113563400_ref349","article-title":"3D equivariant diffusion for target-aware molecule generation and affinity prediction","author":"Guan","year":"2023"},{"key":"2026041607113563400_ref350","first-page":"7919","article-title":"Neurofuid: Fluid dynamics grounding with particle-driven neural radiance fields","author":"Guan","year":"2022"},{"issue":"6","key":"2026041607113563400_ref351","doi-asserted-by":"crossref","first-page":"2198","DOI":"10.1039\/D0SC04823B","article-title":"Regio-selectivity prediction with a machine-learned reaction representation and on-the-fly quantum mechanical descriptors","volume":"12","author":"Guan","year":"2021","journal-title":"Chemical Science"},{"issue":"10","key":"2026041607113563400_ref352","doi-asserted-by":"crossref","first-page":"5249","DOI":"10.1021\/acs.jctc.8b00578","article-title":"AARON: An automated reaction optimizer for new catalysts","volume":"14","author":"Guan","year":"2018","journal-title":"Journal of Chemical Theory and Computation"},{"key":"2026041607113563400_ref353","first-page":"2059","article-title":"GOOD: A graph out-of-distribution benchmark","author":"Gui","year":"2022"},{"key":"2026041607113563400_ref354","article-title":"Joint learning of label and environment causal independence for graph out-of-distribution generalization","author":"Gui","year":"2023","journal-title":"Advances in Neural Information Processing Systems."},{"key":"2026041607113563400_ref355","first-page":"14004","article-title":"Featureflow: robust video interpolation via structure-to-texture generation","author":"Gui","year":"2020"},{"key":"2026041607113563400_ref356","unstructured":"Gui, S., Yuan, H., Wang, J., Lao, Q., Li, K. and Ji, S. (2022b), \u201cFlowX: Towards explainable graph neural networks via message flows\u201d, arXiv preprint arXiv:2206.12987."},{"key":"2026041607113563400_ref357","article-title":"Adaptive Fourier neural operators: efficient token mixers for transformers","author":"Guibas","year":"2022"},{"key":"2026041607113563400_ref358","unstructured":"Gulrajani, I. and Lopez-Paz, D. (2020), \u201cIn search of lost domain generalization\u201d, arXiv preprint arXiv:2007.01434."},{"key":"2026041607113563400_ref359","article-title":"Transformer meets boundary value inverse problems","author":"Guo","year":"2023"},{"issue":"31","key":"2026041607113563400_ref360","doi-asserted-by":"crossref","first-page":"18824","DOI":"10.1021\/acs.jpcc.9b04580","article-title":"Electrical property dominated promising half-Heusler thermoelectrics through high-throughput material computations","volume":"123","author":"Guo","year":"2019","journal-title":"The Journal of Physical Chemistry C"},{"key":"2026041607113563400_ref361","unstructured":"Guo, T., Guo, K., Liang, Z., Guo, Z., Chawla, N.V., Wiest, O. and Zhang, X. (2023b), \u201cWhat indeed can GPT models do in chemistry? A comprehensive benchmark on eight tasks\u201d, arXiv preprint arXiv:2305.18365."},{"key":"2026041607113563400_ref362","unstructured":"Guo, Z., Sharma, P., Martinez, A., Du, L. and Abraham, R. (2021), \u201cMultilingual molecular representation learning via contrastive pre-training\u201d, arXiv preprint arXiv:2109.08830."},{"key":"2026041607113563400_ref363","unstructured":"Gupta, G., Xiao, X. and Bogdan, P. (2021), \u201cMultiwavelet-based operator learning for differential equations\u201d, in Beygelzimer, A., Dauphin, Y., Liang, P. and Vaughan, J.W. (Eds), Advances in Neural Information Processing Systems, available at:https:\/\/openreview.net\/forum?id=LZDiWaC9CGL"},{"key":"2026041607113563400_ref364","unstructured":"Gupta, J.K. and Brandstetter, J. (2023), \u201cTowards multi-spatiotemporal-scale generalized PDE modeling\u201d, Transactions on Machine Learning Research, available at:https:\/\/openreview.net\/forum?id=dPSTDbGtBY"},{"issue":"1","key":"2026041607113563400_ref365","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1038\/s41524-022-00784-w","article-title":"MatSciB-ERT: a materials domain language model for text mining and information extraction","volume":"8","author":"Gupta","year":"2022","journal-title":"npj Computational Materials"},{"issue":"30","key":"2026041607113563400_ref366","doi-asserted-by":"crossref","first-page":"19800","DOI":"10.1039\/C8CP03569E","article-title":"How accurate are static polarizability predictions from density functional theory? An assessment over 132 species at equilibrium geometry","volume":"20","author":"Hait","year":"2018","journal-title":"Physical Chemistry Chemical Physics"},{"issue":"4","key":"2026041607113563400_ref367","doi-asserted-by":"crossref","first-page":"1969","DOI":"10.1021\/acs.jctc.7b01252","article-title":"How accurate is density functional theory at predicting dipole moments? An assessment using a new database of 200 benchmark values","volume":"14","author":"Hait","year":"2018","journal-title":"Journal of Chemical Theory and Computation"},{"key":"2026041607113563400_ref368","article-title":"Variational graph recurrent neural networks","author":"Hajiramezanali","year":"2019","journal-title":"Neural Information Processing Systems."},{"issue":"12","key":"2026041607113563400_ref369","doi-asserted-by":"crossref","first-page":"744","DOI":"10.3390\/sym10120744","article-title":"Noether\u2019s theorem and symmetry","volume":"10","author":"Halder","year":"2018","journal-title":"Symmetry"},{"key":"2026041607113563400_ref370","doi-asserted-by":"crossref","DOI":"10.1021\/jm030644s","article-title":"Glide: a new approach for rapid, accurate docking and scoring. 2. 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(2018), \u201cReliable uncertainty estimate for antibiotic resistance classification with stochastic gradient Langevin dynamics\u201d, arXiv preprint arXiv:1811.11145."},{"key":"2026041607113563400_ref373","article-title":"Self-Attention based model for de-novo antibiotic resistant gene classification with enhanced reliability for Out of Distribution data detection","author":"Hamid","year":"2019"},{"key":"2026041607113563400_ref374","article-title":"LM-switch: lightweight language model conditioning in word embedding space","author":"Han","year":"2023"},{"key":"2026041607113563400_ref375","doi-asserted-by":"crossref","first-page":"108929","DOI":"10.1016\/j.jcp.2019.108929","article-title":"Solving many-electron Schr\u00f6dinger equation using deep neural networks","volume":"399","author":"Han","year":"2019","journal-title":"Journal of Computational Physics"},{"key":"2026041607113563400_ref376","unstructured":"Han, K., Lakshminarayanan, B. and Liu, J. (2021a), \u201cReliable graph neural networks for drug discovery under distributional shift\u201d, arXiv preprint arXiv:2111.12951."},{"key":"2026041607113563400_ref377","article-title":"Predicting physics in mesh-reduced space with temporal attention","author":"Han","year":"2021"},{"issue":"5","key":"2026041607113563400_ref378","doi-asserted-by":"crossref","first-page":"996","DOI":"10.1021\/acs.accounts.6b00037","article-title":"Prediction of stereochemistry using Q2MM","volume":"49","author":"Hansen","year":"2016","journal-title":"Accounts of Chemical Research"},{"issue":"3","key":"2026041607113563400_ref379","doi-asserted-by":"publisher","DOI":"10.1063\/5.0055593","article-title":"Thermal transport in defective and disordered materials","volume":"8","author":"Hanus","year":"2021","journal-title":"Applied Physics Reviews"},{"key":"2026041607113563400_ref380","article-title":"DPOT: auto-regressive denoising operator transformer for large-scale PDE pre-training","author":"Hao","year":"2024"},{"key":"2026041607113563400_ref381","first-page":"12556","article-title":"Gnot: a general neural operator transformer for operator learning","author":"Hao","year":"2023"},{"issue":"18","key":"2026041607113563400_ref382","doi-asserted-by":"crossref","first-page":"12146","DOI":"10.1039\/C5CP01425E","article-title":"Nonseparable exchange-correlation functional for molecules, including homogeneous catalysis involving transition metals","volume":"17","author":"Haoyu","year":"2015","journal-title":"Physical Chemistry Chemical Physics"},{"issue":"4","key":"2026041607113563400_ref383","doi-asserted-by":"crossref","first-page":"044001","DOI":"10.1088\/1361-6595\/ab0f70","article-title":"An overview of discharge plasma modeling for Hall effect thrusters","volume":"28","author":"Hara","year":"2019","journal-title":"Plasma Sources Science and Technology"},{"key":"2026041607113563400_ref384","doi-asserted-by":"crossref","DOI":"10.1088\/1361-6595\/acb28b","article-title":"Effects of macroparticle weighting in axisymmetric particle-in-cell Monte Carlo collision simulations","author":"Hara","year":"2023","journal-title":"Plasma Sources Science and Technology."},{"key":"2026041607113563400_ref385","first-page":"4094","article-title":"Bayesian graph neural networks with adaptive connection sampling","author":"Hasanzadeh","year":"2020"},{"key":"2026041607113563400_ref386","article-title":"Semi-implicit graph variational auto-encoders","author":"Hasanzadeh","year":"2019","journal-title":"Neural Information Processing Systems."},{"issue":"1","key":"2026041607113563400_ref387","doi-asserted-by":"crossref","first-page":"15451","DOI":"10.1038\/s41598-017-15571-7","article-title":"Protein-ligand blind docking using QuickVina-W with inter-process spatiotemporal integration","volume":"7","author":"Hassan","year":"2017","journal-title":"Scientific Reports"},{"issue":"4","key":"2026041607113563400_ref388","doi-asserted-by":"crossref","first-page":"572","DOI":"10.1021\/ci100031x","article-title":"Conformer generation with OMEGA: Algorithm and validation using high quality structures from the Protein Databank and Cambridge Structural Database","volume":"50","author":"Hawkins","year":"2010","journal-title":"Journal of Chemical Information and Modeling"},{"key":"2026041607113563400_ref389","first-page":"770","article-title":"Deep residual learning for image recognition","author":"He","year":"2016"},{"key":"2026041607113563400_ref390","first-page":"41","article-title":"Why ReLU networks yield high-confidence predictions far away from the training data and how to mitigate the problem","author":"Hein","year":"2019"},{"key":"2026041607113563400_ref391","volume-title":"Group Theory in Quantum Mechanics: An Introduction to its Present Usage","author":"Heine","year":"2007"},{"key":"2026041607113563400_ref392","article-title":"Group equivariant Fourier neural operators for partial differential equations","author":"Helwig","year":"2023"},{"issue":"22","key":"2026041607113563400_ref393","doi-asserted-by":"crossref","first-page":"4537","DOI":"10.1021\/ja01483a011","article-title":"Molecular geometry. 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(2024), \u201cPoseidon: efficient foundation models for PDEs\u201d, arXiv preprint arXiv:2405.19101."},{"issue":"10","key":"2026041607113563400_ref395","doi-asserted-by":"crossref","first-page":"891","DOI":"10.1038\/s41557-020-0544-y","article-title":"Deep-neural-network solution of the electronic Schr\u00f6dinger equation","volume":"12","author":"Hermann","year":"2020","journal-title":"Nature Chemistry"},{"key":"2026041607113563400_ref396","doi-asserted-by":"publisher","first-page":"692","DOI":"10.1038\/s41570-023-00516-8","article-title":"Ab initio quantum chemistry with neural-network wavefunctions","volume":"7","author":"Hermann","year":"2023","journal-title":"Nature Review Chemistry"},{"key":"2026041607113563400_ref397","article-title":"Contrastive representation learning for 3d protein structures","author":"Hermosilla","year":"2022"},{"key":"2026041607113563400_ref398","article-title":"Intrinsic-extrinsic convolution and pooling for learning on 3D protein structures","author":"Hermosilla","year":"2021"},{"issue":"730","key":"2026041607113563400_ref399","doi-asserted-by":"crossref","first-page":"1999","DOI":"10.1002\/qj.3803","article-title":"The ERA5 global reanalysis","volume":"146","author":"Hersbach","year":"2020","journal-title":"Quarterly Journal of the Royal Meteorological Society"},{"issue":"9","key":"2026041607113563400_ref400","doi-asserted-by":"crossref","first-page":"2484","DOI":"10.1021\/acs.jctc.2c01216","article-title":"Solving the Schr\u00f6dinger equation in the configuration space with generative machine learning","volume":"19","author":"Herzog","year":"2023","journal-title":"Journal of Chemical Theory and Computation"},{"issue":"18","key":"2026041607113563400_ref401","doi-asserted-by":"publisher","first-page":"8207","DOI":"10.1063\/1.1564060","article-title":"Hybrid functionals based on a screened Coulomb potential","volume":"118","author":"Heyd","year":"2003","journal-title":"The Journal of Chemical Physics"},{"issue":"2","key":"2026041607113563400_ref402","doi-asserted-by":"crossref","first-page":"023358","DOI":"10.1103\/PhysRevResearch.2.023358","article-title":"Recurrent neural network wave functions","volume":"2","author":"Hibat-Allah","year":"2020","journal-title":"Physical Review Research"},{"issue":"5","key":"2026041607113563400_ref403","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1016\/j.cels.2020.09.007","article-title":"Leveraging uncertainty in machine learning accelerates biological discovery and design","volume":"11","author":"Hie","year":"2020","journal-title":"Cell Systems"},{"key":"2026041607113563400_ref404","article-title":"Efficient evolution of human antibodies from general protein language models","author":"Hie","year":"2023","journal-title":"Nature Biotechnology."},{"issue":"8","key":"2026041607113563400_ref405","doi-asserted-by":"crossref","first-page":"3770","DOI":"10.1021\/acs.jcim.0c00502","article-title":"Uncertainty quantification using neural networks for molecular property prediction","volume":"60","author":"Hirschfeld","year":"2020","journal-title":"Journal of Chemical Information and Modeling"},{"key":"2026041607113563400_ref406","first-page":"6840","article-title":"Denoising diffusion probabilistic models","volume":"33","author":"Ho","year":"2020","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026041607113563400_ref407","unstructured":"Ho, J., Kalchbrenner, N., Weissenborn, D. and Salimans, T. (2019), \u201cAxial attention in multidimensional transformers\u201d, arXiv preprint arXiv:1912.12180."},{"key":"2026041607113563400_ref408","first-page":"278","article-title":"Random decision forests","author":"Ho","year":"1995"},{"issue":"2","key":"2026041607113563400_ref409","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1039\/D1DD00009H","article-title":"Natural language processing models that automate programming will transform chemistry research and teaching","volume":"1","author":"Hocky","year":"2022","journal-title":"Digital Discovery"},{"key":"2026041607113563400_ref410","unstructured":"Hoffmann, J., Maestrati, L., Sawada, Y., Tang, J., Sellier, J.M. and Bengio, Y. (2019), \u201cData-driven approach to encoding and decoding 3-D crystal structures\u201d, arXiv preprint arXiv:1909.00949."},{"key":"2026041607113563400_ref411","unstructured":"Hoffmann, M. and No\u00e9, F. (2019), \u201cGenerating valid Euclidean distance matrices\u201d, arXiv preprint arXiv:1910.03131."},{"issue":"3B","key":"2026041607113563400_ref412","doi-asserted-by":"crossref","first-page":"B864","DOI":"10.1103\/PhysRev.136.B864","article-title":"Inhomogeneous electron gas","volume":"136","author":"Hohenberg","year":"1964","journal-title":"Physical Review"},{"issue":"1-2","key":"2026041607113563400_ref413","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/0166-1280(95)04269-C","article-title":"Exact asymptotic form of kinetic-energy density of an atom or a molecule at large distances from its centre","volume":"357","author":"Holas","year":"1995","journal-title":"Journal of Molecular Structure: THEOCHEM"},{"key":"2026041607113563400_ref414","first-page":"4297","article-title":"Equivariant learning of stochastic fields: gaussian processes and steerable conditional neural processes","author":"Holderrieth","year":"2021"},{"key":"2026041607113563400_ref415","unstructured":"Holdijk, L., Du, Y., Hooft, F., Jaini, P., Ensing, B. and Welling, M. (2022), \u201cPath integral stochastic optimal control for sampling transition paths\u201d, arXiv preprint arXiv:2207.02149."},{"key":"2026041607113563400_ref416","article-title":"Learning to control PDEs with differentiable physics","author":"Holl","year":"2020"},{"issue":"24","key":"2026041607113563400_ref417","doi-asserted-by":"publisher","DOI":"10.1063\/1.5025668","article-title":"Can exact conditions improve machine-learned density functionals?","volume":"148","author":"Hollingsworth","year":"2018","journal-title":"The Journal of Chemical Physics"},{"key":"2026041607113563400_ref418","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511919701","volume-title":"Turbulence, Coherent Structures, Dynamical Systems and Symmetry","author":"Holmes","year":"2012"},{"key":"2026041607113563400_ref419","first-page":"8867","article-title":"Equivariant diffusion for molecule generation in 3D","author":"Hoogeboom","year":"2022"},{"key":"2026041607113563400_ref420","unstructured":"Hope, T., Downey, D., Etzioni, O., Weld, D.S. and Horvitz, E. (2022), \u201cA computational infection for scientific discovery\u201d, arXiv preprint arXiv:2205.02007."},{"key":"2026041607113563400_ref421","article-title":"Isometric transformation invariant and equivariant graph convolutional networks","author":"Horie","year":"2021"},{"issue":"8","key":"2026041607113563400_ref422","doi-asserted-by":"crossref","first-page":"1295","DOI":"10.1093\/bioinformatics\/btx780","article-title":"DeepSF: Deep convolutional neural network for mapping protein sequences to folds","volume":"34","author":"Hou","year":"2018","journal-title":"Bioinformatics"},{"key":"2026041607113563400_ref423","first-page":"8946","article-title":"Learning inverse folding from millions of predicted structures","author":"Hsu","year":"2022"},{"key":"2026041607113563400_ref424","doi-asserted-by":"crossref","DOI":"10.18653\/v1\/2021.findings-emnlp.277","article-title":"SciCap: Generating captions for scientific figures","author":"Hsu","year":"2021"},{"key":"2026041607113563400_ref425","article-title":"OGB-LSC: A large-scale challenge for machine learning on graphs","author":"Hu","year":"2021"},{"key":"2026041607113563400_ref426","first-page":"22118","article-title":"Open graph benchmark: Datasets for machine learning on graphs","volume":"33","author":"Hu","year":"2020","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026041607113563400_ref427","article-title":"Strategies for pre-training graph neural networks","author":"Hu","year":"2020"},{"key":"2026041607113563400_ref428","unstructured":"Hu, W., Shuaibi, M., Das, A., Goyal, S., Sriram, A., Leskovec, J., Parikh, D. and Zitnick, C.L. (2021b), \u201cForceNet: a graph neural network for large-scale quantum calculations\u201d, arXiv preprint arXiv:2103.01436."},{"key":"2026041607113563400_ref429","unstructured":"Hu, Y., Anderson, L., Li, T.-M., Sun, Q., Carr, N., Ragan-Kelley, J. and Durand, F. (2019), \u201cDifftaichi: differentiable programming for physical simulation\u201d, arXiv preprint arXiv:1910.00935."},{"issue":"4","key":"2026041607113563400_ref430","first-page":"1","article-title":"A moving least squares material point method with displacement discontinuity and two-way rigid body coupling","volume":"37","author":"Hu","year":"2018","journal-title":"ACM Transactions on Graphics (TOG)"},{"key":"2026041607113563400_ref431","unstructured":"Huang, G., Li, Y., Pleiss, G., Liu, Z., Hopcroft, J.E. and Weinberger, K.Q. (2017), \u201cSnapshot ensembles: train 1, get m for free\u201d, arXiv preprint arXiv:1704.00109."},{"key":"2026041607113563400_ref432","unstructured":"Huang, J. and Chang, K.C.-C. (2022), \u201cTowards reasoning in large language models: A survey\u201d, arXiv preprint arXiv:2212.10403."},{"key":"2026041607113563400_ref433","article-title":"Therapeutics data com-mons: machine learning datasets and tasks for drug discovery and development","author":"Huang","year":"2021","journal-title":"Advances in Neural Information Processing Systems."},{"key":"2026041607113563400_ref434","unstructured":"Huang, K., Jin, Y., Candes, E. and Leskovec, J. (2023a), \u201cUncertainty quantification over graph with conformalized graph neural networks\u201d, arXiv preprint arXiv:2305.14535."},{"key":"2026041607113563400_ref435","article-title":"PRODIGY: enabling in-context learning over graphs","author":"Huang","year":"2023"},{"key":"2026041607113563400_ref436","article-title":"Graphlime: Local interpretable model explanations for graph neural networks","author":"Huang","year":"2022"},{"key":"2026041607113563400_ref437","first-page":"603","article-title":"Ccnet: Criss-cross attention for semantic segmentation","author":"Huang","year":"2019"},{"key":"2026041607113563400_ref438","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1007\/s10994-021-05946-3","article-title":"Aleatoric and epistemic uncertainty in machine learning: An introduction to concepts and methods","volume":"110","author":"H\u00fcllermeier","year":"2021","journal-title":"Machine Learning"},{"issue":"6573","key":"2026041607113563400_ref439","doi-asserted-by":"publisher","first-page":"eabm4805","DOI":"10.1126\/science.abm4805","article-title":"Computed structures of core eukaryotic protein complexes","volume":"374","author":"Humphreys","year":"2021","journal-title":"Science"},{"issue":"19","key":"2026041607113563400_ref440","doi-asserted-by":"crossref","first-page":"194101","DOI":"10.1063\/5.0026133","article-title":"Coarse graining molecular dynamics with graph neural networks","volume":"153","author":"Husic","year":"2020","journal-title":"The Journal of Chemical Physics"},{"issue":"4","key":"2026041607113563400_ref441","article-title":"Estimation of non-normalized statistical models by score matching.","volume":"6","author":"Hyv\u00e4rinen","year":"2005","journal-title":"Journal of Machine Learning Research"},{"key":"2026041607113563400_ref442","unstructured":"Igashov, I., St\u00e4rk, H., Vignac, C., Satorras, V.G., Frossard, P., Welling, M., Bronstein, M. and Correia, B. (2022), \u201cEquivariant 3D-conditional diffusion models for molecular linker design\u201d, arXiv preprint arXiv:2210.05274."},{"key":"2026041607113563400_ref443","first-page":"63","article-title":"Protein structure determination by x-ray crystallography","author":"Ilari","year":"2008","journal-title":"Bioinformatics: Data, Sequence Analysis and Evolution"},{"key":"2026041607113563400_ref444","first-page":"2127","article-title":"Attention-based deep multiple instance learning","author":"Ilse","year":"2018"},{"key":"2026041607113563400_ref445","first-page":"25906","article-title":"Diving into the deep end: machine learning for the chemist","author":"Imberti","year":"2022"},{"key":"2026041607113563400_ref446","doi-asserted-by":"crossref","DOI":"10.1101\/2022.12.01.518682","article-title":"Illuminating protein space with a programmable generative model","author":"Ingraham","year":"2022"},{"key":"2026041607113563400_ref447","article-title":"Generative models for graph-based protein design","volume":"32","author":"Ingraham","year":"2019","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026041607113563400_ref448","article-title":"Subspace inference for Bayesian deep learning","author":"Izmailov","year":"2019","journal-title":"Uncertainty in Artificial Intelligence (UAI)."},{"key":"2026041607113563400_ref449","article-title":"Is GPT-3 all you need for low-data discovery in chemistry?","author":"Jablonka","year":"2023"},{"issue":"1","key":"2026041607113563400_ref450","doi-asserted-by":"crossref","first-page":"011002","DOI":"10.1063\/1.4812323","article-title":"Commentary: the materials project: a materials genome approach to accelerating materials innovation","volume":"1","author":"Jain","year":"2013","journal-title":"APL Materials"},{"key":"2026041607113563400_ref451","article-title":"EAGLE: large-scale learning of turbulent fluid dynamics with mesh transformers","author":"Janny","year":"2023"},{"key":"2026041607113563400_ref452","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-4715-5","volume-title":"An Introduction to Tensors and Group Theory for Physicists","author":"Jeevanjee","year":"2011"},{"key":"2026041607113563400_ref453","article-title":"Steerable partial differential operators for equivariant neural networks","author":"Jenner","year":"2022"},{"issue":"12","key":"2026041607113563400_ref454","doi-asserted-by":"crossref","first-page":"3567","DOI":"10.1039\/C8SC05372C","article-title":"A graph-based genetic algorithm and generative model\/Monte Carlo tree search for the exploration of chemical space","volume":"10","author":"Jensen","year":"2019","journal-title":"Chemical Science"},{"issue":"1","key":"2026041607113563400_ref455","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1109\/TPAMI.2012.59","article-title":"3D convolutional neural networks for human action recognition","volume":"35","author":"Ji","year":"2013","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"2026041607113563400_ref456","doi-asserted-by":"crossref","unstructured":"Ji, Y., Zhang, L., Wu, J., Wu, B., Huang, L.-K., Xu, T., Rong, Y., Li, L., Ren, J., Xue, D., et al. (2022), \u201cDrugOOD: out-of-distribution (OOD) dataset curator and benchmark for AI-aided drug discovery-A focus on affinity prediction problems with noise annotations\u201d, arXiv preprint arXiv:2201.09637.","DOI":"10.1609\/aaai.v37i7.25970"},{"key":"2026041607113563400_ref457","first-page":"1","article-title":"Pushing the limit of molecular dynamics with ab initio accuracy to 100 million atoms with machine learning","author":"Jia","year":"2020"},{"key":"2026041607113563400_ref458","article-title":"Crystal structure prediction by joint equivariant diffusion","author":"Jiao","year":"2023"},{"key":"2026041607113563400_ref459","doi-asserted-by":"publisher","first-page":"166","DOI":"10.1016\/j.neunet.2020.08.017","article-title":"SympNets: intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems","volume":"132","author":"Jin","year":"2020","journal-title":"Neural Networks"},{"key":"2026041607113563400_ref460","article-title":"GeneGPT: Teaching large language models to use NCBI web APIs","author":"Jin","year":"2023"},{"key":"2026041607113563400_ref461","first-page":"2323","article-title":"Junction tree variational autoencoder for molecular graph generation","author":"Jin","year":"2018"},{"key":"2026041607113563400_ref462","unstructured":"Jing, B., Corso, G., Barzilay, R. and Jaakkola, T.S. (2022), \u201cTorsional diffusion for molecular conformer generation\u201d, in ICLR2022 Ma-chine Learning for Drug Discovery, available at:https:\/\/openreview.net\/forum?id=D9IxPlXPJJS"},{"key":"2026041607113563400_ref463","article-title":"Learning from protein structure with geometric vector perceptrons","author":"Jing","year":"2021"},{"issue":"3","key":"2026041607113563400_ref464","doi-asserted-by":"publisher","first-page":"897","DOI":"10.1103\/RevModPhys.87.897","article-title":"Density functional theory: its origins, rise to prominence, and future","volume":"87","author":"Jones","year":"2015","journal-title":"Reviews of Modern Physics"},{"key":"2026041607113563400_ref465","unstructured":"Joshi, C.\n           (2020), \u201cTransformers are graph neural networks\u201d, available at:https:\/\/thegradient.pub\/transformers-are-gaph-neural-networks\/"},{"key":"2026041607113563400_ref466","article-title":"On the expressive power of geometric graph neural 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(2023), \u201cGrounding language models to images for multimodal generation\u201d, arXiv preprint arXiv:2301.13823."},{"key":"2026041607113563400_ref510","first-page":"5637","article-title":"Wilds: A benchmark of in-the-wild distribution shifts","author":"Koh","year":"2021"},{"key":"2026041607113563400_ref511","unstructured":"Kohl, G., Chen, L.-W. and Thuerey, N. (2023), \u201cTurbulent flow simulation using autoregressive conditional diffusion models\u201d, arXiv preprint arXiv:2309.01745."},{"key":"2026041607113563400_ref512","first-page":"5361","article-title":"Equivariant flows: exact likelihood generative learning for symmetric densities","volume-title":"International Conference on Machine Learning","author":"K\u00f6hler","year":"2020"},{"issue":"3","key":"2026041607113563400_ref513","doi-asserted-by":"crossref","first-page":"942","DOI":"10.1021\/acs.jctc.3c00016","article-title":"Flow-matching: efficient coarse-graining of molecular dynamics without forces","volume":"19","author":"K\u00f6hler","year":"2023","journal-title":"Journal of Chemical Theory and Computation"},{"issue":"5","key":"2026041607113563400_ref514","doi-asserted-by":"publisher","first-page":"1253","DOI":"10.1103\/RevModPhys.71.1253","article-title":"Nobel Lecture: electronic structure of matter\u2014wave functions and density functionals","volume":"71","author":"Kohn","year":"1999","journal-title":"Reviews of Modern Physics"},{"issue":"4A","key":"2026041607113563400_ref515","doi-asserted-by":"crossref","first-page":"A1133","DOI":"10.1103\/PhysRev.140.A1133","article-title":"Self-consistent equations including exchange and correlation effects","volume":"140","author":"Kohn","year":"1965","journal-title":"Physical Review"},{"key":"2026041607113563400_ref516","unstructured":"Kondor, R.\n           (2018), \u201cN-body networks: A covariant hierarchical neural network architecture for learning atomic potentials\u201d, arXiv preprint arXiv:1803.01588."},{"key":"2026041607113563400_ref517","article-title":"Clebsch-Gordan nets: a fully Fourier space spherical convolutional neural network","volume":"31","author":"Kondor","year":"2018","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"4","key":"2026041607113563400_ref518","doi-asserted-by":"crossref","first-page":"993","DOI":"10.1021\/ct800511q","article-title":"\u2018Mindless\u2019 DFT benchmarking","volume":"5","author":"Korth","year":"2009","journal-title":"Journal of Chemical Theory and Computation"},{"key":"2026041607113563400_ref519","article-title":"Ewald-based long-range message passing for molecular graphs","author":"Kosmala","year":"2023"},{"key":"2026041607113563400_ref520","unstructured":"Kovachki, N., Li, Z., Liu, B., Azizzadenesheli, K., Bhattacharya, K., Stuart, A. and Anandkumar, A. 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(2021a), \u201cBERT might be overkill: A tiny but effective biomedical entity linker based on residual convolutional neural networks\u201d, arXiv preprint arXiv:2109.02237.","DOI":"10.18653\/v1\/2021.findings-emnlp.140"},{"key":"2026041607113563400_ref535","doi-asserted-by":"crossref","unstructured":"Lai, T., Ji, H., Zhai, C. and Tran, Q.H. 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(2022), \u201cGraphCast: learning skillful medium-range global weather forecasting\u201d, arXiv preprint arXiv:2212.12794.","DOI":"10.1126\/science.adi2336"},{"issue":"3","key":"2026041607113563400_ref540","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1016\/S0893-6080(00)00098-8","article-title":"Bayesian approach for neural networks-review and case studies","volume":"14","author":"Lampinen","year":"2001","journal-title":"Neural Networks"},{"key":"2026041607113563400_ref541","unstructured":"Lan, J., Palizhati, A., Shuaibi, M., Wood, B.M., Wander, B., Das, A., Uyttendaele, M., Zitnick, C.L. and Ulissi, Z.W. 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(2022), \u201cEquivariant graph attention networks for molecular property prediction\u201d, arXiv preprint arXiv:2202.09891."},{"issue":"11","key":"2026041607113563400_ref548","doi-asserted-by":"crossref","first-page":"2278","DOI":"10.1109\/5.726791","article-title":"Gradient-based learning applied to document recognition","volume":"86","author":"LeCun","year":"1998","journal-title":"Proceedings of the IEEE"},{"issue":"2","key":"2026041607113563400_ref549","doi-asserted-by":"publisher","first-page":"785","DOI":"10.1103\/PhysRevB.37.785","article-title":"Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density","volume":"37","author":"Lee","year":"1988","journal-title":"Physical Review B"},{"key":"2026041607113563400_ref550","unstructured":"Lee, S., Lee, D.B. and Hwang, S.J. (2022b), \u201cMOG: Molecular out-of-distribution generation with energy-based models\u201d, available at:https:\/\/openreview.net\/forum?id=qkTEaJ9orc1"},{"key":"2026041607113563400_ref551","unstructured":"Lee, S., Jo, J. and Hwang, S.J. (2022a), \u201cExploring chemical space with score-based out-of-distribution generation\u201d, arXiv preprint arXiv:2206.07632."},{"issue":"1","key":"2026041607113563400_ref552","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41524-021-00662-x","article-title":"Bayesian optimization with adaptive surrogate models for automated experimental design","volume":"7","author":"Lei","year":"2021","journal-title":"npj Computational Materials"},{"issue":"6","key":"2026041607113563400_ref553","doi-asserted-by":"publisher","first-page":"063801","DOI":"10.1103\/PhysRevMaterials.3.063801","article-title":"Design and analysis of machine learning exchange-correlation functionals via rotationally invariant convolutional descriptors","volume":"3","author":"Lei","year":"2019","journal-title":"Physical Review Materials"},{"issue":"2","key":"2026041607113563400_ref554","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1103\/PhysRevA.38.625","article-title":"Exact properties of the Pauli potential for the square root of the electron density and the kinetic energy functional","volume":"38","author":"Levy","year":"1988","journal-title":"Physical Review A"},{"key":"2026041607113563400_ref555","doi-asserted-by":"crossref","DOI":"10.1609\/aaai.v30i1.10200","article-title":"Preconditioned stochastic gradient Langevin dynamics for deep neural networks","volume":"30","author":"Li","year":"2016","journal-title":"Proceedings of the AAAI Conference on Artificial Intelligence"},{"key":"2026041607113563400_ref556","first-page":"5542","article-title":"Deeper, broader and artier domain generalization","author":"Li","year":"2017"},{"issue":"4","key":"2026041607113563400_ref557","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1038\/s43588-023-00424-3","article-title":"Deep-learning electronic-structure calculation of magnetic super-structures","volume":"3","author":"Li","year":"2023","journal-title":"Nature Computational Science"},{"issue":"6","key":"2026041607113563400_ref558","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1038\/s43588-022-00265-6","article-title":"Deep-learning density functional theory Hamiltonian for efficient ab initio electronic-structure calculation","volume":"2","author":"Li","year":"2022","journal-title":"Nature Computational Science"},{"key":"2026041607113563400_ref559","article-title":"BioCre-ative V CDR task corpus: a resource for chemical disease relation extraction","author":"Li","year":"2016"},{"issue":"11","key":"2026041607113563400_ref560","doi-asserted-by":"crossref","first-page":"819","DOI":"10.1002\/qua.25040","article-title":"Under-standing machine-learned density functionals","volume":"116","author":"Li","year":"2016","journal-title":"International Journal of Quantum Chemistry"},{"key":"2026041607113563400_ref561","unstructured":"Li, L., Zeng, L., Gao, Z., Yuan, S., Bian, Y., Wu, B., Zhang, H., Lu, C., Yu, Y., Liu, W., et al. (2022b), \u201cImDrug: A benchmark for deep imbalanced learning in AI-aided drug discovery\u201d, arXiv preprint arXiv:2209.07921."},{"issue":"3","key":"2026041607113563400_ref562","doi-asserted-by":"crossref","first-page":"036401","DOI":"10.1103\/PhysRevLett.126.036401","article-title":"Kohn-Sham equations as regularizer: building prior knowledge into machine-learned physics","volume":"126","author":"Li","year":"2021","journal-title":"Physical Review Letters"},{"issue":"24","key":"2026041607113563400_ref563","doi-asserted-by":"crossref","first-page":"245129","DOI":"10.1103\/PhysRevB.94.245129","article-title":"Pure density functional for strong correlation and the thermodynamic limit from machine learning","volume":"94","author":"Li","year":"2016","journal-title":"Physical Review B"},{"key":"2026041607113563400_ref564","doi-asserted-by":"crossref","DOI":"10.1109\/CVPR52688.2022.01593","article-title":"CLIP-Event: Connecting text and images with event structures","author":"Li","year":"2022"},{"key":"2026041607113563400_ref565","first-page":"2694","article-title":"Pairwise half-graph discrimination: A simple graph-level self-supervised strategy for pre-training graph neural networks","author":"Li","year":"2021"},{"key":"2026041607113563400_ref566","article-title":"D4FT: A deep learning approach to Kohn-Sham density functional theory","author":"Li","year":"2023"},{"key":"2026041607113563400_ref567","doi-asserted-by":"crossref","unstructured":"Li, T., Shetty, S., Kamath, A., Jaiswal, A., Jiang, X., Ding, Y. and Kim, Y. (2023c), \u201cCancerGPT: Few-shot drug pair synergy pre-diction using large pre-trained language models\u201d, arXiv preprint arXiv:2304.10946.","DOI":"10.1038\/s41746-024-01024-9"},{"key":"2026041607113563400_ref568","doi-asserted-by":"publisher","first-page":"829","DOI":"10.1038\/s41578-021-00304-0","article-title":"Phase transitions in 2D materials","volume":"6","author":"Li","year":"2021","journal-title":"Nature Reviews Materials"},{"key":"2026041607113563400_ref569","unstructured":"Li, X., Gui, S., Luo, Y. and Ji, S. (2023d), \u201cGraph structure and feature extrapolation for out-of-distribution generalization\u201d, arXiv preprint arXiv:2306.08076."},{"key":"2026041607113563400_ref570","unstructured":"Li, X., Qiao, Y.-L., Chen, P.Y., Jatavallabhula, K.M., Lin, M., Jiang, C. and Gan, C. (2023e), \u201cPAC-NeRF: physics augmented continuum neural radiance felds for geometry-agnostic system identification\u201d, arXiv preprint arXiv:2303.05512."},{"issue":"41","key":"2026041607113563400_ref571","doi-asserted-by":"crossref","first-page":"13664","DOI":"10.1039\/D1SC04444C","article-title":"Structure-based de novo drug design using 3D deep generative models","volume":"12","author":"Li","year":"2021","journal-title":"Chemical Science"},{"key":"2026041607113563400_ref572","unstructured":"Li, Y., Kong, L., Du, Y., Yu, Y., Zhuang, Y., Mu, W. and Zhang, C. (2023f), \u201cMUBen: Benchmarking the uncertainty of pre-trained models for molecular property prediction\u201d, arXiv preprint arXiv:2306.10060."},{"key":"2026041607113563400_ref573","unstructured":"Li, Y., Yu, R., Shahabi, C. and Liu, Y. (2017b), \u201cDiffusion convolutional recurrent neural network: data-driven traffic forecasting\u201d, arXiv preprint arXiv:1707.01926."},{"issue":"6","key":"2026041607113563400_ref574","doi-asserted-by":"publisher","DOI":"10.1145\/3550454.3555429","article-title":"Fluidic topology optimization with an anisotropic mixture model","volume":"41","author":"Li","year":"2022","journal-title":"ACM Transactions on Graphics (TOG)"},{"key":"2026041607113563400_ref575","doi-asserted-by":"crossref","first-page":"139983","DOI":"10.1109\/ACCESS.2020.3012132","article-title":"Predicting scattering from complex nano-structures via deep learning","volume":"8","author":"Li","year":"2020","journal-title":"IEEE Access"},{"key":"2026041607113563400_ref576","unstructured":"Li, Z., Huang, D.Z., Liu, B. and Anandkumar, A. (2022e), \u201cFourier neural operator with learned deformations for PDEs on general geometries\u201d, arXiv preprint arXiv:2207.05209."},{"key":"2026041607113563400_ref577","unstructured":"Li, Z., Zheng, H., Thiede, E., Liu, J. and Kondor, R. (2022f), \u201cGroup-equivariant neural networks with fusion diagrams\u201d, arXiv preprint arXiv:2211.07482."},{"key":"2026041607113563400_ref578","unstructured":"Li, Z., Zheng, H., Kovachki, N., Jin, D., Chen, H., Liu, B., Azizzadenesheli, K. and Anandkumar, A. (2021g), \u201cPhysics-informed neural operator for learning partial differential equations\u201d, arXiv preprint arXiv:2111.03794."},{"key":"2026041607113563400_ref579","article-title":"Transformer for partial differential equations\u2019 operator learning","author":"Li","year":"2022","journal-title":"Transactions on Machine Learning Research."},{"issue":"14","key":"2026041607113563400_ref580","doi-asserted-by":"crossref","first-page":"144103","DOI":"10.1063\/5.0083060","article-title":"Graph neural networks accelerated molecular dynamics","volume":"156","author":"Li","year":"2022","journal-title":"The Journal of Chemical Physics"},{"key":"2026041607113563400_ref581","unstructured":"Li, Z., Liu-Schiaffini, M., Kovachki, N., Azizzadenesheli, K., Liu, B., Bhattacharya, K., Stuart, A. and Anandkumar, A. (2021f), \u201cLearning dissipative dynamics in chaotic systems\u201d, arXiv preprint arXiv:2106. 06898."},{"key":"2026041607113563400_ref582","first-page":"6755","article-title":"Multipole graph neural operator for parametric partial differential equations","volume":"33","author":"Li","year":"2020","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026041607113563400_ref583","unstructured":"Li, Z., Kovachki, N., Azizzadenesheli, K., Liu, B., Bhattacharya, K., Stuart, A. and Anandkumar, A. (2020b), \u201cNeural operator: graph kernel network for partial differential equations\u201d, arXiv preprint arXiv:2003.03485."},{"key":"2026041607113563400_ref584","unstructured":"Li, Z., Kovachki, N.B., Choy, C., Li, B., Kossaif, J., Otta, S.P., Nabian, M.A., Stadler, M., Hundt, C., Azizzadenesheli, K., et al. (2023g), \u201cGeometry-informed neural operator for large-scale 3D PDEs\u201d, arXiv preprint arXiv:2309.00583."},{"key":"2026041607113563400_ref585","article-title":"Fourier neural operator for parametric partial differential equations","author":"Li","year":"2021"},{"key":"2026041607113563400_ref586","doi-asserted-by":"crossref","DOI":"10.1101\/2022.08.04.502811","article-title":"Uni-Fold: An open-source platform for developing protein folding models beyond AlphaFold","author":"Li","year":"2022"},{"issue":"10","key":"2026041607113563400_ref587","doi-asserted-by":"crossref","first-page":"2565","DOI":"10.1002\/prot.24620","article-title":"Direct prediction of profiles of sequences compatible with a protein structure by neural networks with fragment-based local and energy-based nonlocal profiles","volume":"82","author":"Li","year":"2014","journal-title":"Proteins: Structure, Function, and Bioinformatics"},{"issue":"10","key":"2026041607113563400_ref588","doi-asserted-by":"crossref","first-page":"104426","DOI":"10.1103\/PhysRevB.98.104426","article-title":"Solving frustrated quantum many-particle models with convolutional neural networks","volume":"98","author":"Liang","year":"2018","journal-title":"Physical Review B"},{"key":"2026041607113563400_ref589","article-title":"DrugChat: Towards enabling ChatGPT-like capabilities on drug molecule graphs","author":"Liang","year":"2023"},{"key":"2026041607113563400_ref590","article-title":"Equiformer: Equivariant graph attention transformer for 3D atomistic graphs","author":"Liao","year":"2023"},{"key":"2026041607113563400_ref591","unstructured":"Liao, Y.-L., Wood, B., Das, A. and Smidt, T. (2023), \u201cEquiformerV2: Improved equivariant transformer for scaling to higher-degree representations\u201d, arXiv preprint arXiv:2306.12059."},{"key":"2026041607113563400_ref592","article-title":"Learning the dynamics of physical systems from sparse observations with finite element networks","author":"Lienen","year":"2022"},{"key":"2026041607113563400_ref593","unstructured":"Lienen, M., Hansen-Palmus, J., L\u00fcdke, D. and G\u00fcnnemann, S. (2023), \u201cGenerative diffusion for 3D turbulent flows\u201d, arXiv preprint arXiv: 2306.01776."},{"key":"2026041607113563400_ref594","unstructured":"Lin, H., Huang, Y., Liu, M., Li, X., Ji, S. and Li, S.Z. (2022), \u201cDiffBP: Generative diffusion of 3D molecules for target protein binding\u201d, arXiv preprint arXiv:2211.11214."},{"key":"2026041607113563400_ref595","doi-asserted-by":"crossref","first-page":"111765","DOI":"10.1016\/j.jcp.2022.111765","article-title":"Explicitly antisymmetrized neural network layers for variational Monte Carlo simulation","volume":"474","author":"Lin","year":"2023","journal-title":"Journal of Computational Physics"},{"key":"2026041607113563400_ref596","first-page":"2980","article-title":"Focal loss for dense object detection","author":"Lin","year":"2017"},{"key":"2026041607113563400_ref597","doi-asserted-by":"crossref","unstructured":"Lin, W., Zhao, Z., Zhang, X., Wu, C., Zhang, Y., Wang, Y. and Xie, W. (2023b), \u201cPMC-CLIP: contrastive language-image pre-training using biomedical documents\u201d, arXiv preprintarXiv:2303.07240.","DOI":"10.1007\/978-3-031-43993-3_51"},{"key":"2026041607113563400_ref598","unstructured":"Lin, Y. and AlQuraishi, M. (2023), \u201cGenerating novel, designable, and diverse protein structures by equivariantly diffusing oriented residue clouds\u201d, arXiv preprintarXiv:2301.12485."},{"issue":"1","key":"2026041607113563400_ref599","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1109\/MSP.2022.3217658","article-title":"Physics-guided data-driven seismic inversion: recent progress and future opportunities in full-waveform inversion","volume":"40","author":"Lin","year":"2023","journal-title":"IEEE Signal Processing Magazine"},{"key":"2026041607113563400_ref600","article-title":"Equivariance via minimal frame averaging for more symmetries and efficiency","author":"Lin","year":"2024"},{"key":"2026041607113563400_ref601","article-title":"Efficient approximations of complete interatomic potentials for crystal property prediction","author":"Lin","year":"2023"},{"issue":"6637","key":"2026041607113563400_ref602","doi-asserted-by":"crossref","first-page":"1123","DOI":"10.1126\/science.ade2574","article-title":"Evolutionary-scale prediction of atomic-level protein structure with a language model","volume":"379","author":"Lin","year":"2023","journal-title":"Science"},{"issue":"6055","key":"2026041607113563400_ref603","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1126\/science.1208351","article-title":"How fast-folding proteins fold","volume":"334","author":"Lindorff-Larsen","year":"2011","journal-title":"Science"},{"key":"2026041607113563400_ref604","article-title":"On explaining equivariant graph networks via improved relevance propagation","author":"Ling","year":"2025"},{"key":"2026041607113563400_ref605","unstructured":"Lippe, P., Veeling, B.S., Perdikaris, P., Turner, R.E. and Brandstetter, J. (2023), \u201cPDE-Refner: achieving accurate long rollouts with neural PDE solvers\u201d, arXiv preprintarXiv:2308.05732."},{"issue":"4","key":"2026041607113563400_ref606","doi-asserted-by":"crossref","first-page":"633","DOI":"10.1107\/S2053273319005606","article-title":"Using a machine learning approach to determine the space group of a structure from the atomic pair distribution function","volume":"75","author":"Liu","year":"2019","journal-title":"Acta Crystallographica Section A: Foundations and Advances"},{"key":"2026041607113563400_ref607","doi-asserted-by":"publisher","first-page":"4228","DOI":"10.18653\/v1\/2021.naacl-main.334","article-title":"Self-alignment pretraining for biomedical entity representations","author":"Liu","year":"2021"},{"key":"2026041607113563400_ref608","first-page":"13912","article-title":"Generating 3D molecules for target protein binding","author":"Liu","year":"2022"},{"key":"2026041607113563400_ref609","article-title":"GraphEBM: molecular graph generation with energy-based models","author":"Liu","year":"2021"},{"issue":"9","key":"2026041607113563400_ref610","first-page":"1","article-title":"Pre-train, prompt, and predict: a systematic survey of prompting methods in natural language processing","volume":"55","author":"Liu","year":"2023","journal-title":"ACM Computing Surveys"},{"key":"2026041607113563400_ref611","first-page":"29","article-title":"Stein variational gradient descent: a general purpose Bayesian inference algorithm","author":"Liu","year":"2016","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"1","key":"2026041607113563400_ref612","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1021\/acs.jcim.8b00597","article-title":"Molecular similarity-based domain applicability metric efficiently identifes out-of-domain compounds","volume":"59","author":"Liu","year":"2018","journal-title":"Journal of Chemical Information and Modeling"},{"key":"2026041607113563400_ref613","unstructured":"Liu, S., Nie, W., Wang, C., Lu, J., Qiao, Z., Liu, L., Tang, J., Xiao, C. and Anandkumar, A. (2022b), \u201cMulti-modal molecule structure-text model for text-based retrieval and editing\u201d, arXiv preprintarXiv:2212.10789."},{"key":"2026041607113563400_ref614","article-title":"Pre-training molecular graph representation with 3D geometry","author":"Liu","year":"2022"},{"key":"2026041607113563400_ref615","unstructured":"Liu, S., Wang, J., Yang, Y., Wang, C., Liu, L., Guo, H. and Xiao, C. (2023c), \u201cChatGPT-powered conversational drug editing using retrieval and domain feedback\u201d, arXiv preprintarXiv:2305.18090."},{"key":"2026041607113563400_ref616","unstructured":"Liu, S., Zhu, Y., Lu, J., Xu, Z., Nie, W., Gitter, A., Xiao, C., Tang, J., Guo, H. and Anandkumar, A. (2023d), \u201cA text-guided protein design framework\u201d, arXiv preprintarXiv:2302.04611."},{"key":"2026041607113563400_ref617","unstructured":"Liu, S., (Jim) Fan, L., Johns, E., Yu, Z., Xiao, C. and Anandkumar, A. (2023e), \u201cPrismer: a vision-language model with an ensemble of experts\u201d, arXiv preprintarXiv:2303.02506."},{"key":"2026041607113563400_ref618","article-title":"Flow straight and fast: learning to generate and transfer data with rectifed fow","author":"Liu","year":"2022","journal-title":"NeurIPS 2022 Workshop on Score-Based Methods."},{"key":"2026041607113563400_ref619","article-title":"Spherical message passing for 3d molecular graphs","author":"Liu","year":"2022"},{"key":"2026041607113563400_ref620","first-page":"1","article-title":"The amorphous state as a frontier in computational materials design","author":"Liu","year":"2024","journal-title":"Nature Reviews Materials"},{"key":"2026041607113563400_ref621","doi-asserted-by":"crossref","unstructured":"Liu, Y., Wang, Y., Vu, O.T., Moretti, R., Bodenheimer, B., Meiler, J. and Derr, T. (2022f), \u201cInterpretable chirality-aware graph neural network for quantitative structure activity relationship modeling in drug discovery\u201d, bioRxiv: 2022\u201308.","DOI":"10.1101\/2022.08.24.505155"},{"key":"2026041607113563400_ref622","first-page":"10012","article-title":"Swin transformer: hierarchical vision transformer using shifted windows","author":"Liu","year":"2021"},{"key":"2026041607113563400_ref623","unstructured":"Liu, Z., Zhang, W., Xia, Y., Wu, L., Xie, S., Qin, T., Zhang, M. and Liu, T.Y. (2023f), \u201cMolXPT: wrapping molecules with text for generative pre-training\u201d, arXiv preprintarXiv:2305.10688."},{"key":"2026041607113563400_ref624","first-page":"12009","article-title":"Swin transformer v2: scaling up capacity and resolution","author":"Liu","year":"2022"},{"issue":"11","key":"2026041607113563400_ref625","doi-asserted-by":"crossref","first-page":"2593","DOI":"10.1016\/j.drudis.2021.06.009","article-title":"AI-based language models powering drug discovery and development","volume":"26","author":"Liu","year":"2021","journal-title":"Drug Discovery Today"},{"issue":"3","key":"2026041607113563400_ref626","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1093\/bioinformatics\/btu626","article-title":"PDB-wide collection of binding data: current status of the PDBbind database","volume":"31","author":"Liu","year":"2015","journal-title":"Bioinformatics"},{"issue":"2","key":"2026041607113563400_ref627","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1021\/acs.accounts.6b00491","article-title":"Forging the basis for developing protein\u2013ligand interaction scoring functions","volume":"50","author":"Liu","year":"2017","journal-title":"Accounts of Chemical Research"},{"key":"2026041607113563400_ref628","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-23099-8","volume-title":"Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book","author":"Logg","year":"2012"},{"key":"2026041607113563400_ref629","first-page":"97","article-title":"Learning transferable features with deep adaptation networks","author":"Long","year":"2015"},{"key":"2026041607113563400_ref630","doi-asserted-by":"crossref","unstructured":"Lou, W.T., Sutterud, H., Cassella, G., Foulkes, W.M.C., Knolle, J., Pfau, D. and Spencer, J.S. (2023), \u201cNeural wave functions for superfuids\u201d, arXiv preprintarXiv:2305.06989.","DOI":"10.1103\/PhysRevX.14.021030"},{"issue":"32","key":"2026041607113563400_ref631","doi-asserted-by":"crossref","first-page":"18141","DOI":"10.1039\/D0CP01474E","article-title":"Graph convolutional neural networks with global attention for improved materials property prediction","volume":"22","author":"Louis","year":"2020","journal-title":"Physical Chemistry Chemical Physics"},{"issue":"4","key":"2026041607113563400_ref632","doi-asserted-by":"crossref","first-page":"043178","DOI":"10.1103\/PhysRevResearch.4.043178","article-title":"Hidden-nucleons neural-network quantum states for the nuclear many-body problem","volume":"4","author":"Lovato","year":"2022","journal-title":"Physical Review Research"},{"key":"2026041607113563400_ref633","article-title":"In-variant causal representation learning for out-of-distribution generalization","author":"Lu","year":"2021"},{"issue":"3","key":"2026041607113563400_ref634","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1038\/s42256-021-00302-5","article-title":"Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators","volume":"3","author":"Lu","year":"2021","journal-title":"Nature Machine Intelligence"},{"key":"2026041607113563400_ref635","doi-asserted-by":"crossref","first-page":"114778","DOI":"10.1016\/j.cma.2022.114778","article-title":"A comprehensive and fair comparison of two neural operators (with practical extensions) based on fair data","volume":"393","author":"Lu","year":"2022","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"issue":"6","key":"2026041607113563400_ref636","doi-asserted-by":"crossref","first-page":"B1105","DOI":"10.1137\/21M1397908","article-title":"Physics-informed neural networks with hard constraints for inverse design","volume":"43","author":"Lu","year":"2021","journal-title":"SIAM Journal on Scientifc Computing"},{"key":"2026041607113563400_ref637","first-page":"3855","article-title":"Parameter-efficient domain knowledge integration from multiple sources for biomedical pre-trained language models","author":"Lu","year":"2021"},{"key":"2026041607113563400_ref638","unstructured":"Lu, S., Gao, Z., He, D., Zhang, L. and Ke, G. (2023a), \u201cHighly accurate quantum chemical property prediction with uni-mol+\u201d, arXiv preprintarXiv:2303.16982."},{"key":"2026041607113563400_ref639","unstructured":"Lu, S., Yao, L., Chen, X., Zheng, H., He, D. and Ke, G. (2023b), \u201c3D molecular generation via virtual dynamics\u201d, arXiv preprintarXiv:2302.05847."},{"key":"2026041607113563400_ref640","doi-asserted-by":"crossref","DOI":"10.1101\/2022.06.06.495043","article-title":"Tankbind: trigonometry-aware neural networks for drug-protein binding structure prediction","author":"Lu","year":"2022"},{"key":"2026041607113563400_ref641","doi-asserted-by":"crossref","first-page":"1013","DOI":"10.1086\/112164","article-title":"A numerical approach to the testing of the fssion hypothesis","volume":"82","author":"Lucy","year":"1977","journal-title":"Astronomical Journal"},{"issue":"27","key":"2026041607113563400_ref642","doi-asserted-by":"crossref","first-page":"276402","DOI":"10.1103\/PhysRevLett.127.276402","article-title":"Gauge equiv-ariant neural networks for quantum lattice gauge theories","volume":"127","author":"Luo","year":"2021","journal-title":"Physical Review Letters"},{"issue":"22","key":"2026041607113563400_ref643","doi-asserted-by":"crossref","first-page":"226401","DOI":"10.1103\/PhysRevLett.122.226401","article-title":"Backfow transformations via neural networks for quantum many-body wave functions","volume":"122","author":"Luo","year":"2019","journal-title":"Physical Review Letters"},{"key":"2026041607113563400_ref644","unstructured":"Luo, D., Yuan, S., Stokes, J. and Clark, B.K. (2022a), \u201cGauge equiv-ariant neural networks for 2+ 1d u (1) gauge theory simulations in hamiltonian formulation\u201d, arXiv preprintarXiv:2211.03198."},{"issue":"6","key":"2026041607113563400_ref645","article-title":"BioGPT: generative pre-trained transformer for biomedical text generation and mining","volume":"23","author":"Luo","year":"2022","journal-title":"Briefngs in Bioinformatics"},{"key":"2026041607113563400_ref646","article-title":"One transformer can understand both 2D & 3D molecular data","author":"Luo","year":"2023"},{"key":"2026041607113563400_ref647","first-page":"6229","article-title":"A 3D generative model for structure-based drug design","volume":"34","author":"Luo","year":"2021","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026041607113563400_ref648","article-title":"An autoregressive fow model for 3D molecular geometry generation from scratch","author":"Luo","year":"2022"},{"key":"2026041607113563400_ref649","article-title":"Towards symmetry-aware generation of periodic materials","author":"Luo","year":"2023"},{"issue":"4","key":"2026041607113563400_ref650","doi-asserted-by":"crossref","first-page":"044123","DOI":"10.1063\/5.0012911","article-title":"A deep neural network for molecular wave functions in quasi-atomic minimal basis representation","volume":"153","author":"Luya","year":"2020","journal-title":"The Journal of Chemical Physics"},{"issue":"7743","key":"2026041607113563400_ref651","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1038\/s41586-019-0917-9","article-title":"Ultra-large library docking for discovering new chemotypes","volume":"566","author":"Lyu","year":"2019","journal-title":"Nature"},{"issue":"36","key":"2026041607113563400_ref652","doi-asserted-by":"publisher","first-page":"eabq0279","DOI":"10.1126\/sciadv.abq0279","article-title":"Evolving symbolic density functionals","volume":"8","author":"Ma","year":"2022","journal-title":"Science Advances"},{"key":"2026041607113563400_ref653","unstructured":"Ma, P., Chen, P.Y., Deng, B., Tenenbaum, J.B., Du, T., Gan, C. and Matusik, W. (2023), \u201cLearning neural constitutive laws from mo-tion observations for generalizable PDE dynamics\u201d, arXiv preprintarXiv:2304.14369."},{"issue":"1","key":"2026041607113563400_ref654","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1021\/acsphyschemau.4c00063","article-title":"Is the future of materials amorphous? 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(2020), \u201cProgen: language modeling for protein generation\u201d, arXiv preprintarXiv:2004.03497.","DOI":"10.1101\/2020.03.07.982272"},{"key":"2026041607113563400_ref657","first-page":"1","article-title":"Large language models generate functional protein sequences across diverse families","author":"Madani","year":"2023","journal-title":"Nature Biotechnology"},{"key":"2026041607113563400_ref658","first-page":"32","article-title":"A simple baseline for Bayesian uncertainty in deep learning","author":"Maddox","year":"2019","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"23","key":"2026041607113563400_ref659","doi-asserted-by":"crossref","first-page":"235130","DOI":"10.1103\/PhysRevB.102.235130","article-title":"Learning the electronic density of states in condensed matter","volume":"102","author":"Mahmoud","year":"2020","journal-title":"Physical Review B"},{"issue":"4","key":"2026041607113563400_ref660","doi-asserted-by":"crossref","first-page":"1005","DOI":"10.1190\/1.1778243","article-title":"Expanded uncertainty quantifcation in inverse problems: hierarchical Bayes and empirical Bayes","volume":"69","author":"Malinverno","year":"2004","journal-title":"Geophysics"},{"issue":"1","key":"2026041607113563400_ref661","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1021\/acs.jcim.0c00876","article-title":"Machine learning classifcation of one-chiral-center organic molecules according to optical rotation","volume":"61","author":"Mamede","year":"2020","journal-title":"Journal of Chemical Information and Modeling"},{"issue":"1","key":"2026041607113563400_ref662","doi-asserted-by":"crossref","first-page":"20381","DOI":"10.1038\/s41598-019-56773-5","article-title":"Molecular geometry prediction using a deep generative graph neural network","volume":"9","author":"Mansimov","year":"2019","journal-title":"Scientifc Reports"},{"issue":"1","key":"2026041607113563400_ref663","doi-asserted-by":"publisher","DOI":"10.1088\/2632-2153\/ab7d30","article-title":"Machine learning for the solution of the Schr\u00f6dinger equation","volume":"1","author":"Manzhos","year":"2020","journal-title":"Machine Learning: Science and Technology"},{"issue":"19","key":"2026041607113563400_ref664","doi-asserted-by":"crossref","first-page":"2315","DOI":"10.1080\/00268976.2017.1333644","article-title":"Thirty years of density functional theory in computational chemistry: an overview and extensive assessment of 200 density functionals","volume":"115","author":"Mardirossian","year":"2017","journal-title":"Molecular Physics"},{"issue":"1","key":"2026041607113563400_ref665","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1038\/s41467-017-02388-1","article-title":"VAMPnets for deep learning of molecular kinetics","volume":"9","author":"Mardt","year":"2018","journal-title":"Nature Communications"},{"issue":"15","key":"2026041607113563400_ref666","doi-asserted-by":"crossref","first-page":"9798","DOI":"10.1039\/C7CP00757D","article-title":"Automatic generation of reaction energy databases from highly accurate atomization energy benchmark sets","volume":"19","author":"Margraf","year":"2017","journal-title":"Physical Chemistry Chemical Physics"},{"key":"2026041607113563400_ref667","article-title":"Deep uncertainty and the search for proteins","author":"Mariet","year":"2020","journal-title":"Workshop: Machine Learning for Molecules."},{"key":"2026041607113563400_ref668","first-page":"10","article-title":"A framework for multiple-instance learning","author":"Maron","year":"1997","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"11","key":"2026041607113563400_ref669","doi-asserted-by":"publisher","first-page":"117701","DOI":"10.1103\/PhysRevLett.120.117701","article-title":"Prediction of a large-gap and switchable Kane-Mele quantum spin hall insulator","volume":"120","author":"Marrazzo","year":"2018","journal-title":"Physical Review Letters"},{"issue":"1188","key":"2026041607113563400_ref670","first-page":"48","article-title":"Antiferromagnetism","volume":"232","author":"Marshall","year":"1955","journal-title":"Proceedings of the Royal Society of London. 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(2016), \u201cExtrapolation and learning equations\u201d, arXiv preprintarXiv:1610.02995."},{"issue":"8","key":"2026041607113563400_ref677","doi-asserted-by":"crossref","first-page":"081601","DOI":"10.1103\/PhysRevLett.131.081601","article-title":"Variational neural-network ansatz for continuum quantum feld theory","volume":"131","author":"Martyn","year":"2023","journal-title":"Physical Review Letters"},{"issue":"4","key":"2026041607113563400_ref678","doi-asserted-by":"crossref","first-page":"1419","DOI":"10.1103\/RevModPhys.84.1419","article-title":"Maximally localized Wannier functions: theory and applications","volume":"84","author":"Marzari","year":"2012","journal-title":"Reviews of Modern Physics"},{"issue":"20","key":"2026041607113563400_ref679","doi-asserted-by":"crossref","first-page":"12847","DOI":"10.1103\/PhysRevB.56.12847","article-title":"Maximally localized generalized Wannier functions for composite energy bands","volume":"56","author":"Marzari","year":"1997","journal-title":"Physical Review B"},{"key":"2026041607113563400_ref680","unstructured":"Masters, D., Dean, J., Klaser, K., Li, Z., Maddrell-Mander, S., Sanders, A., Helal, H., Beker, D., Ramp\u00e1\u0161ek, L. and Beaini, D. (2022), \u201cGPS++: an optimised hybrid MPNN\/transformer for molecular property prediction\u201d, arXiv preprintarXiv:2212.02229."},{"key":"2026041607113563400_ref681","doi-asserted-by":"crossref","DOI":"10.24963\/ijcai.2017\/661","article-title":"Concrete problems for autonomous vehicle safety: advantages of Bayesian deep learning","author":"McAllister","year":"2017"},{"key":"2026041607113563400_ref682","article-title":"Multiple physics pretraining for physical surrogate models","author":"McCabe","year":"2023"},{"issue":"2","key":"2026041607113563400_ref683","first-page":"70","article-title":"Stereochemistry in drug action","volume":"5","author":"McConathy","year":"2003","journal-title":"Primary Care Companion to the Journal of Clinical Psychiatry"},{"issue":"1","key":"2026041607113563400_ref684","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s13321-021-00522-2","article-title":"GNINA 1.0: molecular docking with deep learning","volume":"13","author":"McNutt","year":"2021","journal-title":"Journal of Cheminformatics"},{"issue":"14","key":"2026041607113563400_ref685","doi-asserted-by":"crossref","first-page":"5677","DOI":"10.1021\/jo034344u","article-title":"Racemization barriers of 1,10-Binaphthyl and 1,10-Binaphthalene-2, 20-diol: a DFT study","volume":"68","author":"Meca","year":"2003","journal-title":"The Journal of Organic Chemistry"},{"issue":"4","key":"2026041607113563400_ref686","doi-asserted-by":"crossref","first-page":"040302","DOI":"10.1103\/PRXQuantum.4.040302","article-title":"Variational quantum dynamics of two-dimensional rotor models","volume":"4","author":"Medvidovi\u0107","year":"2023","journal-title":"PRX Quantum"},{"key":"2026041607113563400_ref687","article-title":"Enhanced sampling with machine learning: a review","author":"Mehdi","year":"2023"},{"key":"2026041607113563400_ref688","unstructured":"Melnyk, I., Chenthamarakshan, V., Chen, P.Y., Das, P., Dhurandhar, A., Padhi, I. and Das, D. 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(2023b), \u201cScaling the leading accuracy of deep equivariant models to biomolecular simulations of realistic size\u201d, arXiv preprintarXiv:2304.10061."},{"issue":"5","key":"2026041607113563400_ref716","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1039\/C7SC04665K","article-title":"Machine learning for the structure\u2013energy\u2013property landscapes of molecular crystals","volume":"9","author":"Musil","year":"2018","journal-title":"Chemical Science"},{"key":"2026041607113563400_ref717","first-page":"493","article-title":"Information network or social network? 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(2023), \u201cCapabilities of GPT-4 on medical challenge problems\u201d, arXiv: 2303.13375, available at:www.microsoft.com\/en-us\/research\/publication\/capabilities-of-gpt-4-on-medical-challenge-problems\/"},{"key":"2026041607113563400_ref738","first-page":"36","article-title":"Proteingym: large-scale benchmarks for protein ftness prediction and design","author":"Notin","year":"2024","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026041607113563400_ref739","doi-asserted-by":"publisher","first-page":"74","DOI":"10.1016\/j.mtcomm.2018.11.008","article-title":"Improving accuracy of interatomic potentials: more physics or more data? A case study of silica","volume":"18","author":"Novikov","year":"2019","journal-title":"Materials Today Communications"},{"key":"2026041607113563400_ref740","unstructured":"NVIDIA Corporation\n           (2022), \u201cMegaMolBART v0.2\u201d, available at:https:\/\/catalog.ngc.nvidia.com\/orgs\/nvidia\/teams\/clara\/models\/megamolbart_0_2"},{"key":"2026041607113563400_ref741","doi-asserted-by":"crossref","unstructured":"Nys, J., Pescia, G. and Carleo, G. (2024), \u201cAb-initio variational wave functions for the time-dependent many-electron Schr\u00f6dinger equation\u201d, arXiv preprintarXiv:2403.07447.","DOI":"10.1038\/s41467-024-53672-w"},{"key":"2026041607113563400_ref742","unstructured":"Okabe, R., Chotrattanapituk, A., Boonkird, A., Andrejevic, N., Fu, X., Jaakkola, T.S., Song, Q., Nguyen, T., Drucker, N., Mu, S., Liao, B., Cheng, Y. and Li, M. (2023), \u201cVirtual node graph neural network for full phonon prediction\u201d, arXiv preprintarXiv:2301.02197."},{"key":"2026041607113563400_ref743","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-02099-0","volume-title":"Introduction to Partial Differential Equations","author":"Olver","year":"2014"},{"key":"2026041607113563400_ref744","article-title":"GPT-4 technical report","author":"OpenAI","year":"2023"},{"issue":"8","key":"2026041607113563400_ref745","doi-asserted-by":"crossref","first-page":"1093","DOI":"10.1016\/S0969-2126(97)00260-8","article-title":"CATH\u2013a hierarchic classifcation of protein domain structures","volume":"5","author":"Orengo","year":"1997","journal-title":"Structure"},{"issue":"8","key":"2026041607113563400_ref746","doi-asserted-by":"crossref","first-page":"083802","DOI":"10.1103\/PhysRevMaterials.2.083802","article-title":"SISSO: a compressed-sensing method for identifying the best low-dimensional descriptor in an immensity of offered candidates","volume":"2","author":"Ouyang","year":"2018","journal-title":"Physical Review Materials"},{"key":"2026041607113563400_ref747","doi-asserted-by":"crossref","unstructured":"Owen, C.J., Torrisi, S.B., Xie, Y., Batzner, S., Coulter, J., Musaelian, A., Sun, L. and Kozinsky, B. 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(2023), \u201cReducing SO (3) convolutions to SO (2) for efficient equivariant GNNs\u201d, arXiv preprintarXiv:2302.03655."},{"issue":"3","key":"2026041607113563400_ref758","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1109\/MSP.2014.2347059","article-title":"Visual domain adaptation: a survey of recent advances","volume":"32","author":"Patel","year":"2015","journal-title":"IEEE Signal Processing Magazine"},{"key":"2026041607113563400_ref759","unstructured":"Pathak, J., Subramanian, S., Harrington, P., Raja, S., Chattopadhyay, A., Mardani, M., Kurth, T., Hall, D., Li, Z., Azizzadenesheli, K., et al. (2022), \u201cFourcastnet: a global data-driven high-resolution weather model using adaptive fourier neural operators\u201d, arXiv preprintarXiv:2202.11214."},{"key":"2026041607113563400_ref760","unstructured":"Pattanaik, L., Ganea, O.E., Coley, I., Jensen, K.F., Green, W.H. and Coley, C.W. 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(2023), \u201cMessage-passing neural quantum states for the homogeneous electron gas\u201d, arXiv preprintarXiv:2305.07240.","DOI":"10.1103\/PhysRevB.110.035108"},{"key":"2026041607113563400_ref778","doi-asserted-by":"crossref","first-page":"947","DOI":"10.1111\/rssb.12167","article-title":"Causal inference by using invariant prediction: identifcation and confdence intervals","author":"Peters","year":"2016","journal-title":"Journal of the Royal Statistical Society. 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(2023), \u201cGenCast: diffusion-based ensemble forecasting for medium-range weather\u201d, arXiv preprintarXiv:2312.15796."},{"issue":"13","key":"2026041607113563400_ref799","doi-asserted-by":"crossref","first-page":"6490","DOI":"10.1016\/j.jcp.2008.03.013","article-title":"Adjoint-based optimization of PDE systems with alternative gradients","volume":"227","author":"Protas","year":"2008","journal-title":"Journal of Computational Physics"},{"key":"2026041607113563400_ref800","doi-asserted-by":"crossref","first-page":"111902","DOI":"10.1016\/j.jcp.2022.111902","article-title":"Uncertainty quantifcation in scientifc machine learning: methods, metrics, and comparisons","author":"Psaros","year":"2023","journal-title":"Journal of Computational Physics"},{"key":"2026041607113563400_ref801","doi-asserted-by":"crossref","first-page":"111897","DOI":"10.1016\/j.commatsci.2022.111897","article-title":"CASM \u2013 a software package for frst-principles based study of multicomponent crystalline 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(2022a), \u201cGenerative adversarial neural operators\u201d, arXiv preprintarXiv:2205.03017."},{"key":"2026041607113563400_ref818","unstructured":"Rahman, M.A., Ross, Z.E. and Azizzadenesheli, K. (2022b), \u201cUno: U-shaped neural operators\u201d, arXiv preprintarXiv:2204.11127."},{"key":"2026041607113563400_ref819","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1016\/j.jcp.2018.10.045","article-title":"Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations","volume":"378","author":"Raissi","year":"2019","journal-title":"Journal of Computational Physics"},{"issue":"6481","key":"2026041607113563400_ref820","doi-asserted-by":"crossref","first-page":"1026","DOI":"10.1126\/science.aaw4741","article-title":"Hidden fuid mechanics: learning velocity and pressure felds from fow visualizations","volume":"367","author":"Raissi","year":"2020","journal-title":"Science"},{"issue":"5","key":"2026041607113563400_ref821","doi-asserted-by":"publisher","first-page":"2087","DOI":"10.1021\/acs.jctc.5b00099","article-title":"Big data meets quantum chemistry approximations: the \u0394-machine learning approach","volume":"11","author":"Ramakrishnan","year":"2015","journal-title":"Journal of Chemical Theory and Computation"},{"issue":"1","key":"2026041607113563400_ref822","doi-asserted-by":"crossref","first-page":"140022","DOI":"10.1038\/sdata.2014.22","article-title":"Quantum chemistry structures and properties of 134 kilo molecules","volume":"1","author":"Ramakrishnan","year":"2014","journal-title":"Scientifc Data"},{"key":"2026041607113563400_ref823","first-page":"8821","article-title":"Zero-shot text-to-image generation","author":"Ramesh","year":"2021"},{"key":"2026041607113563400_ref824","unstructured":"Ramos, M.C., Michtavy, S.S., Porosoff, M.D. and White, A.D. (2023), \u201cBayesian optimization of catalysts with in-context learning\u201d, arXiv preprint arXiv: 2304.05341."},{"key":"2026041607113563400_ref825","first-page":"36","article-title":"Convolutional neural operators for robust and accurate learning of PDEs","author":"Raonic","year":"2024","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026041607113563400_ref826","volume-title":"Gaussian Processes for Machine Learning","author":"Rasmussen","year":"2006"},{"key":"2026041607113563400_ref827","doi-asserted-by":"publisher","first-page":"104954","DOI":"10.1016\/j.envsoft.2020.104954","article-title":"The future of sensitivity analysis: an essential discipline for systems modeling and policy support","volume":"137","author":"Razavi","year":"2021","journal-title":"Environmental Modelling & Software"},{"key":"2026041607113563400_ref828","unstructured":"Reddy, R.G., Dasigi, P., Sultan, M.A., Cohan, A., Sil, A., Ji, H. and Hajishirzi, H. (2023), \u201cInference-time re-ranker relevance feedback for neural information retrieval\u201d, arXiv preprintarXiv:2305.11744."},{"issue":"1","key":"2026041607113563400_ref829","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1038\/s43246-022-00315-6","article-title":"Graph neural networks for materials science and chemistry","volume":"3","author":"Reiser","year":"2022","journal-title":"Communications Materials"},{"issue":"1","key":"2026041607113563400_ref830","doi-asserted-by":"publisher","first-page":"1860","DOI":"10.1038\/s41467-023-37609-3","article-title":"Towards the ground state of molecules via diffusion Monte Carlo on neural networks","volume":"14","author":"Ren","year":"2023","journal-title":"Nature Communications"},{"issue":"1","key":"2026041607113563400_ref831","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1016\/j.matt.2021.11.032","article-title":"An invertible crystallographic representation for general inverse design of inorganic crystals with targeted properties","volume":"5","author":"Ren","year":"2022","journal-title":"Matter"},{"issue":"1","key":"2026041607113563400_ref832","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1038\/s42005-024-01732-4","article-title":"A simple linear algebra identity to optimize large-scale neural network quantum states","volume":"7","author":"Rende","year":"2024","journal-title":"Communications Physics"},{"key":"2026041607113563400_ref833","first-page":"1530","article-title":"Variational inference with nor-malizing fows","author":"Rezende","year":"2015"},{"issue":"32","key":"2026041607113563400_ref834","doi-asserted-by":"crossref","first-page":"e2122059119","DOI":"10.1073\/pnas.2122059119","article-title":"Fermionic wave functions from neural-network constrained hidden states","volume":"119","author":"Robledo Moreno","year":"2022","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"3","key":"2026041607113563400_ref835","doi-asserted-by":"crossref","first-page":"337","DOI":"10.13182\/NSE13-32","article-title":"Efficient use of Monte Carlo: uncertainty propagation","volume":"177","author":"Rochman","year":"2014","journal-title":"Nuclear Science and Engineering"},{"issue":"2","key":"2026041607113563400_ref836","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3485128","article-title":"Tackling climate change with machine learning","volume":"55","author":"Rolnick","year":"2022","journal-title":"ACM Computing Surveys (CSUR)"},{"key":"2026041607113563400_ref837","first-page":"10684","article-title":"High-resolution image synthesis with latent diffusion models","author":"Rombach","year":"2022"},{"key":"2026041607113563400_ref838","article-title":"Learning partial equivariances from data","author":"Romero","year":"2022","journal-title":"Advances in Neural Information Processing Systems."},{"key":"2026041607113563400_ref839","article-title":"Self-supervised graph transformer on large-scale molecular data","author":"Rong","year":"2020","journal-title":"Advances in Neural Information Processing Systems."},{"key":"2026041607113563400_ref840","first-page":"234","article-title":"U-net: convolutional networks for biomedical image segmentation","author":"Ronneberger","year":"2015"},{"key":"2026041607113563400_ref841","doi-asserted-by":"crossref","DOI":"10.1101\/2023.02.03.526939","article-title":"Towards universal cell embeddings: integrating single-cell RNA-seq datasets across species with SATURN","author":"Rosen","year":"2023"},{"key":"2026041607113563400_ref842","unstructured":"Rosenfeld, E., Ravikumar, P. and Risteski, A. (2020), \u201cThe risks of invariant risk minimization\u201d, arXiv preprintarXiv:2010.05761."},{"key":"2026041607113563400_ref843","unstructured":"Roth, C. and MacDonald, A.H. (2021), \u201cGroup convolutional neu-ral networks improve quantum state accuracy\u201d, arXiv preprintarXiv:2104.05085."},{"issue":"11","key":"2026041607113563400_ref844","doi-asserted-by":"crossref","first-page":"2864","DOI":"10.1021\/ci300415d","article-title":"Enumeration of 166 billion organic small molecules in the chemical universe database GDB-17","volume":"52","author":"Ruddigkeit","year":"2012","journal-title":"Journal of Chemical Information and Modeling"},{"issue":"4","key":"2026041607113563400_ref845","doi-asserted-by":"crossref","first-page":"e1602614","DOI":"10.1126\/sciadv.1602614","article-title":"Data-driven discovery of partial differential equations","volume":"3","author":"Rudy","year":"2017","journal-title":"Science Advances"},{"key":"2026041607113563400_ref846","doi-asserted-by":"crossref","unstructured":"Ruhe, D., Brandstetter, J. and Forr\u00e9, P. (2023a), \u201cClifford group equiv-ariant neural networks\u201d, arXiv preprintarXiv:2305.11141.","DOI":"10.52202\/075280-2748"},{"key":"2026041607113563400_ref847","article-title":"Geometric clifford algebra networks","author":"Ruhe","year":"2023"},{"issue":"1","key":"2026041607113563400_ref848","doi-asserted-by":"publisher","first-page":"8000","DOI":"10.1038\/s41598-020-64619-8","article-title":"Neural network in-terpolation of exchange-correlation functional","volume":"10","author":"Ryabov","year":"2020","journal-title":"Scientifc Reports"},{"issue":"12","key":"2026041607113563400_ref849","doi-asserted-by":"publisher","first-page":"7695","DOI":"10.1021\/acs.jctc.2c00483","article-title":"Machine learning diffusion Monte Carlo energies","volume":"18","author":"Ryczko","year":"2022","journal-title":"Journal of Chemical Theory and Computation"},{"issue":"2","key":"2026041607113563400_ref850","doi-asserted-by":"crossref","first-page":"1122","DOI":"10.1021\/acs.jctc.1c00812","article-title":"Toward orbital-free density functional theory with small data sets and deep learning","volume":"18","author":"Ryczko","year":"2022","journal-title":"Journal of Chemical Theory and Computation"},{"issue":"36","key":"2026041607113563400_ref851","doi-asserted-by":"crossref","first-page":"8438","DOI":"10.1039\/C9SC01992H","article-title":"A Bayesian graph convolutional network for reliable prediction of molecular properties with uncertainty quantifcation","volume":"10","author":"Ryu","year":"2019","journal-title":"Chemical Science"},{"key":"2026041607113563400_ref852","unstructured":"Sagawa, S., Koh, P.W., Lee, T., Gao, I., Xie, S.M., Shen, K., Kumar, A., Hu, W., Yasunaga, M., Marklund, H., et al. (2021), \u201cExtending the wilds benchmark for unsupervised adaptation\u201d, arXiv preprintarXiv:2112.05090."},{"key":"2026041607113563400_ref853","first-page":"76","article-title":"Optimal design of nose and tail of an autonomous underwater vehicle hull to reduce drag force using numerical simulation","author":"Saghafi","year":"2020"},{"key":"2026041607113563400_ref854","first-page":"4442","article-title":"Learning equations for extrapolation and control","author":"Sahoo","year":"2018"},{"issue":"9","key":"2026041607113563400_ref855","doi-asserted-by":"crossref","first-page":"093001","DOI":"10.7566\/JPSJ.86.093001","article-title":"Solving the bose\u2013hubbard model with machine learning","author":"Saito","year":"2017","journal-title":"Journal of the Physical Society of Japan"},{"issue":"7","key":"2026041607113563400_ref856","doi-asserted-by":"crossref","first-page":"074002","DOI":"10.7566\/JPSJ.87.074002","article-title":"Method to solve quantum few-body problems with artifcial neural networks","volume":"87","author":"Saito","year":"2018","journal-title":"Journal of the Physical Society of Japan"},{"issue":"1","key":"2026041607113563400_ref857","doi-asserted-by":"crossref","first-page":"014001","DOI":"10.7566\/JPSJ.87.014001","article-title":"Machine learning technique to fnd quantum many-body ground states of Bosons on a Lattice","volume":"87","author":"Saito","year":"2018","journal-title":"Journal of the Physical Society of Japan"},{"key":"2026041607113563400_ref858","doi-asserted-by":"crossref","DOI":"10.1017\/9781108587280","volume-title":"Modern Quantum Mechanics","author":"Sakurai","year":"2020"},{"key":"2026041607113563400_ref859","unstructured":"Sanchez-Gonzalez, A., Bapst, V., Cranmer, K. and Battaglia, P. (2019), \u201cHamiltonian graph networks with ode integrators\u201d, arXiv preprintarXiv:1909.12790."},{"key":"2026041607113563400_ref860","first-page":"8459","article-title":"Learning to simulate complex physics with graph networks","author":"Sanchez-Gonzalez","year":"2020"},{"key":"2026041607113563400_ref861","article-title":"E(n) equivariant normalizing fows","author":"Satorras","year":"2021","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026041607113563400_ref862","first-page":"9323","article-title":"E (n) equiv-ariant graph neural networks","author":"Satorras","year":"2021"},{"issue":"6","key":"2026041607113563400_ref863","doi-asserted-by":"crossref","first-page":"2697","DOI":"10.1021\/acs.jcim.9b00975","article-title":"Evaluating scalable uncertainty estimation methods for deep learning-based molecular property prediction","volume":"60","author":"Scalia","year":"2020","journal-title":"Journal of Chemical Information and Modeling"},{"issue":"2197","key":"2026041607113563400_ref864","doi-asserted-by":"crossref","first-page":"20160446","DOI":"10.1098\/rspa.2016.0446","article-title":"Learning partial differential equations via data discovery and sparse optimization","volume":"473","author":"Schaeffer","year":"2017","journal-title":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences"},{"key":"2026041607113563400_ref865","unstructured":"Scherbela, M., Gerard, L. and Grohs, P. (2023), \u201cTowards a foun-dation model for neural network wavefunctions\u201d, arXiv preprintarXiv:2303.09949."},{"issue":"5","key":"2026041607113563400_ref866","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1038\/s43588-022-00228-x","article-title":"Solving the electronic Schr\u00f6dinger equation for multiple nuclear geometries with weight-sharing deep neural networks","volume":"2","author":"Scherbela","year":"2022","journal-title":"Nature Computational Science"},{"key":"2026041607113563400_ref867","article-title":"Toolformer: language models can teach themselves to use tools","author":"Schick","year":"2023"},{"key":"2026041607113563400_ref868","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-6351-2","volume-title":"Molecular Modeling and Simulation: An Interdisciplinary Guide","author":"Schlick","year":"2010"},{"issue":"10","key":"2026041607113563400_ref869","doi-asserted-by":"crossref","first-page":"100503","DOI":"10.1103\/PhysRevLett.125.100503","article-title":"Quantum many-body dynamics in two dimensions with artifcial neural networks","volume":"125","author":"Schmitt","year":"2020","journal-title":"Physical Review Letters"},{"issue":"11","key":"2026041607113563400_ref870","doi-asserted-by":"crossref","first-page":"7581","DOI":"10.1109\/TPAMI.2021.3115452","article-title":"Higher-order explanations of graph neural networks via relevant walks","volume":"44","author":"Schnake","year":"2021","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"2026041607113563400_ref871","unstructured":"Schneuing, A., Du, Y., Harris, C., Jamasb, A., Igashov, I., Du, W., Blundell, T., Li\u00f3, P., Gomes, C., Welling, M., et al. (2022), \u201cStructure-based drug design with equivariant diffusion models\u201d, arXiv preprintarXiv:2210.13695."},{"key":"2026041607113563400_ref872","first-page":"33","article-title":"Jax md: a framework for differentiable physics","author":"Schoenholz","year":"2020","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"1","key":"2026041607113563400_ref873","doi-asserted-by":"crossref","first-page":"13890","DOI":"10.1038\/ncomms13890","article-title":"Quantum-chemical insights from deep tensor neural networks","volume":"8","author":"Sch\u00fctt","year":"2017","journal-title":"Nature Communications"},{"issue":"1","key":"2026041607113563400_ref874","doi-asserted-by":"crossref","first-page":"5024","DOI":"10.1038\/s41467-019-12875-2","article-title":"Unifying machine learning and quantum chemistry with a deep neural network for molecular wavefunctions","volume":"10","author":"Sch\u00fctt","year":"2019","journal-title":"Nature Communications"},{"issue":"24","key":"2026041607113563400_ref875","doi-asserted-by":"crossref","first-page":"241722","DOI":"10.1063\/1.5019779","article-title":"SchNet\u2013a deep learning architecture for molecules and materials","volume":"148","author":"Sch\u00fctt","year":"2018","journal-title":"The Journal of Chemical Physics"},{"key":"2026041607113563400_ref876","first-page":"9377","article-title":"Equivariant message passing for the prediction of tensorial properties and molecular spectra","author":"Sch\u00fctt","year":"2021"},{"issue":"2","key":"2026041607113563400_ref877","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1038\/s42256-020-00284-w","article-title":"Mapping the space of chemical reactions using attention-based neural networks","volume":"3","author":"Schwaller","year":"2021","journal-title":"Nature Machine Intelligence"},{"key":"2026041607113563400_ref878","unstructured":"Seidl, P., Vall, A., Hochreiter, S. and Klambauer, G. (2023), \u201cEnhancing activity prediction models in drug discovery with the ability to understand human language\u201d, arXiv preprintarXiv:2303.03363."},{"key":"2026041607113563400_ref879","first-page":"5601","article-title":"NO-MAD: nonlinear manifold decoders for operator learning","volume":"35","author":"Seidman","year":"2022","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"24","key":"2026041607113563400_ref880","doi-asserted-by":"crossref","first-page":"241705","DOI":"10.1063\/1.5007230","article-title":"Semi-local machine-learned kinetic energy density functional with third-order gradients of electron density","volume":"148","author":"Seino","year":"2018","journal-title":"The Journal of Chemical Physics"},{"issue":"7792","key":"2026041607113563400_ref881","doi-asserted-by":"crossref","first-page":"706","DOI":"10.1038\/s41586-019-1923-7","article-title":"Improved protein structure prediction using potentials from deep learning","volume":"577","author":"Senior","year":"2020","journal-title":"Nature"},{"key":"2026041607113563400_ref882","first-page":"31","article-title":"Evidential deep learning to quantify classifcation uncertainty","author":"Sensoy","year":"2018","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"11","key":"2026041607113563400_ref883","doi-asserted-by":"crossref","first-page":"962","DOI":"10.1038\/s42256-021-00408-w","article-title":"Out-of-distribution generalization from labelled and unlabelled gene expression data for drug response prediction","volume":"3","author":"Sharifi-Noghabi","year":"2021","journal-title":"Nature Machine Intelligence"},{"issue":"2","key":"2026041607113563400_ref884","doi-asserted-by":"crossref","first-page":"020503","DOI":"10.1103\/PhysRevLett.124.020503","article-title":"Deep autoregressive models for the efficient variational simulation of many-body quantum systems","volume":"124","author":"Sharir","year":"2020","journal-title":"Physical Review Letters"},{"issue":"7075","key":"2026041607113563400_ref885","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1038\/nature04421","article-title":"Atomic packing and short-to-medium-range order in metallic glasses","volume":"439","author":"Sheng","year":"2006","journal-title":"Nature"},{"issue":"6","key":"2026041607113563400_ref886","doi-asserted-by":"crossref","first-page":"1912","DOI":"10.1021\/ci049782w","article-title":"Similarity to molecules in the training set is a good discriminator for prediction accuracy in QSAR","volume":"44","author":"Sheridan","year":"2004","journal-title":"Journal of Chemical Information and Computer Sciences"},{"key":"2026041607113563400_ref887","article-title":"Learning gradient felds for molecular conformation generation","author":"Shi","year":"2021"},{"key":"2026041607113563400_ref888","article-title":"GraphAF: a flow-based autoregressive model for molecular graph generation","author":"Shi","year":"2020"},{"key":"2026041607113563400_ref889","unstructured":"Shi, J., Sun, S. and Zhu, J. (2017), \u201cKernel implicit variational inference\u201d, arXiv preprintarXiv:1705.10119."},{"issue":"2","key":"2026041607113563400_ref890","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/S0378-3758(00)00115-4","article-title":"Improving predictive inference under covariate shift by weighting the log-likelihood function","volume":"90","author":"Shimodaira","year":"2000","journal-title":"Journal of Statistical Planning and Inference"},{"key":"2026041607113563400_ref891","doi-asserted-by":"crossref","DOI":"10.1002\/9780470447710","volume-title":"Density Functional Theory: A Practical Introduction","author":"Sholl","year":"2009"},{"key":"2026041607113563400_ref892","unstructured":"Shuaibi, M., Kolluru, A., Das, A., Grover, A., Sriram, A., Ulissi, Z. and Zitnick, C.L. (2021), \u201cRotation invariant graph neural networks using spin convolutions\u201d, arXiv preprintarXiv:2106.09575."},{"issue":"5","key":"2026041607113563400_ref893","doi-asserted-by":"crossref","first-page":"e1737742","DOI":"10.1080\/00268976.2020.1737742","article-title":"Machine learning for collective variable discovery and enhanced sampling in biomolecular simulation","volume":"118","author":"Sidky","year":"2020","journal-title":"Molecular Physics"},{"issue":"35","key":"2026041607113563400_ref894","doi-asserted-by":"crossref","first-page":"9459","DOI":"10.1039\/D0SC03635H","article-title":"Molecular latent space simulators","volume":"11","author":"Sidky","year":"2020","journal-title":"Chemical Science"},{"key":"2026041607113563400_ref895","article-title":"MISATO-machine learning dataset for structure-based drug discovery","author":"Siebenmorgen","year":"2023"},{"key":"2026041607113563400_ref896","unstructured":"Simm, G.N.C. and Hern\u00e1ndez-Lobato, J.M. (2019), \u201cA generative model for molecular distance geometry\u201d, arXiv preprintarXiv:1909.11459."},{"issue":"12","key":"2026041607113563400_ref897","doi-asserted-by":"crossref","first-page":"657","DOI":"10.1038\/s41570-020-00228-3","article-title":"Designing disorder into crys-talline materials","volume":"4","author":"Simonov","year":"2020","journal-title":"Nature Reviews Chemistry"},{"issue":"3","key":"2026041607113563400_ref898","doi-asserted-by":"crossref","first-page":"1146","DOI":"10.1107\/S1600576714008668","article-title":"Yell: a computer program for diffuse scattering analysis via three-dimensional delta pair distribution function refnement","volume":"47","author":"Simonov","year":"2014","journal-title":"Journal of Applied Crystallography"},{"key":"2026041607113563400_ref899","unstructured":"Singhal, K., Tu, T., Gottweis, J., Sayres, R., Wulczyn, E., Hou, L., Clark, K., Pfohl, S.R., Cole-Lewis, H.J., Neal, D., Schaekermann, M., Wang, A., Amin, M., Lachgar, S., Mansfeld, P.A., Prakash, S., Green, B., Dominowska, E., y Arcas, B.A., Tomasev, N., Liu, Y., Wong, R.C., Semturs, C., Mahdavi, S.S., Barral, J.K., Webster, D.R., Corrado, G.S., Matias, Y., Azizi, S., Karthikesalingam, A. and Natarajan, V. (2023), \u201cTowards expert-level medical question answering with large language models\u201d, arXiv preprint arXiv:2305.09617."},{"issue":"12","key":"2026041607113563400_ref900","doi-asserted-by":"crossref","first-page":"6007","DOI":"10.1021\/acs.jcim.0c00884","article-title":"Critical assessment of artifcial intelligence methods for prediction of hERG channel inhibition in the \u2018Big Data\u2019 era","volume":"60","author":"Siramshetty","year":"2020","journal-title":"Journal of Chemical Information and Modeling"},{"issue":"2","key":"2026041607113563400_ref901","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1007\/s00245-022-09852-5","article-title":"Online adjoint methods for optimization of PDEs","volume":"85","author":"Sirignano","year":"2022","journal-title":"Applied Mathematics & Optimization"},{"issue":"2","key":"2026041607113563400_ref902","doi-asserted-by":"publisher","first-page":"732","DOI":"10.1063\/1.349629","article-title":"A novel experimental procedure for removing ambiguity from the interpretation of neutron and x-ray refectivity measurements: \u2018speckle holography","volume":"70","author":"Sivia","year":"1991","journal-title":"Journal of Applied Physics"},{"issue":"10","key":"2026041607113563400_ref903","doi-asserted-by":"crossref","first-page":"4282","DOI":"10.1021\/acs.molpharmaceut.9b00634","article-title":"From target to drug: generative modeling for the multimodal structure-based ligand design","volume":"16","author":"Skalic","year":"2019","journal-title":"Molecular Pharmaceutics"},{"issue":"1","key":"2026041607113563400_ref904","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1103\/PhysRev.36.57","article-title":"Atomic shielding constants","volume":"36","author":"Slater","year":"1930","journal-title":"Physical Review"},{"issue":"10","key":"2026041607113563400_ref905","doi-asserted-by":"crossref","first-page":"1293","DOI":"10.1103\/PhysRev.34.1293","article-title":"The theory of complex 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(2022), \u201cDissipative Hamiltonian neural networks: learning dissipative and conservative dynamics separately\u201d, arXiv preprintarXiv:2201.10085."},{"issue":"3","key":"2026041607113563400_ref923","doi-asserted-by":"publisher","DOI":"10.3390\/galaxies11030063","article-title":"Language models for multimes-senger astronomy","volume":"11","author":"Sotnikov","year":"2023","journal-title":"Galaxies"},{"issue":"3","key":"2026041607113563400_ref924","doi-asserted-by":"crossref","first-page":"035109","DOI":"10.1103\/PhysRevB.65.035109","article-title":"Maximally localized Wannier functions for entangled energy bands","volume":"65","author":"Souza","year":"2001","journal-title":"Physical Review B"},{"issue":"30","key":"2026041607113563400_ref925","doi-asserted-by":"crossref","first-page":"6896","DOI":"10.1021\/acs.jpclett.2c00643","article-title":"Uniting nonempirical and empirical density functional approximation strategies using constraint-based regularization","volume":"13","author":"Sparrow","year":"2022","journal-title":"The Journal of Physical Chemistry Letters"},{"key":"2026041607113563400_ref926","article-title":"Better, faster fermionic neural networks","author":"Spencer","year":"2020"},{"issue":"1","key":"2026041607113563400_ref927","first-page":"1929","article-title":"Dropout: a simple way to prevent neural networks from overftting","volume":"15","author":"Srivastava","year":"2014","journal-title":"The Journal of Machine Learning Research"},{"key":"2026041607113563400_ref928","article-title":"Learned coarse models for efficient turbulence simulation","author":"Stachenfeld","year":"2021"},{"key":"2026041607113563400_ref929","first-page":"18033","article-title":"Graph posterior network: bayesian predictive uncertainty for node classifcation","volume":"34","author":"Stadler","year":"2021","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026041607113563400_ref930","first-page":"20479","article-title":"3D infomax improves gnns for molecular property prediction","author":"St\u00e4rk","year":"2022"},{"key":"2026041607113563400_ref931","first-page":"20503","article-title":"EquiBind: geometric deep learning for drug binding structure prediction","author":"St\u00e4rk","year":"2022"},{"issue":"2","key":"2026041607113563400_ref932","doi-asserted-by":"publisher","first-page":"978","DOI":"10.1103\/PhysRevA.25.978","article-title":"Hidden structure in liquids","volume":"25","author":"Stillinger","year":"1982","journal-title":"Physical Review A"},{"issue":"4","key":"2026041607113563400_ref933","first-page":"045010","article-title":"How robust are modern graph neural network potentials in long and hot molecular dynamics simulations?","volume":"3","author":"Stocker","year":"2022","journal-title":"Machine Learning: Science and Technology"},{"key":"2026041607113563400_ref934","doi-asserted-by":"crossref","DOI":"10.1007\/b95211","volume-title":"Symmetry breaking","author":"Strocchi","year":"2005"},{"key":"2026041607113563400_ref935","unstructured":"Su, B., Du, D., Yang, Z., Zhou, Y., Li, J., Rao, A., Sun, H., Lu, Z. and Wen, J.R. (2022), \u201cA molecular multimodal foundation model as-sociating molecule graphs with natural language\u201d, arXiv preprintarXiv:2209.05481."},{"key":"2026041607113563400_ref936","first-page":"36","article-title":"Towards foundation models for scientifc machine learning: characterizing scaling and transfer behavior","author":"Subramanian","year":"2024","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"4","key":"2026041607113563400_ref937","doi-asserted-by":"crossref","first-page":"854","DOI":"10.1107\/S1600576719008665","article-title":"BraggNet: integrating Bragg peaks using neural networks","volume":"52","author":"Sullivan","year":"2019","journal-title":"Journal of Applied Crystallography"},{"key":"2026041607113563400_ref938","first-page":"443","article-title":"Deep coral: correlation alignment for deep domain adaptation","author":"Sun","year":"2016"},{"issue":"1","key":"2026041607113563400_ref939","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1038\/s41524-020-0328-3","article-title":"Enabling materials informatics for 29Si solid-state NMR of crystalline materials","volume":"6","author":"Sun","year":"2020","journal-title":"npj Computational Materials"},{"key":"2026041607113563400_ref940","unstructured":"Sun, H., Ross, Z.E., Zhu, W. and Azizzadenesheli, K. 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(2022), \u201cGalactica: a large language model for science\u201d, arXiv preprintarXiv:2211.09085."},{"key":"2026041607113563400_ref965","article-title":"Equivariant transformers for neural network based molecular potentials","volume-title":"International Conference on Learning Representations.","author":"Th\u00f6lke","year":"2022"},{"key":"2026041607113563400_ref966","unstructured":"Thomas, N., Smidt, T., Kearnes, S., Yang, L., Li, L., Kohlhoff, K. and Riley, P. (2018), \u201cTensor feld networks: rotation-and translation-equivariant neural networks for 3D point clouds\u201d, arXiv preprintarXiv:1802.08219."},{"key":"2026041607113563400_ref967","first-page":"567","volume-title":"Artifcial Intelligence and Statistics","author":"Titsias","year":"2009"},{"key":"2026041607113563400_ref968","first-page":"128","article-title":"Bayesian methods for neural networks and related models","author":"Titterington","year":"2004","journal-title":"Statistical Science"},{"key":"2026041607113563400_ref969","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.scriptamat.2015.07.021","article-title":"First principles phonon calculations in materials science","volume":"108","author":"Togo","year":"2015","journal-title":"Scripta Materialia"},{"key":"2026041607113563400_ref970","first-page":"3424","article-title":"Accelerating eulerian fuid simulation with convolutional networks","author":"Tompson","year":"2017"},{"key":"2026041607113563400_ref971","doi-asserted-by":"crossref","first-page":"242","DOI":"10.4018\/978-1-60566-766-9.ch011","volume-title":"Handbook of Research on Machine Learning Applications and Trends: Algorithms, Methods, and Techniques","author":"Torrey","year":"2010"},{"key":"2026041607113563400_ref972","doi-asserted-by":"crossref","DOI":"10.1101\/2022.04.20.488898","article-title":"Improving the assessment of deep learning models in the context of drug-target interaction prediction","author":"Torrisi","year":"2022"},{"key":"2026041607113563400_ref973","unstructured":"Toshev, A.P., Erbesdobler, J.A., Adams, N.A. and Brandstetter, J. 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(2020), \u201cAtom3d: tasks on molecules in three dimensions\u201d, arXiv preprintarXiv:2012.04035."},{"issue":"20","key":"2026041607113563400_ref977","doi-asserted-by":"publisher","first-page":"9200","DOI":"10.1063\/1.472753","article-title":"Exchange\u2019 correlation potentials","volume":"105","author":"Tozer","year":"1996","journal-title":"The Journal of Chemical Physics"},{"key":"2026041607113563400_ref978","unstructured":"Tran, A., Mathews, A., Xie, L. and Ong, C.S. (2021), \u201cFactorized fourier neural operators\u201d, arXiv preprintarXiv:2111.13802."},{"issue":"2","key":"2026041607113563400_ref979","first-page":"025006","article-title":"Methods for comparing uncertainty quantifcations for material property predictions","volume":"1","author":"Tran","year":"2020","journal-title":"Machine Learning: Science and Technology"},{"issue":"5","key":"2026041607113563400_ref980","doi-asserted-by":"crossref","first-page":"3066","DOI":"10.1021\/acscatal.2c05426","article-title":"The open catalyst 2022 (OC22) dataset and challenges for oxide electrocatalysts","volume":"13","author":"Tran","year":"2023","journal-title":"ACS Catalysis"},{"issue":"16","key":"2026041607113563400_ref981","doi-asserted-by":"crossref","first-page":"1104","DOI":"10.1002\/jcc.26872","article-title":"Data-driven and constrained optimization of semi-local exchange and nonlocal correlation functionals for materials and surface chemistry","volume":"43","author":"Trepte","year":"2022","journal-title":"Journal of Computational Chemistry"},{"key":"2026041607113563400_ref982","unstructured":"Trippe, B.L., Yim, J., Tischer, D., Broderick, T., Baker, D., Barzilay, R. and Jaakkola, T. (2022), \u201cDiffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem\u201d, arXiv preprintarXiv:2206.04119."},{"issue":"2","key":"2026041607113563400_ref983","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1002\/jcc.21334","article-title":"AutoDock Vina: improving the speed and accuracy of docking with a new scoring function, efficient opti-mization, and multithreading","volume":"31","author":"Trott","year":"2010","journal-title":"Journal of Computational Chemistry"},{"issue":"17","key":"2026041607113563400_ref984","doi-asserted-by":"crossref","first-page":"170201","DOI":"10.1103\/PhysRevLett.94.170201","article-title":"Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations","volume":"94","author":"Troyer","year":"2005","journal-title":"Physical Review Letters"},{"key":"2026041607113563400_ref985","first-page":"7472","article-title":"Learning to adapt structured output space for semantic 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and partial charges","volume":"15","author":"Unke","year":"2019","journal-title":"Journal of Chemical Theory and Computation"},{"key":"2026041607113563400_ref994","first-page":"14434","article-title":"SE(3)-equivariant prediction of molecular wave-functions and electronic densities","volume":"34","author":"Unke","year":"2021","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"4","key":"2026041607113563400_ref995","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1016\/S0364-5916(02)80006-2","article-title":"The alloy theoretic automated toolkit: a user guide","volume":"26","author":"van de Walle","year":"2002","journal-title":"Calphad"},{"key":"2026041607113563400_ref996","article-title":"Relaxing equivariance constraints with non-stationary continuous flters","author":"Van der Ouderaa","year":"2022","journal-title":"Advances in Neural Information Processing 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(2019b), \u201cPaperrobot: incremental draft generation of scientifc ideas\u201d, arXiv preprintarXiv:1905.07870.","DOI":"10.18653\/v1\/P19-1191"},{"key":"2026041607113563400_B1029","unstructured":"Wang, Q., Zhou, Z., Huang, L., Whitehead, S., Zhang, B., Ji, H. and Knight, K. (2018), \u201cPaper abstract writing through editing mechanism\u201d, arXiv preprintarXiv:1805.06064."},{"key":"2026041607113563400_B1030","doi-asserted-by":"crossref","unstructured":"Wang, Q., Li, M., Wang, X., Parulian, N., Han, G., Ma, J., Tu, J., Lin, Y., Zhang, H., Liu, W., et al. (2020a), \u201cCOVID-19 literature knowledge graph construction and drug repurposing report generation\u201d, arXiv preprintarXiv:2007.00576.","DOI":"10.18653\/v1\/2021.naacl-demos.8"},{"issue":"12","key":"2026041607113563400_B1031","doi-asserted-by":"crossref","first-page":"2977","DOI":"10.1021\/jm030580l","article-title":"The PDBbind database: collection of binding affinities for protein-ligand complexes with known three-dimensional structures","volume":"47","author":"Wang","year":"2004","journal-title":"Journal of Medicinal Chemistry"},{"key":"2026041607113563400_B1032","unstructured":"Wang, R., Walters, R. and Smidt, T.E. (2023b), \u201cRelaxed octahedral group convolution for learning symmetry breaking in 3D physical systems\u201d, arXiv preprintarXiv:2310.02299."},{"key":"2026041607113563400_B1033","article-title":"Incorporating symmetry into deep dynamics models for improved generalization","author":"Wang","year":"2021"},{"key":"2026041607113563400_B1034","first-page":"23078","article-title":"Approximately equivariant networks for imperfectly symmetric dynamics","volume-title":"International Conference on Machine Learning","author":"Wang","year":"2022"},{"key":"2026041607113563400_B1035","author":"Wang","year":"2022"},{"issue":"1","key":"2026041607113563400_B1036","doi-asserted-by":"crossref","first-page":"e1005324","DOI":"10.1371\/journal.pcbi.1005324","article-title":"Accurate de novo prediction of protein contact map by ultra-deep learning model","volume":"13","author":"Wang","year":"2017","journal-title":"PLOS Computational Biology"},{"issue":"4","key":"2026041607113563400_B1037","doi-asserted-by":"crossref","first-page":"2044","DOI":"10.1021\/acs.jcim.0c00025","article-title":"Improving conformer generation for small rings and macrocycles based on distance geometry and experimental torsional-angle preferences","volume":"60","author":"Wang","year":"2020","journal-title":"Journal of Chemical Information and Modeling"},{"issue":"40","key":"2026041607113563400_B1038","doi-asserted-by":"crossref","first-page":"eabi8605","DOI":"10.1126\/sciadv.abi8605","article-title":"Learning the solution operator of parametric partial differential equations with physics-informed deeponets","volume":"7","author":"Wang","year":"2021","journal-title":"Science Advances"},{"issue":"1","key":"2026041607113563400_B1039","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1038\/s41524-019-0261-5","article-title":"Coarse-graining auto-encoders for molecular dynamics","volume":"5","author":"Wang","year":"2019","journal-title":"npj Computational Materials"},{"key":"2026041607113563400_B1040","unstructured":"Wang, W., Xu, M., Cai, C., Miller, B.K., Smidt, T., Wang, Y., Tang, J. and G\u00f3mez-Bombarelli, R. (2022f), \u201cGenerative coarse-graining of molecular conformations\u201d, arXiv preprintarXiv:2201.12176."},{"key":"2026041607113563400_B1041","doi-asserted-by":"crossref","DOI":"10.1145\/3560905.3568417","article-title":"Attention-based deep Bayesian counting for AI-augmented agriculture","author":"Wang","year":"2022"},{"key":"2026041607113563400_B1042","unstructured":"Wang, Y., Li, S., He, X., Li, M., Wang, Z., Zheng, N., Shao, B., Wang, T. and Liu, T.Y. (2022h), \u201cViSNet: a scalable and accurate geometric deep learning potential for molecular dynamics simulation\u201d, arXiv preprintarXiv:2210.16518."},{"issue":"3","key":"2026041607113563400_B1043","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1038\/s42256-022-00447-x","article-title":"Molecular contrastive learning of representations via graph neural networks","volume":"4","author":"Wang","year":"2022","journal-title":"Nature Machine Intelligence"},{"key":"2026041607113563400_B1044","unstructured":"Wang, Z., Zhang, G., Yang, K., Shi, N., Zhou, W., Hao, S., Xiong, G., Li, Y., Sim, M.Y., Chen, X., et al. (2023c), \u201cInteractive natural language processing\u201d, arXiv preprintarXiv:2305.13246."},{"issue":"9","key":"2026041607113563400_B1045","doi-asserted-by":"crossref","first-page":"2579","DOI":"10.1093\/bioinformatics\/btac112","article-title":"Advanced graph and sequence neural networks for molecular property prediction and drug discovery","volume":"38","author":"Wang","year":"2022","journal-title":"Bioinformatics"},{"key":"2026041607113563400_B1046","article-title":"Language models with image descriptors are strong few-shot video-language learners","author":"Wang","year":"2022"},{"issue":"1","key":"2026041607113563400_B1047","doi-asserted-by":"crossref","first-page":"6832","DOI":"10.1038\/s41598-022-10775-y","article-title":"Lm-gvp: an extensible sequence and structure informed deep learning framework for protein property prediction","volume":"12","author":"Wang","year":"2022","journal-title":"Scientifc Reports"},{"key":"2026041607113563400_B1048","unstructured":"Wang, Z., Han, C., Bao, W. and Ji, H. (2023d), \u201cUnderstanding the effect of data augmentation on knowledge distillation\u201d, arXiv preprintarXiv:2305.12565."},{"key":"2026041607113563400_B1049","doi-asserted-by":"crossref","DOI":"10.1101\/2022.12.09.519842","article-title":"Broadly applicable and accurate protein design by integrating structure prediction networks and diffusion generative models","author":"Watson","year":"2022"},{"key":"2026041607113563400_B1050","volume-title":"Enzyme Nomenclature 1992. 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(2023), \u201cEquivariant and coordinate independent convolutional networks\u201d, available at:https:\/\/maurice-weiler.gitlab.io\/cnn_book\/EquivariantAndCoordinateIndependentCNNs.pdf","DOI":"10.1142\/14143"},{"key":"2026041607113563400_B1058","article-title":"3D steerable CNNs: learning rotationally equivariant features in volumetric data","author":"Weiler","year":"2018"},{"key":"2026041607113563400_B1059","unstructured":"Weinan, E., Han, J. and Zhang, L. (2020), \u201cIntegrating machine learning with physics-based modeling\u201d, arXiv preprintarXiv:2006.02619."},{"issue":"1","key":"2026041607113563400_B1060","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1021\/ci00057a005","article-title":"SMILES, a chemical language and information system. 1. introduction to methodology and encoding rules","volume":"28","author":"Weininger","year":"1988","journal-title":"Journal of Chemical Information and Computer Sciences"},{"issue":"2","key":"2026041607113563400_B1061","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1021\/ci00062a008","article-title":"SMILES. 2. 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(2021), \u201cSimulations of state-of-the-art fermionic neural network wave functions with diffusion Monte Carlo\u201d, arXiv preprintarXiv:2103.12570."},{"issue":"23","key":"2026041607113563400_B1074","doi-asserted-by":"publisher","first-page":"235139","DOI":"10.1103\/PhysRevB.107.235139","article-title":"Neural network ansatz for periodic wave functions and the homogeneous electron gas","volume":"107","author":"Wilson","year":"2023","journal-title":"Physical Review B"},{"key":"2026041607113563400_B1075","volume-title":"Dynamic Stereochemistry of Chiral Compounds: Principles and Applications","author":"Wolf","year":"2007"},{"key":"2026041607113563400_B1076","article-title":"Uncertainty estimation for molecules: desiderata and methods","author":"Wollschl\u00e4ger","year":"2023"},{"key":"2026041607113563400_B1077","first-page":"32","article-title":"Deep scale-spaces: equivariance over scale","author":"Worrall","year":"2019","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"2","key":"2026041607113563400_B1078","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/s11005-023-01649-z","article-title":"Some problems in density functional theory","volume":"113","author":"Wrighton","year":"2023","journal-title":"Letters in Mathematical Physics"},{"key":"2026041607113563400_B1079","unstructured":"Wu, D., Rossi, R., Vicentini, F., Astrakhantsev, N., Becca, F., Cao, X., Carrasquilla, J., Ferrari, F., Georges, A., Hibat-Allah, M.\n          et al. (2023), \u201cVariational benchmarks for quantum many-body problems\u201d, arXiv preprintarXiv:2302.04919."},{"key":"2026041607113563400_B1080","unstructured":"Wu, D., Gao, L., Xiong, X., Chinazzi, M., Vespignani, A., Ma, Y.A. and Yu, R. (2021), \u201cDeepGLEAM: a hybrid mechanistic and deep learning model for COVID-19 forecasting\u201d, arXiv preprintarXiv:2102.06684."},{"key":"2026041607113563400_B1081","unstructured":"Wu, K.E., Yang, K.K., Berg, R.V.D., Zou, J.Y., Lu, A.X. and Amini, A.P. (2022a), \u201cProtein structure generation via folding diffusion\u201d, arXiv preprintarXiv:2209.15611."},{"key":"2026041607113563400_B1082","first-page":"2240","article-title":"Learning to accelerate partial differential equations via latent global evolution","volume":"35","author":"Wu","year":"2022","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026041607113563400_B1083","article-title":"Compositional generative inverse design","author":"Wu","year":"2024"},{"key":"2026041607113563400_B1084","article-title":"Learning controllable adaptive simulation for multi-scale physics","author":"Wu","year":"2022"},{"key":"2026041607113563400_B1085","first-page":"4184","article-title":"Learning large-scale subsurface simulations with a hybrid graph network simulator","author":"Wu","year":"2022"},{"key":"2026041607113563400_B1086","article-title":"Discovering invariant rationales for graph neural networks","author":"Wu","year":"2022"},{"issue":"2","key":"2026041607113563400_B1087","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1039\/C7SC02664A","article-title":"MoleculeNet: a bench-mark for molecular machine learning","volume":"9","author":"Wu","year":"2018","journal-title":"Chemical Science"},{"key":"2026041607113563400_B1088","doi-asserted-by":"crossref","first-page":"10414","DOI":"10.1609\/aaai.v35i12.17247","article-title":"Physics-constrained automatic feature engineering for predictive modeling in materials science","volume":"35","author":"Xiang","year":"2021","journal-title":"Proceedings of the AAAI Conference on Artifcial Intelligence"},{"key":"2026041607113563400_B1089","doi-asserted-by":"publisher","first-page":"1028","DOI":"10.1038\/s41567-020-0947-0","article-title":"Berry curvature memory through electrically driven stacking transitions","volume":"16","author":"Xiao","year":"2020","journal-title":"Nature Physics"},{"key":"2026041607113563400_B1090","article-title":"Crystal diffusion variational autoencoder for periodic material generation","author":"Xie","year":"2022"},{"key":"2026041607113563400_B1091","article-title":"Crystal diffusion variational autoencoder for periodic material generation","author":"Xie","year":"2022"},{"issue":"14","key":"2026041607113563400_B1092","doi-asserted-by":"crossref","first-page":"145301","DOI":"10.1103\/PhysRevLett.120.145301","article-title":"Crystal graph convolutional neural networks for an accurate and interpretable prediction of material properties","volume":"120","author":"Xie","year":"2018","journal-title":"Physical Review Letters"},{"key":"2026041607113563400_B1093","doi-asserted-by":"crossref","unstructured":"Xie, T., Wa, Y., Huang, W., Zhou, Y., Liu, Y., Linghu, Q., Wang, S., Kit, C., Grazian, C. and Hoex, B. 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(2018), \u201cHow powerful are graph neural networks?\u201d, arXiv preprintarXiv:1810.00826."},{"issue":"7","key":"2026041607113563400_B1100","doi-asserted-by":"crossref","first-page":"3240","DOI":"10.1021\/acs.jcim.0c01494","article-title":"De novo molecule design through the molecular generative model conditioned by 3D information of protein binding sites","volume":"61","author":"Xu","year":"2021","journal-title":"Journal of Chemical Information and Modeling"},{"key":"2026041607113563400_B1101","article-title":"Learning neural generative dynamics for molecular conformation generation","author":"Xu","year":"2021"},{"key":"2026041607113563400_B1102","article-title":"Geometric latent diffusion models for 3D molecule generation","author":"Xu","year":"2023"},{"key":"2026041607113563400_B1103","article-title":"An end-to-end framework for molecular con-formation generation via bilevel programming","author":"Xu","year":"2021"},{"key":"2026041607113563400_B1104","article-title":"GeoDiff: a geometric diffusion model for molecular conformation generation","author":"Xu","year":"2022"},{"key":"2026041607113563400_B1105","article-title":"Poisson fow generative models","author":"Xu","year":"2022","journal-title":"Advances in Neural Information Processing Systems."},{"key":"2026041607113563400_B1106","unstructured":"Xu, Z., Luo, Y., Zhang, X., Xu, X., Xie, Y., Liu, M., Dickerson, K., Deng, C., Nakata, M. and Ji, S. (2021d), \u201cMolecule3d: a benchmark for predicting 3d geometries from molecular graphs\u201d, arXiv preprintarXiv:2110.01717."},{"key":"2026041607113563400_B1107","doi-asserted-by":"crossref","unstructured":"Xu, Z., Xie, Y., Luo, Y., Zhang, X., Xu, X., Liu, M., Dickerson, K., Deng, C., Nakata, M. and Ji, S. (2023c), \u201c3D molecular geometry analysis with 2D graphs\u201d, arXiv preprintarXiv:2305.13315.","DOI":"10.1137\/1.9781611978032.39"},{"key":"2026041607113563400_B1108","article-title":"Equivariant graph network approximations of high-degree polynomials for force feld prediction","author":"Xu","year":"2024","journal-title":"Transactions on Machine Learning Research"},{"issue":"1","key":"2026041607113563400_B1109","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/ncomms11241","article-title":"Accelerated search for materials with targeted properties by adaptive design","volume":"7","author":"Xue","year":"2016","journal-title":"Nature Communications"},{"issue":"47","key":"2026041607113563400_B1110","first-page":"13301","article-title":"Accelerated search for BaTiO3-based piezoelectrics with vertical morphotropic phase boundary using Bayesian learning","volume":"113","author":"Xue","year":"2016","journal-title":"Proceedings of the National Academy of Sciences of the United States of America (PNAS)"},{"key":"2026041607113563400_B1111","article-title":"Invariant tokenization of crystalline materials for language model enabled generation","author":"Yan","year":"2024"},{"key":"2026041607113563400_B1112","first-page":"15066","article-title":"Periodic graph transformers for crystal material property prediction","author":"Yan","year":"2022"},{"key":"2026041607113563400_B1113","unstructured":"Yang, C., Woicik, A., Poon, H. and Wang, S. (2023a), \u201cBLIAM: literature-based data synthesis for synergistic drug combination prediction\u201d, arXiv preprintarXiv:2302.06860."},{"issue":"1","key":"2026041607113563400_B1114","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1186\/s13321-023-00682-3","article-title":"Explainable uncertainty quantifcations for deep learning-based molecular property prediction","volume":"15","author":"Yang","year":"2023","journal-title":"Journal of Cheminformatics"},{"issue":"8","key":"2026041607113563400_B1115","doi-asserted-by":"crossref","first-page":"3370","DOI":"10.1021\/acs.jcim.9b00237","article-title":"Analyzing learned molecular representations for property prediction","volume":"59","author":"Yang","year":"2019","journal-title":"Journal of Chemical Information and Modeling"},{"key":"2026041607113563400_B1116","unstructured":"Yang, L., Hu, W. and Li, L. (2020), \u201cScalable variational Monte Carlo with graph neural ansatz\u201d, arXiv preprintarXiv:2011.12453."},{"key":"2026041607113563400_B1117","doi-asserted-by":"crossref","first-page":"109913","DOI":"10.1016\/j.jcp.2020.109913","article-title":"B-PINNs: bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data","volume":"425","author":"Yang","year":"2021","journal-title":"Journal of Computational Physics"},{"key":"2026041607113563400_B1118","doi-asserted-by":"crossref","DOI":"10.1145\/3534678.3539391","article-title":"Learning task-relevant representations for generalization via characteristic functions of reward sequence distributions","author":"Yang","year":"2022"},{"key":"2026041607113563400_B1119","first-page":"1","article-title":"Rapid seismic waveform modeling and inversion with neural operators","volume":"61","author":"Yang","year":"2023","journal-title":"IEEE Transactions on Geoscience and Remote Sensing"},{"issue":"3","key":"2026041607113563400_B1120","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1785\/0320210026","article-title":"Seismic wave propagation and inversion with neural operators","volume":"1","author":"Yang","year":"2021","journal-title":"The Seismic Record"},{"issue":"1","key":"2026041607113563400_B1121","doi-asserted-by":"crossref","DOI":"10.1107\/S1600577522011274","article-title":"Artifact identifcation in X-ray diffraction data using machine learning methods","volume":"30","author":"Yanxon","year":"2023","journal-title":"Journal of Synchrotron Radiation"},{"issue":"3","key":"2026041607113563400_B1122","doi-asserted-by":"crossref","first-page":"1139","DOI":"10.1021\/acs.jctc.5b01011","article-title":"Kinetic energy of hydrocarbons as a function of electron density and convolutional neural networks","volume":"12","author":"Yao","year":"2016","journal-title":"Journal of Chemical Theory and Computation"},{"key":"2026041607113563400_B1123","unstructured":"Yao, S., Yu, D., Zhao, J., Shafran, I., Griffiths, T.L., Cao, Y. and Narasimhan, K. (2023a), \u201cTree of thoughts: deliberate problem solving with large language models\u201d, arXiv preprintarXiv:2305.10601."},{"key":"2026041607113563400_B1124","article-title":"ReAct: synergizing reasoning and acting in language models","author":"Yao","year":"2023"},{"key":"2026041607113563400_B1125","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1007\/s00365-021-09546-1","article-title":"Universal approximations of invariant maps by neural networks","volume":"55","author":"Yarotsky","year":"2018","journal-title":"Constructive Approximation"},{"key":"2026041607113563400_B1126","doi-asserted-by":"crossref","unstructured":"Yasunaga, M., Leskovec, J. and Liang, P. (2022), \u201cLinkbert: pretraining language models with document links\u201d, arXiv preprintarXiv:2203.15827.","DOI":"10.18653\/v1\/2022.acl-long.551"},{"key":"2026041607113563400_B1127","unstructured":"Yi, K., Zhang, Q., Hu, L., He, H., An, N., Cao, L. and Niu, Z. (2022), \u201cEdge-varying Fourier graph networks for multivariate time series forecasting\u201d, arXiv preprintarXiv:2210.03093."},{"key":"2026041607113563400_B1128","unstructured":"Yim, J., Trippe, B.L., De Bortoli, V., Mathieu, E., Doucet, A., Barzilay, R. and Jaakkola, T. (2023a), \u201cSE (3) diffusion model with application to protein backbone generation\u201d, arXiv preprintarXiv:2302.02277."},{"key":"2026041607113563400_B1129","unstructured":"Yim, J., Campbell, A., Foong, A.Y.K., Gastegger, M., Jim\u00e9nez-Luna, J., Lewis, S., Satorras, V.G., Veeling, B.S., Barzilay, R., Jaakkola, T., et al. (2023b), \u201cFast protein backbone generation with SE (3) fow matching\u201d, arXiv preprintarXiv:2310.05297."},{"issue":"12","key":"2026041607113563400_B1130","doi-asserted-by":"crossref","first-page":"124012","DOI":"10.1088\/1742-5468\/ac3ae5","article-title":"Augmenting physical models with deep networks for complex dynamics forecasting","volume":"2021","author":"Yin","year":"2021","journal-title":"Journal of Statistical Mechanics: Theory and Experiment"},{"key":"2026041607113563400_B1131","first-page":"28877","article-title":"Do transformers really perform badly for graph repre-sentation?","volume":"34","author":"Ying","year":"2021","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026041607113563400_B1132","first-page":"9244","volume-title":"Advances in Neural Information Processing Systems","author":"Ying","year":"2019"},{"key":"2026041607113563400_B1133","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-3286-8","volume-title":"Handbook of 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(2022), \u201cRetrieval-enhanced machine learning\u201d, arXiv preprint arXiv:2205.01230.","DOI":"10.1145\/3477495.3531722"},{"issue":"10","key":"2026041607113563400_B1150","doi-asserted-by":"crossref","first-page":"4913","DOI":"10.1021\/acs.jcim.1c00692","article-title":"QSAR modeling based on conformation ensembles using a multi-instance learning approach","volume":"61","author":"Zankov","year":"2021","journal-title":"Journal of Chemical Information and Modeling"},{"key":"2026041607113563400_B1151","volume-title":"Group Theory in a Nutshell for Physicists","author":"Zee","year":"2016"},{"issue":"1","key":"2026041607113563400_B1152","doi-asserted-by":"crossref","first-page":"862","DOI":"10.1038\/s41467-022-28494-3","article-title":"A deep-learning system bridging molecule structure and biomedical text with comprehension comparable to human professionals","volume":"13","author":"Zeng","year":"2022","journal-title":"Nature Communications"},{"key":"2026041607113563400_B1153","first-page":"1","article-title":"A generative model for inorganic materials design","author":"Zeni","year":"2025","journal-title":"Nature"},{"issue":"6","key":"2026041607113563400_B1154","doi-asserted-by":"crossref","first-page":"063020","DOI":"10.1088\/1367-2630\/aac7f0","article-title":"Performance of various density-functional approximations for cohesive properties of 64 bulk solids","volume":"20","author":"Zhang","year":"2018","journal-title":"New Journal of Physics"},{"issue":"1","key":"2026041607113563400_B1155","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1038\/s41524-022-00779-7","article-title":"Composition design of high-entropy alloys with deep sets learning","volume":"8","author":"Zhang","year":"2022","journal-title":"npj Computational Materials"},{"key":"2026041607113563400_B1156","unstructured":"Zhang, L., Zhang, Y., Ren, K., Li, D. and Yang, Y. (2023a), \u201cMLCopilot: unleashing the power of large language models in solving machine learning tasks\u201d, arXiv preprintarXiv:2304.14979."},{"issue":"14","key":"2026041607113563400_B1157","doi-asserted-by":"crossref","first-page":"143001","DOI":"10.1103\/PhysRevLett.120.143001","article-title":"Deep potential molecular dynamics: a scalable model with the accuracy of quantum mechanics","volume":"120","author":"Zhang","year":"2018","journal-title":"Physical Review Letters"},{"key":"2026041607113563400_B1158","unstructured":"Zhang, X., Zhou, L., Xu, R., Cui, P., Shen, Z. and Liu, H. (2022b), \u201cNICO++: towards better benchmarking for domain generalization\u201d, arXiv preprintarXiv:2204.08040."},{"issue":"6","key":"2026041607113563400_B1159","first-page":"1","article-title":"Nerfactor: neural factorization of shape and refectance under an unknown illumination","volume":"40","author":"Zhang","year":"2021","journal-title":"ACM Transactions on Graphics (ToG)"},{"key":"2026041607113563400_B1160","article-title":"SineNet: learning temporal dynamics in time-dependent partial differential equations","author":"Zhang","year":"2024"},{"key":"2026041607113563400_B1161","unstructured":"Zhang, X., Xu, S. and Ji, S. (2023b), \u201cA score-based model for learning neural wavefunctions\u201d, arXiv preprintarXiv:2305.16540."},{"key":"2026041607113563400_B1162","article-title":"E3Bind: an end-to-end equivariant network for protein-ligand docking","author":"Zhang","year":"2023"},{"key":"2026041607113563400_B1163","doi-asserted-by":"crossref","first-page":"5829","DOI":"10.1609\/aaai.v33i01.33015829","article-title":"Bayesian graph convolutional neural networks for semi-supervised classifcation","volume":"33","author":"Zhang","year":"2019","journal-title":"Proceedings of the AAAI Conference on Artifcial Intelligence"},{"key":"2026041607113563400_B1164","unstructured":"Zhang, Z. and Liu, Q. (2023), \u201cLearning subpocket prototypes for generalizable structure-based drug design\u201d, arXiv preprintarXiv:2305.13997."},{"issue":"35","key":"2026041607113563400_B1165","doi-asserted-by":"crossref","first-page":"8154","DOI":"10.1039\/C9SC00616H","article-title":"Bayesian semi-supervised learning for un-certainty-calibrated prediction of molecular properties and active learning","volume":"10","author":"Zhang","year":"2019","journal-title":"Chemical Science"},{"key":"2026041607113563400_B1166","article-title":"Molecule generation for target protein binding with structural motifs","author":"Zhang","year":"2023"},{"key":"2026041607113563400_B1167","article-title":"Fine-grained information extraction from biomedical litera-ture based on knowledge-enriched abstract meaning representation","author":"Zhang","year":"2021"},{"key":"2026041607113563400_B1168","article-title":"Protein representation learning by geometric structure pretraining","author":"Zhang","year":"2023"},{"key":"2026041607113563400_B1169","article-title":"Bayesian active learning by soft mean objective cost of uncertainty","author":"Zhao","year":"2021"},{"key":"2026041607113563400_B1170","article-title":"Efficient active learning for Gaussian process classifcation by error reduction","author":"Zhao","year":"2021"},{"key":"2026041607113563400_B1171","article-title":"Uncertainty-aware active learning for optimal Bayesian classifer","author":"Zhao","year":"2021"},{"key":"2026041607113563400_B1172","doi-asserted-by":"crossref","first-page":"3849","DOI":"10.1109\/TSP.2020.3001384","article-title":"Model-based robust fltering and experimental design for stochastic differential equation systems","volume":"68","author":"Zhao","year":"2020","journal-title":"IEEE Transactions on Signal Processing"},{"issue":"16","key":"2026041607113563400_B1173","doi-asserted-by":"crossref","first-page":"12289","DOI":"10.1039\/D4CP00878B","article-title":"Deep mind 21 functional does not extrapolate to transition metal chemistry","volume":"26","author":"Zhao","year":"2024","journal-title":"Physical Chemistry Chemical Physics."},{"key":"2026041607113563400_B1174","first-page":"26895","article-title":"Learning to solve PDE-constrained inverse problems with graph networks","author":"Zhao","year":"2022"},{"issue":"3","key":"2026041607113563400_B1175","doi-asserted-by":"publisher","first-page":"2138","DOI":"10.1103\/PhysRevA.50.2138","article-title":"From electron densities to Kohn-Sham kinetic energies, orbital energies, exchange-correlation potentials, and exchange-correlation energies","volume":"50","author":"Zhao","year":"1994","journal-title":"Physical Review A"},{"key":"2026041607113563400_B1176","article-title":"Adversarial modality alignment network for cross-modal molecule retrieval","author":"Zhao","year":"2023","journal-title":"IEEE Transactions on Artifcial Intelligence."},{"key":"2026041607113563400_B1177","article-title":"Implicit neural convolutional kernels for steerable CNNs","author":"Zhdanov","year":"2023"},{"key":"2026041607113563400_B1178","article-title":"Lyapunov regularized forecaster","author":"Zheng","year":"2022"},{"issue":"1-3","key":"2026041607113563400_B1179","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1016\/j.cplett.210.1016\/j.cplett.2","article-title":"A generalized exchange-correlation functional: the neural-networks approach","volume":"390","author":"Zheng","year":"2004","journal-title":"Chemical Physics Letters"},{"key":"2026041607113563400_B1180","doi-asserted-by":"crossref","DOI":"10.1101\/2023.02.03.526917","article-title":"Structure-informed language models are protein designers","author":"Zheng","year":"2023"},{"key":"2026041607113563400_B1181","article-title":"Reconstructing continuous distributions of 3D protein structure from cryo-EM images","author":"Zhong","year":"2020"},{"key":"2026041607113563400_B1182","unstructured":"Zhong, R., Zhang, P., Li, S., Ahn, J., Klein, D. and Steinhardt, J. (2023a), \u201cGoal driven discovery of distributional differences via language descriptions\u201d, arXiv preprintarXiv:2302.14233."},{"issue":"1","key":"2026041607113563400_B1183","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1038\/s41524-023-01130-4","article-title":"Transferable equivariant graph neural networks for the Hamiltonians of molecules and solids","volume":"9","author":"Zhong","year":"2023","journal-title":"npj Computational Materials"},{"key":"2026041607113563400_B1184","doi-asserted-by":"crossref","DOI":"10.26434\/chemrxiv-2022-jjm0j-v4","article-title":"Uni-Mol: a universal 3D molecular representation learning framework","author":"Zhou","year":"2023"},{"key":"2026041607113563400_B1185","volume-title":"Advances in Neural Information Processing Systems","author":"Zhou","year":"2019"},{"issue":"1","key":"2026041607113563400_B1186","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1038\/s41524-023-00968-y","article-title":"A generative deep learning framework for inverse design of compositionally complex bulk metallic glasses","volume":"9","author":"Zhou","year":"2023","journal-title":"npj Computational Materials"},{"key":"2026041607113563400_B1187","unstructured":"Zhu, J., Xia, Y., Liu, C., Wu, L., Xie, S., Wang, Y., Wang, T., Qin, T., Zhou, W., Li, H., et al. (2022), \u201cDirect molecular conformation generation\u201d, arXiv preprintarXiv:2202.01356."},{"key":"2026041607113563400_B1188","first-page":"34","article-title":"Shift-robust GNNs: overcoming the limitations of localized graph training data","author":"Zhu","year":"2021","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"1","key":"2026041607113563400_B1189","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1109\/JPROC.2020.3004555","article-title":"A comprehensive survey on transfer learning","volume":"109","author":"Zhuang","year":"2020","journal-title":"Proceedings of the IEEE"},{"key":"2026041607113563400_B1190","unstructured":"Zitnick, C.L., Das, A., Kolluru, A., Lan, J., Shuaibi, M., Sriram, A., Ulissi, Z.W. and Wood, B.M. (2022), \u201cSpherical channels for modeling atomic interactions\u201d, in Oh, A.H., Agarwal, A., Belgrave, D. and Cho, K. (Eds), Advances in Neural Information Processing Systems, available at:https:\/\/openreview.net\/forum?id=5Z3GURcqwT"},{"key":"2026041607113563400_B1191","unstructured":"Zitnick, C.L., Chanussot, L., Das, A., Goyal, S., Heras-Domingo, J., Ho, C., Hu, W., Lavril, T., Palizhati, A., Riviere, M., et al. (2020), \u201cAn introduction to electrocatalyst design using machine learning for renewable energy storage\u201d, arXiv preprintarXiv:2010.09435."},{"key":"2026041607113563400_B1192","unstructured":"Ziyin, L. and Ueda, M. (2022), \u201cExact phase transitions in deep learning\u201d, arXiv preprintarXiv:2205.12510."},{"issue":"11","key":"2026041607113563400_B1193","doi-asserted-by":"crossref","first-page":"957","DOI":"10.1038\/s43588-023-00550-y","article-title":"A deep learning model for predicting selected organic molecular spectra","volume":"3","author":"Zou","year":"2023","journal-title":"Nature Computational Science"},{"issue":"3","key":"2026041607113563400_B1194","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1103\/PhysRevLett.65.353","article-title":"Special quasirandom structures","volume":"65","author":"Zunger","year":"1990","journal-title":"Phys. Rev. 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