{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,20]],"date-time":"2026-06-20T02:56:08Z","timestamp":1781924168791,"version":"3.54.5"},"reference-count":79,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,12,30]],"date-time":"2022-12-30T00:00:00Z","timestamp":1672358400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,12,30]],"date-time":"2022-12-30T00:00:00Z","timestamp":1672358400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100004189","name":"Max-Planck-Gesellschaft","doi-asserted-by":"publisher","award":["740233"],"award-info":[{"award-number":["740233"]}],"id":[{"id":"10.13039\/501100004189","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004189","name":"Max-Planck-Gesellschaft","doi-asserted-by":"publisher","award":["740233"],"award-info":[{"award-number":["740233"]}],"id":[{"id":"10.13039\/501100004189","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004189","name":"Max-Planck-Gesellschaft","doi-asserted-by":"publisher","award":["740233"],"award-info":[{"award-number":["740233"]}],"id":[{"id":"10.13039\/501100004189","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004189","name":"Max-Planck-Gesellschaft","doi-asserted-by":"publisher","award":["740233"],"award-info":[{"award-number":["740233"]}],"id":[{"id":"10.13039\/501100004189","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004189","name":"Max-Planck-Gesellschaft","doi-asserted-by":"publisher","award":["740233"],"award-info":[{"award-number":["740233"]}],"id":[{"id":"10.13039\/501100004189","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["RE 3977\/1"],"award-info":[{"award-number":["RE 3977\/1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["RE 3977\/1"],"award-info":[{"award-number":["RE 3977\/1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010661","name":"EC | Horizon 2020 Framework Programme","doi-asserted-by":"publisher","award":["ERC-2015-CoG-682843"],"award-info":[{"award-number":["ERC-2015-CoG-682843"]}],"id":[{"id":"10.13039\/100010661","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010661","name":"EC | Horizon 2020 Framework Programme","doi-asserted-by":"publisher","award":["ERC-2015-CoG-682843"],"award-info":[{"award-number":["ERC-2015-CoG-682843"]}],"id":[{"id":"10.13039\/100010661","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002790","name":"Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002790","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Nat Comput Sci"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>The electronic band structure and crystal structure are the two complementary identifiers of solid-state materials. Although convenient instruments and reconstruction algorithms have made large, empirical, crystal structure databases possible, extracting the quasiparticle dispersion (closely related to band structure) from photoemission band mapping data is currently limited by the available computational methods. To cope with the growing size and scale of photoemission data, here we develop a pipeline including probabilistic machine learning and the associated data processing, optimization and evaluation methods for band-structure reconstruction, leveraging theoretical calculations. The pipeline reconstructs all 14 valence bands of a semiconductor and shows excellent performance on benchmarks and other materials datasets. The reconstruction uncovers previously inaccessible momentum-space structural information on both global and local scales, while realizing a path towards integration with materials science databases. Our approach illustrates the potential of combining machine learning and domain knowledge for scalable feature extraction in multidimensional data.<\/jats:p>","DOI":"10.1038\/s43588-022-00382-2","type":"journal-article","created":{"date-parts":[[2022,12,30]],"date-time":"2022-12-30T12:07:29Z","timestamp":1672402049000},"page":"101-114","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["A machine learning route between band mapping and band structure"],"prefix":"10.1038","volume":"3","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9895-6956","authenticated-orcid":false,"given":"R. Patrick","family":"Xian","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4965-4297","authenticated-orcid":false,"given":"Vincent","family":"Stimper","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7052-5684","authenticated-orcid":false,"given":"Marios","family":"Zacharias","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Maciej","family":"Dendzik","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7940-9583","authenticated-orcid":false,"given":"Shuo","family":"Dong","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Samuel","family":"Beaulieu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bernhard","family":"Sch\u00f6lkopf","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7226-9592","authenticated-orcid":false,"given":"Martin","family":"Wolf","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0725-6696","authenticated-orcid":false,"given":"Laurenz","family":"Rettig","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0635-8364","authenticated-orcid":false,"given":"Christian","family":"Carbogno","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1712-060X","authenticated-orcid":false,"given":"Stefan","family":"Bauer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6665-3520","authenticated-orcid":false,"given":"Ralph","family":"Ernstorfer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2022,12,30]]},"reference":[{"key":"382_CR1","doi-asserted-by":"publisher","first-page":"1540","DOI":"10.1021\/acs.chemmater.7b04496","volume":"30","author":"EB Isaacs","year":"2018","unstructured":"Isaacs, E. B. & Wolverton, C. Inverse band structure design via materials database screening: application to square planar thermoelectrics. Chem. Mater. 30, 1540\u20131546 (2018).","journal-title":"Chem. Mater."},{"key":"382_CR2","doi-asserted-by":"publisher","first-page":"4167","DOI":"10.1109\/TED.2018.2854902","volume":"65","author":"EG Marin","year":"2018","unstructured":"Marin, E. G., Perucchini, M., Marian, D., Iannaccone, G. & Fiori, G. Modeling of electron devices based on 2-D materials. IEEE Trans. Electron Devices 65, 4167\u20134179 (2018).","journal-title":"IEEE Trans. Electron Devices"},{"key":"382_CR3","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1103\/PhysRev.50.58","volume":"50","author":"LP Bouckaert","year":"1936","unstructured":"Bouckaert, L. P., Smoluchowski, R. & Wigner, E. Theory of Brillouin zones and symmetry properties of wave functions in crystals. Phys. Rev. 50, 58\u201367 (1936).","journal-title":"Phys. Rev."},{"key":"382_CR4","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1002\/andp.200151301-211","volume":"10","author":"T-C Chiang","year":"2001","unstructured":"Chiang, T.-C. & Seitz, F. Photoemission spectroscopy in solids. Ann. Phys. 10, 61\u201374 (2001).","journal-title":"Ann. Phys."},{"key":"382_CR5","doi-asserted-by":"publisher","first-page":"473","DOI":"10.1103\/RevModPhys.75.473","volume":"75","author":"A Damascelli","year":"2003","unstructured":"Damascelli, A., Hussain, Z. & Shen, Z.-X. Angle-resolved photoemission studies of the cuprate superconductors. Rev. Mod. Phys. 75, 473\u2013541 (2003).","journal-title":"Rev. Mod. Phys."},{"key":"382_CR6","doi-asserted-by":"publisher","first-page":"54","DOI":"10.1038\/s43586-022-00133-7","volume":"2","author":"H Zhang","year":"2022","unstructured":"Zhang, H. et al. Angle-resolved photoemission spectroscopy. Nat. Rev. Methods Primers 2, 54 (2022).","journal-title":"Nat. Rev. Methods Primers"},{"key":"382_CR7","doi-asserted-by":"publisher","first-page":"94","DOI":"10.1016\/j.elspec.2015.05.016","volume":"200","author":"G Sch\u00f6nhense","year":"2015","unstructured":"Sch\u00f6nhense, G., Medjanik, K. & Elmers, H.-J. Space-, time- and spin-resolved photoemission. J. Electron Spectros. Relat. Phenomena 200, 94\u2013118 (2015).","journal-title":"J. Electron Spectros. Relat. Phenomena"},{"key":"382_CR8","doi-asserted-by":"publisher","first-page":"615","DOI":"10.1038\/nmat4875","volume":"16","author":"K Medjanik","year":"2017","unstructured":"Medjanik, K. et al. Direct 3D mapping of the Fermi surface and Fermi velocity. Nat. Mater. 16, 615\u2013621 (2017).","journal-title":"Nat. Mater."},{"key":"382_CR9","doi-asserted-by":"publisher","first-page":"023104","DOI":"10.1063\/1.5081938","volume":"90","author":"M Puppin","year":"2019","unstructured":"Puppin, M. et al. Time- and angle-resolved photoemission spectroscopy of solids in the extreme ultraviolet at 500-kHz repetition rate. Rev. Sci. Instrum. 90, 023104 (2019).","journal-title":"Rev. Sci. Instrum."},{"key":"382_CR10","doi-asserted-by":"publisher","first-page":"093101","DOI":"10.1063\/5.0018834","volume":"128","author":"A Gauthier","year":"2020","unstructured":"Gauthier, A. et al. Tuning time and energy resolution in time-resolved photoemission spectroscopy with nonlinear crystals. J. Appl. Phys. 128, 093101 (2020).","journal-title":"J. Appl. Phys."},{"key":"382_CR11","doi-asserted-by":"publisher","first-page":"835","DOI":"10.1038\/nphys3105","volume":"10","author":"JM Riley","year":"2014","unstructured":"Riley, J. M. et al. Direct observation of spin-polarized bulk bands in an inversion-symmetric semiconductor. Nat. Phys. 10, 835\u2013839 (2014).","journal-title":"Nat. Phys."},{"key":"382_CR12","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1038\/nmat5031","volume":"17","author":"MS Bahramy","year":"2018","unstructured":"Bahramy, M. S. et al. Ubiquitous formation of bulk Dirac cones and topological surface states from a single orbital manifold in transition-metal dichalcogenides. Nat. Mater. 17, 21\u201328 (2018).","journal-title":"Nat. Mater."},{"key":"382_CR13","doi-asserted-by":"publisher","first-page":"759","DOI":"10.1038\/s41567-019-0511-y","volume":"15","author":"NBM Schr\u00f6ter","year":"2019","unstructured":"Schr\u00f6ter, N. B. M. et al. Chiral topological semimetal with multifold band crossings and long Fermi arcs. Nat. Phys. 15, 759\u2013765 (2019).","journal-title":"Nat. Phys."},{"key":"382_CR14","doi-asserted-by":"publisher","first-page":"2110","DOI":"10.1126\/science.285.5436.2110","volume":"285","author":"T Valla","year":"1999","unstructured":"Valla, T. et al. Evidence for quantum critical behavior in the optimally doped cuprate Bi2Sr2CaCu2O8\u2009+\u2009\u03b4. Science 285, 2110\u20132113 (1999).","journal-title":"Science"},{"key":"382_CR15","doi-asserted-by":"publisher","first-page":"045150","DOI":"10.1103\/PhysRevB.90.045150","volume":"90","author":"G Levy","year":"2014","unstructured":"Levy, G., Nettke, W., Ludbrook, B. M., Veenstra, C. N. & Damascelli, A. Deconstruction of resolution effects in angle-resolved photoemission. Phys. Rev. B 90, 045150 (2014).","journal-title":"Phys. Rev. B"},{"key":"382_CR16","doi-asserted-by":"publisher","first-page":"043712","DOI":"10.1063\/1.3585113","volume":"82","author":"P Zhang","year":"2011","unstructured":"Zhang, P. et al. A precise method for visualizing dispersive features in image plots. Rev. Sci. Instrum. 82, 043712 (2011).","journal-title":"Rev. Sci. Instrum."},{"key":"382_CR17","doi-asserted-by":"publisher","first-page":"073903","DOI":"10.1063\/1.4993919","volume":"88","author":"Y He","year":"2017","unstructured":"He, Y., Wang, Y. & Shen, Z.-X. Visualizing dispersive features in 2D image via minimum gradient method. Rev. Sci. Instrum. 88, 073903 (2017).","journal-title":"Rev. Sci. Instrum."},{"key":"382_CR18","doi-asserted-by":"publisher","first-page":"033905","DOI":"10.1063\/1.5132586","volume":"91","author":"H Peng","year":"2020","unstructured":"Peng, H. et al. Super resolution convolutional neural network for feature extraction in spectroscopic data. Rev. Sci. Instrum. 91, 033905 (2020).","journal-title":"Rev. Sci. Instrum."},{"key":"382_CR19","doi-asserted-by":"publisher","first-page":"073901","DOI":"10.1063\/5.0054920","volume":"92","author":"Y Kim","year":"2021","unstructured":"Kim, Y. et al. Deep learning-based statistical noise reduction for multidimensional spectral data. Rev. Sci. Instrum. 92, 073901 (2021).","journal-title":"Rev. Sci. Instrum."},{"key":"382_CR20","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/j.elspec.2016.11.007","volume":"214","author":"S Moser","year":"2017","unstructured":"Moser, S. An experimentalist\u2019s guide to the matrix element in angle resolved photoemission. J. Electron Spectros. Relat. Phenomena 214, 29\u201352 (2017).","journal-title":"J. Electron Spectros. Relat. Phenomena"},{"key":"382_CR21","unstructured":"Murphy, K. P. Machine Learning: A Probabilistic Perspective (MIT Press, 2012)."},{"key":"382_CR22","doi-asserted-by":"publisher","first-page":"452","DOI":"10.1038\/nature14541","volume":"521","author":"Z Ghahramani","year":"2015","unstructured":"Ghahramani, Z. Probabilistic machine learning and artificial intelligence. Nature 521, 452\u2013459 (2015).","journal-title":"Nature"},{"key":"382_CR23","doi-asserted-by":"publisher","first-page":"1610\u20131627","DOI":"10.1016\/j.cviu.2013.07.004","volume":"117","author":"C Wang","year":"2013","unstructured":"Wang, C., Komodakis, N. & Paragios, N. Markov random field modeling, inference and learning in computer vision and image understanding: a survey. Comput. Vis. Image Underst. 117, 1610\u20131627 (2013).","journal-title":"Comput. Vis. Image Underst."},{"key":"382_CR24","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1109\/MSP.2021.3123564","volume":"39","author":"M Comer","year":"2022","unstructured":"Comer, M. & Simmons, J. The Markov random field in materials applications: a synoptic view for signal processing and materials readers. IEEE Signal Process. Mag. 39, 16\u201324 (2022).","journal-title":"IEEE Signal Process. Mag."},{"key":"382_CR25","doi-asserted-by":"publisher","first-page":"564","DOI":"10.1126\/science.aay3062","volume":"367","author":"K Kaufmann","year":"2020","unstructured":"Kaufmann, K. et al. Crystal symmetry determination in electron diffraction using machine learning. Science 367, 564\u2013568 (2020).","journal-title":"Science"},{"key":"382_CR26","doi-asserted-by":"publisher","first-page":"10392","DOI":"10.1103\/PhysRevB.55.10392","volume":"55","author":"M Traving","year":"1997","unstructured":"Traving, M. et al. Electronic structure of WSe2: a combined photoemission and inverse photoemission study. Phys. Rev. B 55, 10392\u201310399 (1997).","journal-title":"Phys. Rev. B"},{"key":"382_CR27","doi-asserted-by":"publisher","first-page":"10400","DOI":"10.1103\/PhysRevB.55.10400","volume":"55","author":"T Finteis","year":"1997","unstructured":"Finteis, T. et al. Occupied and unoccupied electronic band structure of WSe2. Phys. Rev. B 55, 10400\u201310411 (1997).","journal-title":"Phys. Rev. B"},{"key":"382_CR28","doi-asserted-by":"publisher","first-page":"022001","DOI":"10.1088\/2053-1583\/2\/2\/022001","volume":"2","author":"A Korm\u00e1nyos","year":"2015","unstructured":"Korm\u00e1nyos, A. et al. k\u22c5p theory for two-dimensional transition metal dichalcogenide semiconductors. 2D Mater. 2, 022001 (2015).","journal-title":"2D Mater."},{"key":"382_CR29","doi-asserted-by":"publisher","first-page":"165437","DOI":"10.1109\/ACCESS.2019.2952899","volume":"7","author":"V Stimper","year":"2019","unstructured":"Stimper, V., Bauer, S., Ernstorfer, R., Scholkopf, B. & Xian, R. P. Multidimensional contrast limited adaptive histogram equalization. IEEE Access 7, 165437\u2013165447 (2019).","journal-title":"IEEE Access"},{"key":"382_CR30","doi-asserted-by":"crossref","unstructured":"Perdew, J. P. & Schmidt, K. Jacob\u2019s ladder of density functional approximations for the exchange-correlation energy. In AIP Conference Proceedings (Eds Doren, V. V. et al.) 1\u201320 (AIP, 2001).","DOI":"10.1063\/1.1390175"},{"key":"382_CR31","doi-asserted-by":"publisher","first-page":"377","DOI":"10.3389\/fchem.2019.00377","volume":"7","author":"D Golze","year":"2019","unstructured":"Golze, D., Dvorak, M. & Rinke, P. The GW Compendium: a practical guide to theoretical photoemission spectroscopy. Front. Chem. 7, 377 (2019).","journal-title":"Front. Chem."},{"key":"382_CR32","doi-asserted-by":"publisher","first-page":"045126","DOI":"10.1103\/PhysRevB.102.045126","volume":"102","author":"M Zacharias","year":"2020","unstructured":"Zacharias, M., Scheffler, M. & Carbogno, C. Fully anharmonic nonperturbative theory of vibronically renormalized electronic band structures. Phys. Rev. B 102, 045126 (2020).","journal-title":"Phys. Rev. B"},{"key":"382_CR33","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.patcog.2003.07.008","volume":"37","author":"D Zhang","year":"2004","unstructured":"Zhang, D. & Lu, G. Review of shape representation and description techniques. Pattern Recognit. 37, 1\u201319 (2004).","journal-title":"Pattern Recognit."},{"key":"382_CR34","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1109\/34.55109","volume":"12","author":"A Khotanzad","year":"1990","unstructured":"Khotanzad, A. & Hong, Y. Invariant image recognition by Zernike moments. IEEE Trans. Pattern Anal. Mach. Intell. 12, 489\u2013497 (1990).","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"382_CR35","doi-asserted-by":"publisher","first-page":"2994","DOI":"10.1364\/JOSAA.24.002994","volume":"24","author":"VN Mahajan","year":"2007","unstructured":"Mahajan, V. N. & Dai, G.-m. Orthonormal polynomials in wavefront analysis: analytical solution. J. Opt. Soc. Am. A 24, 2994\u20133016 (2007).","journal-title":"J. Opt. Soc. Am. A"},{"key":"382_CR36","doi-asserted-by":"publisher","first-page":"1900808","DOI":"10.1002\/advs.201900808","volume":"6","author":"L Himanen","year":"2019","unstructured":"Himanen, L., Geurts, A., Foster, A. S. & Rinke, P. Data driven materials science: status, challenges and perspectives. Adv. Sci. 6, 1900808 (2019).","journal-title":"Adv. Sci."},{"key":"382_CR37","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1038\/s43588-020-00016-5","volume":"1","author":"MK Horton","year":"2021","unstructured":"Horton, M. K., Dwaraknath, S. & Persson, K. A. Promises and perils of computational materials databases. Nat. Comput. Sci. 1, 3\u20135 (2021).","journal-title":"Nat. Comput. Sci."},{"key":"382_CR38","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1016\/j.strusafe.2008.06.020","volume":"31","author":"AD Kiureghian","year":"2009","unstructured":"Kiureghian, A. D. & Ditlevsen, O. Aleatory or epistemic? Does it matter? Struct. Safety 31, 105\u2013112 (2009).","journal-title":"Struct. Safety"},{"key":"382_CR39","unstructured":"Nocedal, J. & Wright, S. J. Numerical Optimization 2nd edn (Springer, 2006)."},{"key":"382_CR40","unstructured":"Xian, R. P., Ernstorfer, R. & Pelz, P. M. Scalable multicomponent spectral analysis for high-throughput data annotation. Preprint at https:\/\/arxiv.org\/abs\/2102.05604 (2021)."},{"key":"382_CR41","doi-asserted-by":"publisher","first-page":"202","DOI":"10.1016\/j.earscirev.2014.05.016","volume":"136","author":"MW Smith","year":"2014","unstructured":"Smith, M. W. Roughness in the Earth Sciences. Earth Sci. Rev. 136, 202\u2013225 (2014).","journal-title":"Earth Sci. Rev."},{"key":"382_CR42","doi-asserted-by":"publisher","first-page":"205415","DOI":"10.1103\/PhysRevB.91.205415","volume":"91","author":"H Guo","year":"2015","unstructured":"Guo, H. et al. Double resonance Raman modes in monolayer and few-layer MoTe2. Phys. Rev. B 91, 205415 (2015).","journal-title":"Phys. Rev. B"},{"key":"382_CR43","doi-asserted-by":"publisher","first-page":"17049","DOI":"10.1038\/natrevmats.2017.49","volume":"2","author":"JP Heremans","year":"2017","unstructured":"Heremans, J. P., Cava, R. J. & Samarth, N. Tetradymites as thermoelectrics and topological insulators. Nat. Rev. Mater. 2, 17049 (2017).","journal-title":"Nat. Rev. Mater."},{"key":"382_CR44","doi-asserted-by":"crossref","unstructured":"Ehrhardt, M. & Koprucki, T. (eds) Multi-band effective mass approximations. In Lecture Notes in Computational Science and Engineering Vol. 94 (Springer, 2014).","DOI":"10.1007\/978-3-319-01427-2"},{"key":"382_CR45","doi-asserted-by":"publisher","first-page":"635","DOI":"10.1038\/s41586-022-04501-x","volume":"604","author":"M Scheffler","year":"2022","unstructured":"Scheffler, M. et al. FAIR data enabling new horizons for materials research. Nature 604, 635\u2013642 (2022).","journal-title":"Nature"},{"key":"382_CR46","doi-asserted-by":"publisher","first-page":"214513","DOI":"10.1103\/PhysRevB.71.214513","volume":"71","author":"AA Kordyuk","year":"2005","unstructured":"Kordyuk, A. A. et al. Bare electron dispersion from experiment: self-consistent self-energy analysis of photoemission data. Phys. Rev. B 71, 214513 (2005).","journal-title":"Phys. Rev. B"},{"key":"382_CR47","doi-asserted-by":"publisher","first-page":"685","DOI":"10.1038\/s42254-021-00345-y","volume":"3","author":"MM Noack","year":"2021","unstructured":"Noack, M. M. et al. Gaussian processes for autonomous data acquisition at large-scale synchrotron and neutron facilities. Nat. Rev. Phys. 3, 685\u2013697 (2021).","journal-title":"Nat. Rev. Phys."},{"key":"382_CR48","doi-asserted-by":"publisher","first-page":"eabd9275","DOI":"10.1126\/sciadv.abd9275","volume":"7","author":"S Beaulieu","year":"2021","unstructured":"Beaulieu, S. et al. Ultrafast dynamical Lifshitz transition. Sci. Adv. 7, eabd9275 (2021).","journal-title":"Sci. Adv."},{"key":"382_CR49","doi-asserted-by":"publisher","first-page":"236403","DOI":"10.1103\/PhysRevLett.125.236403","volume":"125","author":"D Curcio","year":"2020","unstructured":"Curcio, D. et al. Accessing the spectral function in a current-carrying device. Phys. Rev. Lett. 125, 236403 (2020).","journal-title":"Phys. Rev. Lett."},{"key":"382_CR50","doi-asserted-by":"publisher","first-page":"e1601832","DOI":"10.1126\/sciadv.1601832","volume":"3","author":"NR Wilson","year":"2017","unstructured":"Wilson, N. R. et al. Determination of band offsets, hybridization, and exciton binding in 2D semiconductor heterostructures. Sci. Adv. 3, e1601832 (2017).","journal-title":"Sci. Adv."},{"key":"382_CR51","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-019-11253-2","volume":"10","author":"S Ulstrup","year":"2019","unstructured":"Ulstrup, S. et al. Nanoscale mapping of quasiparticle band alignment. Nat. Commun. 10, 3283 (2019).","journal-title":"Nat. Commun."},{"key":"382_CR52","doi-asserted-by":"publisher","first-page":"132","DOI":"10.1016\/j.nima.2016.07.036","volume":"834","author":"R Ewings","year":"2016","unstructured":"Ewings, R. et al. Horace: software for the analysis of data from single crystal spectroscopy experiments at time-of-flight neutron instruments. Nucl. Instrum. Methods Phys. Res. A 834, 132\u2013142 (2016).","journal-title":"Nucl. Instrum. Methods Phys. Res. A"},{"key":"382_CR53","doi-asserted-by":"publisher","first-page":"097401","DOI":"10.1103\/PhysRevLett.120.097401","volume":"120","author":"CE Whittaker","year":"2018","unstructured":"Whittaker, C. E. et al. Exciton polaritons in a two-dimensional Lieb lattice with spin-orbit coupling. Phys. Rev. Lett. 120, 097401 (2018).","journal-title":"Phys. Rev. Lett."},{"key":"382_CR54","doi-asserted-by":"publisher","first-page":"849","DOI":"10.1002\/adom.201400150","volume":"2","author":"A Fr\u00f6lich","year":"2014","unstructured":"Fr\u00f6lich, A., Fischer, J., Wolff, C., Busch, K. & Wegener, M. Frequency-resolved reciprocal-space mapping of visible spontaneous emission from 3D photonic crystals. Adv. Opt. Mater. 2, 849\u2013853 (2014).","journal-title":"Adv. Opt. Mater."},{"key":"382_CR55","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms14402","volume":"8","author":"I Amenabar","year":"2017","unstructured":"Amenabar, I. et al. Hyperspectral infrared nanoimaging of organic samples based on Fourier transform infrared nanospectroscopy. Nat. Commun. 8, 14402 (2017).","journal-title":"Nat. Commun."},{"key":"382_CR56","unstructured":"von Rueden, L. et al. Informed machine learning\u2014a taxonomy and survey of integrating prior knowledge into learning systems. IEEE Trans. Knowl. Data Eng. 35, 614\u2013633 (2023)."},{"key":"382_CR57","doi-asserted-by":"publisher","first-page":"3968","DOI":"10.1063\/1.1405781","volume":"72","author":"A Oelsner","year":"2001","unstructured":"Oelsner, A. et al. Microspectroscopy and imaging using a delay line detector in time-of-flight photoemission microscopy. Rev. Sci. Instrum. 72, 3968\u20133974 (2001).","journal-title":"Rev. Sci. Instrum."},{"key":"382_CR58","doi-asserted-by":"publisher","DOI":"10.1038\/s41597-020-00769-8","volume":"7","author":"RP Xian","year":"2020","unstructured":"Xian, R. P. et al. An open-source, end-to-end workflow for multidimensional photoemission spectroscopy. Sci. Data 7, 442 (2020).","journal-title":"Sci. Data"},{"key":"382_CR59","unstructured":"SPECS GmbH. METIS 1000 Brochure (SPECS, 2019); https:\/\/www.specs-group.com\/fileadmin\/user_upload\/products\/brochures\/SPECS_Brochure-METIS_RZ_web.pdf"},{"key":"382_CR60","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1016\/j.ultramic.2019.04.004","volume":"202","author":"RP Xian","year":"2019","unstructured":"Xian, R. P., Rettig, L. & Ernstorfer, R. Symmetry-guided nonrigid registration: the case for distortion correction in multidimensional photoemission spectroscopy. Ultramicroscopy 202, 133\u2013139 (2019).","journal-title":"Ultramicroscopy"},{"key":"382_CR61","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1016\/0262-8856(84)90040-4","volume":"2","author":"J Kittler","year":"1984","unstructured":"Kittler, J. & F\u00f6glein, J. Contextual classification of multispectral pixel data. Image Vision Comput. 2, 13\u201329 (1984).","journal-title":"Image Vision Comput."},{"key":"382_CR62","unstructured":"Abadi, M. et al. TensorFlow: large-scale machine learning on heterogeneous distributed systems. Preprint at https:\/\/arxiv.org\/abs\/1603.04467 (2016)."},{"key":"382_CR63","unstructured":"Li, S. Markov Random Field Modeling in Image Analysis 3rd edn (Springer, 2009)."},{"key":"382_CR64","unstructured":"Stimper, V. & Xian, R. P. Fuller. https:\/\/github.com\/mpes-kit\/fuller"},{"key":"382_CR65","doi-asserted-by":"publisher","first-page":"140","DOI":"10.1016\/j.commatsci.2016.10.015","volume":"128","author":"Y Hinuma","year":"2017","unstructured":"Hinuma, Y., Pizzi, G., Kumagai, Y., Oba, F. & Tanaka, I. Band structure diagram paths based on crystallography. Comput. Mater. Sci. 128, 140\u2013184 (2017).","journal-title":"Comput. Mater. Sci."},{"key":"382_CR66","doi-asserted-by":"publisher","first-page":"566","DOI":"10.1103\/PhysRevLett.45.566","volume":"45","author":"DM Ceperley","year":"1980","unstructured":"Ceperley, D. M. & Alder, B. J. Ground state of the electron gas by a stochastic method. Phys. Rev. Lett. 45, 566\u2013569 (1980).","journal-title":"Phys. Rev. Lett."},{"key":"382_CR67","doi-asserted-by":"publisher","first-page":"13244","DOI":"10.1103\/PhysRevB.45.13244","volume":"45","author":"JP Perdew","year":"1992","unstructured":"Perdew, J. P. & Wang, Y. Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Rev. B 45, 13244\u201313249 (1992).","journal-title":"Phys. Rev. B"},{"key":"382_CR68","doi-asserted-by":"publisher","first-page":"3865","DOI":"10.1103\/PhysRevLett.77.3865","volume":"77","author":"JP Perdew","year":"1996","unstructured":"Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865\u20133868 (1996).","journal-title":"Phys. Rev. Lett."},{"key":"382_CR69","doi-asserted-by":"publisher","first-page":"136406","DOI":"10.1103\/PhysRevLett.100.136406","volume":"100","author":"JP Perdew","year":"2008","unstructured":"Perdew, J. P. et al. Restoring the density-gradient expansion for exchange in solids and surfaces. Phys. Rev. Lett. 100, 136406 (2008).","journal-title":"Phys. Rev. Lett."},{"key":"382_CR70","doi-asserted-by":"publisher","first-page":"8207","DOI":"10.1063\/1.1564060","volume":"118","author":"J Heyd","year":"2003","unstructured":"Heyd, J., Scuseria, G. E. & Ernzerhof, M. Hybrid functionals based on a screened Coulomb potential. J. Chem. Phys. 118, 8207\u20138215 (2003).","journal-title":"J. Chem. Phys."},{"key":"382_CR71","doi-asserted-by":"publisher","first-page":"2175","DOI":"10.1016\/j.cpc.2009.06.022","volume":"180","author":"V Blum","year":"2009","unstructured":"Blum, V. et al. Ab initio molecular simulations with numeric atom-centered orbitals. Comput. Phys. Commun. 180, 2175\u20132196 (2009).","journal-title":"Comput. Phys. Commun."},{"key":"382_CR72","doi-asserted-by":"publisher","first-page":"033803","DOI":"10.1103\/PhysRevMaterials.1.033803","volume":"1","author":"WP Huhn","year":"2017","unstructured":"Huhn, W. P. & Blum, V. One-hundred-three compound band-structure benchmark of post-self-consistent spin-orbit coupling treatments in density functional theory. Phys. Rev. Mater. 1, 033803 (2017).","journal-title":"Phys. Rev. Mater."},{"key":"382_CR73","unstructured":"Wyant, J. C. & Creath, K. in Applied Optics and Optical Engineering Vol. Xl (eds Shannon, R R. & Wyant, J. C.) 1\u201353 (Academic Press, 1992)."},{"key":"382_CR74","unstructured":"Watkins, D. S. Fundamentals of Matrix Computations 3rd edn (Wiley, 2010)."},{"key":"382_CR75","unstructured":"Zacharias, M. & Carbogno, C. First-principles calculations for 2H-WSe2. NOMAD Repository https:\/\/nomad-lab.eu\/prod\/rae\/gui\/dataset\/id\/CS7f_obIQd6hE3-2JHfSuw (2020)."},{"key":"382_CR76","doi-asserted-by":"publisher","unstructured":"Xian, R. P. et al. Dataset of photoemission valence-band mapping and band reconstruction of 2H-WSe2. Zenodo https:\/\/doi.org\/10.5281\/zenodo.7314278 (2022).","DOI":"10.5281\/zenodo.7314278"},{"key":"382_CR77","doi-asserted-by":"publisher","unstructured":"Dendzik, M. et al. Excited-state photoemission band mapping data of the topological insulator Bi2Te2Se. Zenodo https:\/\/doi.org\/10.5281\/zenodo.7317667 (2022).","DOI":"10.5281\/zenodo.7317667"},{"key":"382_CR78","doi-asserted-by":"publisher","unstructured":"Dendzik, M. et al. Synchrotron bulk photoemission data from Au(111) and DFT calculations. Zenodo https:\/\/doi.org\/10.5281\/zenodo.7305241 (2022).","DOI":"10.5281\/zenodo.7305241"},{"key":"382_CR79","doi-asserted-by":"publisher","unstructured":"Xian, R. P. et al. Fuller: code and examples for the band structure reconstruction workflow. Zenodo https:\/\/doi.org\/10.5281\/zenodo.7325584 (2022).","DOI":"10.5281\/zenodo.7325584"}],"container-title":["Nature Computational Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s43588-022-00382-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s43588-022-00382-2","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s43588-022-00382-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,29]],"date-time":"2023-01-29T19:08:25Z","timestamp":1675019305000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s43588-022-00382-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,30]]},"references-count":79,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["382"],"URL":"https:\/\/doi.org\/10.1038\/s43588-022-00382-2","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-1407122\/v1","asserted-by":"object"}]},"ISSN":["2662-8457"],"issn-type":[{"value":"2662-8457","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,30]]},"assertion":[{"value":"1 March 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 November 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 December 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 January 2023","order":4,"name":"change_date","label":"Change Date","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Update","order":5,"name":"change_type","label":"Change Type","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"In the version of this article initially published online, refs. 76\u201379 were not presented as doi-based references, while the Editor recognition statement was missing. The changes have been made in the HTML and PDF versions of the article.","order":6,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}]}}