{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T23:10:28Z","timestamp":1773184228083,"version":"3.50.1"},"reference-count":45,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/100018928","name":"Westlake University","doi-asserted-by":"publisher","award":["WU2024A001"],"award-info":[{"award-number":["WU2024A001"]}],"id":[{"id":"10.13039\/100018928","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Neurocomputing"],"published-print":{"date-parts":[[2026,5]]},"DOI":"10.1016\/j.neucom.2026.133000","type":"journal-article","created":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T16:48:48Z","timestamp":1770828528000},"page":"133000","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Latent selective state-space models for partial differential equations via progressive learning"],"prefix":"10.1016","volume":"676","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-4850-833X","authenticated-orcid":false,"given":"A.Aoming","family":"Liang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"B.Zhaoyang","family":"Mu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"C.Pengxiao","family":"Lin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/j.neucom.2026.133000_bib0005","first-page":"1","article-title":"Machine learning applied to weather forecasting","volume":"10","author":"Holmstrom","year":"2016","journal-title":"Meteorol. Appl."},{"key":"10.1016\/j.neucom.2026.133000_bib0010","doi-asserted-by":"crossref","DOI":"10.1016\/j.engappai.2022.105697","article-title":"Review of artificial intelligence applications in engineering design perspective","volume":"118","author":"Y\u00fcksel","year":"2023","journal-title":"Eng. Appl. Artif. Intell."},{"key":"10.1016\/j.neucom.2026.133000_bib0015","doi-asserted-by":"crossref","DOI":"10.1088\/1361-6587\/acc60f","article-title":"Machine learning and Bayesian inference in nuclear fusion research: an overview","volume":"65","author":"Pavone","year":"2023","journal-title":"Plasma Phys. Control. Fusion"},{"key":"10.1016\/j.neucom.2026.133000_bib0020","doi-asserted-by":"crossref","first-page":"e55","DOI":"10.1017\/hpl.2023.47","article-title":"Data-driven science and machine learning methods in laser\u2013plasma Physics","volume":"11","author":"D\u00f6pp","year":"2023","journal-title":"High Power Laser Sci. Eng."},{"key":"10.1016\/j.neucom.2026.133000_bib0025","first-page":"2240","article-title":"Learning to accelerate partial differential equations via latent global evolution","volume":"35","author":"Wu","year":"2022","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"10.1016\/j.neucom.2026.133000_bib0030","author":"Hu"},{"key":"10.1016\/j.neucom.2026.133000_bib0035","series-title":"Large-Scale PDE-Constrained Optimization","first-page":"3","article-title":"Large-scale pde-constrained optimization: an introduction","author":"Biegler","year":"2003"},{"key":"10.1016\/j.neucom.2026.133000_bib0040","author":"Li"},{"key":"10.1016\/j.neucom.2026.133000_bib0045","first-page":"1","article-title":"Deep hidden Physics models: deep learning of nonlinear partial differential equations","volume":"19","author":"Raissi","year":"2018","journal-title":"J. Mach. Learn. Res."},{"key":"10.1016\/j.neucom.2026.133000_bib0050","article-title":"Applications of Physics informed neural operators","volume":"4","author":"Rosofsky","year":"2023","journal-title":"Mach. Learn.: Sci. Technol."},{"key":"10.1016\/j.neucom.2026.133000_bib0055","doi-asserted-by":"crossref","first-page":"1339","DOI":"10.1016\/j.jcp.2018.08.029","article-title":"DGM: a deep learning algorithm for solving partial differential equations","volume":"375","author":"Sirignano","year":"2018","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.neucom.2026.133000_bib0060","series-title":"Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining","first-page":"481","article-title":"Convolutional neural networks for steady flow approximation","author":"Guo","year":"2016"},{"key":"10.1016\/j.neucom.2026.133000_bib0065","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1017\/S0956792520000182","article-title":"Solving parametric PDE problems with artificial neural networks","volume":"32","author":"Khoo","year":"2021","journal-title":"Eur. J. Appl. Math."},{"key":"10.1016\/j.neucom.2026.133000_bib0070","author":"Li"},{"key":"10.1016\/j.neucom.2026.133000_bib0075","first-page":"6755","article-title":"Multipole graph neural operator for parametric partial differential equations","volume":"33","author":"Li","year":"2020","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"10.1016\/j.neucom.2026.133000_bib0080","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":"Nat. Mach. Intell."},{"key":"10.1016\/j.neucom.2026.133000_bib0085","author":"Chalapathi"},{"key":"10.1016\/j.neucom.2026.133000_bib0090","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2023.116204","article-title":"Adaptive learning of effective dynamics for online modeling of complex systems","volume":"415","author":"Ki\u010di\u0107","year":"2023","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"10.1016\/j.neucom.2026.133000_bib0095","author":"Gu"},{"key":"10.1016\/j.neucom.2026.133000_bib0100","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1007\/s40687-019-0197-x","article-title":"PDE acceleration: a convergence rate analysis and applications to obstacle problems","volume":"6","author":"Calder","year":"2019","journal-title":"Res. Math. Sci."},{"key":"10.1016\/j.neucom.2026.133000_bib0105","series-title":"The International Conference on Artificial Intelligence and Logistics Engineering","first-page":"3","article-title":"Accelerating simulation of the PDE solution by the structure of the convolutional neural network modifying","author":"Kuzmych","year":"2022"},{"key":"10.1016\/j.neucom.2026.133000_bib0110","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/j.cag.2022.02.004","article-title":"Graph neural network-accelerated Lagrangian fluid simulation","volume":"103","author":"Li","year":"2022","journal-title":"Comput. Graph."},{"key":"10.1016\/j.neucom.2026.133000_bib0115","first-page":"1","article-title":"Neural operator: learning maps between function spaces with applications to PDES","volume":"24","author":"Kovachki","year":"2023","journal-title":"J. Mach. Learn. Res."},{"key":"10.1016\/j.neucom.2026.133000_bib0120","author":"Wu"},{"key":"10.1016\/j.neucom.2026.133000_bib0125","author":"Huang"},{"key":"10.1016\/j.neucom.2026.133000_bib0130","author":"Wang"},{"key":"10.1016\/j.neucom.2026.133000_bib0135","author":"Kumar"},{"key":"10.1016\/j.neucom.2026.133000_bib0140","series-title":"Proceedings of the AAAI Conference on Artificial Intelligence","first-page":"11561","article-title":"SNN-PDE: learning dynamic PDEs from data with simplicial neural networks","volume":"vol. 38","author":"Choi","year":"2024"},{"key":"10.1016\/j.neucom.2026.133000_bib0145","author":"Wang"},{"key":"10.1016\/j.neucom.2026.133000_bib0150","doi-asserted-by":"crossref","DOI":"10.1016\/j.jcp.2024.113194","article-title":"Koopman neural operator as a mesh-free solver of non-linear partial differential equations","author":"Xiong","year":"2024","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.neucom.2026.133000_bib0155","author":"Brandstetter"},{"key":"10.1016\/j.neucom.2026.133000_bib0160","first-page":"24924","article-title":"Choose a transformer: Fourier or Galerkin","volume":"34","author":"Cao","year":"2021","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"10.1016\/j.neucom.2026.133000_bib0165","author":"Li"},{"key":"10.1016\/j.neucom.2026.133000_bib0170","series-title":"ICLR 2025 Workshop on Foundation Models in the Wild","article-title":"Unisolver: PDE-conditional transformers are universal neural PDE solvers","author":"Zhou","year":"2025"},{"key":"10.1016\/j.neucom.2026.133000_bib0175","author":"Cheng"},{"key":"10.1016\/j.neucom.2026.133000_bib0180","series-title":"The Thirteenth International Conference on Learning Representations","article-title":"Mamko: mamba-based koopman operator for modeling and predictive control","author":"Li","year":"2025"},{"key":"10.1016\/j.neucom.2026.133000_bib0185","first-page":"52962","article-title":"Alias-free mamba neural operator","volume":"37","author":"Zheng","year":"2024","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"10.1016\/j.neucom.2026.133000_bib0190","author":"Liang"},{"key":"10.1016\/j.neucom.2026.133000_bib0195","first-page":"1474","article-title":"Hippo: Recurrent memory with optimal polynomial projections","volume":"33","author":"Gu","year":"2020","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"10.1016\/j.neucom.2026.133000_bib0200","author":"Brandstetter"},{"key":"10.1016\/j.neucom.2026.133000_bib0205","series-title":"Proceedings of the Fifth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining","first-page":"23","article-title":"Efficient progressive sampling","author":"Provost","year":"1999"},{"key":"10.1016\/j.neucom.2026.133000_bib0210","article-title":"Scheduled sampling for sequence prediction with recurrent neural networks","volume":"28","author":"Bengio","year":"2015","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"10.1016\/j.neucom.2026.133000_bib0215","first-page":"4555","article-title":"A survey on curriculum learning","volume":"44","author":"Wang","year":"2021","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"10.1016\/j.neucom.2026.133000_bib0220","author":"Tali"},{"key":"10.1016\/j.neucom.2026.133000_bib0225","series-title":"Controlling Laplacian eigenfluids","author":"B\u00f6rcs\u00f6k","year":"2023"}],"container-title":["Neurocomputing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0925231226003978?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0925231226003978?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T03:51:45Z","timestamp":1773114705000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0925231226003978"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5]]},"references-count":45,"alternative-id":["S0925231226003978"],"URL":"https:\/\/doi.org\/10.1016\/j.neucom.2026.133000","relation":{},"ISSN":["0925-2312"],"issn-type":[{"value":"0925-2312","type":"print"}],"subject":[],"published":{"date-parts":[[2026,5]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Latent selective state-space models for partial differential equations via progressive learning","name":"articletitle","label":"Article Title"},{"value":"Neurocomputing","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.neucom.2026.133000","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"133000"}}