{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T16:08:28Z","timestamp":1770739708317,"version":"3.49.0"},"reference-count":68,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"3","license":[{"start":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T00:00:00Z","timestamp":1772323200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T00:00:00Z","timestamp":1772323200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T00:00:00Z","timestamp":1772323200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U22B2054"],"award-info":[{"award-number":["U22B2054"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62406230"],"award-info":[{"award-number":["62406230"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62076192"],"award-info":[{"award-number":["62076192"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62276199"],"award-info":[{"award-number":["62276199"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62431020"],"award-info":[{"award-number":["62431020"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62276201"],"award-info":[{"award-number":["62276201"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013314","name":"Higher Education Discipline Innovation Project","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100013314","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Program for Cheung Kong Scholars and Innovative Research Team in University","award":["IRT 15R53"],"award-info":[{"award-number":["IRT 15R53"]}]},{"name":"Science and Technology Innovation Project from the Chinese Ministry of Education"},{"name":"National Key Laboratory of Human-Machine Hybrid Augmented Intelligence"},{"name":"Xi&#x2019;an Jiaotong University","award":["HMHAI-202404"],"award-info":[{"award-number":["HMHAI-202404"]}]},{"name":"Xi&#x2019;an Jiaotong University","award":["HMHAI-202405"],"award-info":[{"award-number":["HMHAI-202405"]}]},{"name":"Postdoctoral Fellowship Program of CPSF","award":["GZC20232037"],"award-info":[{"award-number":["GZC20232037"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Pattern Anal. Mach. Intell."],"published-print":{"date-parts":[[2026,3]]},"DOI":"10.1109\/tpami.2025.3640844","type":"journal-article","created":{"date-parts":[[2025,12,5]],"date-time":"2025-12-05T18:37:55Z","timestamp":1764959875000},"page":"3556-3570","source":"Crossref","is-referenced-by-count":0,"title":["Physics-Informed Matrix Factorization Operator"],"prefix":"10.1109","volume":"48","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0892-2109","authenticated-orcid":false,"given":"Wenming","family":"Wu","sequence":"first","affiliation":[{"name":"Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, International Research Center for Intelligent Perception and Computation, School of Artificial Intelligence, Xidian University, Xi&#x2019;an, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4582-2847","authenticated-orcid":false,"given":"Chenxi","family":"Tian","sequence":"additional","affiliation":[{"name":"Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, International Research Center for Intelligent Perception and Computation, School of Artificial Intelligence, Xidian University, Xi&#x2019;an, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3354-9617","authenticated-orcid":false,"given":"Licheng","family":"Jiao","sequence":"additional","affiliation":[{"name":"Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, International Research Center for Intelligent Perception and Computation, School of Artificial Intelligence, Xidian University, Xi&#x2019;an, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6130-2518","authenticated-orcid":false,"given":"Lingling","family":"Li","sequence":"additional","affiliation":[{"name":"Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, International Research Center for Intelligent Perception and Computation, School of Artificial Intelligence, Xidian University, Xi&#x2019;an, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8780-5455","authenticated-orcid":false,"given":"Xu","family":"Liu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, International Research Center for Intelligent Perception and Computation, School of Artificial Intelligence, Xidian University, Xi&#x2019;an, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5669-9354","authenticated-orcid":false,"given":"Fang","family":"Liu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, International Research Center for Intelligent Perception and Computation, School of Artificial Intelligence, Xidian University, Xi&#x2019;an, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8872-2195","authenticated-orcid":false,"given":"Wenping","family":"Ma","sequence":"additional","affiliation":[{"name":"Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, International Research Center for Intelligent Perception and Computation, School of Artificial Intelligence, Xidian University, Xi&#x2019;an, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4796-5737","authenticated-orcid":false,"given":"Shuyuan","family":"Yang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, International Research Center for Intelligent Perception and Computation, School of Artificial Intelligence, Xidian University, Xi&#x2019;an, China"}]}],"member":"263","reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2020.3000512"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1109\/MGRS.2022.3145854"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1109\/TGRS.2023.3315970"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2019.2900306"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2025.3534435"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2024.3510048"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2019.2962679"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1109\/tpami.2024.3380568"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1038\/44565"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1137\/1035134"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1016\/0169-7439(87)80084-9"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1007\/s10462-024-10874-4"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1109\/PROC.1969.7278"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2023.3241779"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1109\/TGRS.2023.3277973"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2020.2986830"},{"key":"ref17","first-page":"26548","article-title":"Characterizing possible failure modes in physics-informed neural networks","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","volume":"34","author":"Krishnapriyan","year":"2021"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2022.3152723"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1109\/TKDE.2023.3335223"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2023.3238104"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-67658-2_20"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2021.3054635"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1016\/j.inffus.2023.101884"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2023.3238419"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2021.3111824"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1109\/TGRS.2019.2893116"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2020.3034462"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2022.3184286"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2024.3442435"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2024.3450575"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2023.3327631"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2022.3224978"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v36i8.20830"},{"key":"ref34","first-page":"10773","article-title":"Composing partial differential equations with physics-aware neural networks","volume-title":"Proc. Int. Conf. Mach. Learn.","author":"Karlbauer","year":"2022"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2023.116172"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2023.115396"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1007\/s44379-025-00016-0"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1109\/CVPRW63382.2024.00446"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-023-41597-9"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2023.3338178"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2022.0576"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2023.3348948"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1109\/MLSP.2019.8918835"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139086967"},{"key":"ref45","volume-title":"Computational Science and Engineering","author":"Strang","year":"2007"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.56021\/9781421407944"},{"key":"ref47","article-title":"DifFormer: Scalable (graph) transformers induced by energy constrained diffusion","author":"Wu","year":"2023"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511623783"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1016\/j.patcog.2007.09.010"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2008.79"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2018.2828815"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1109\/TKDE.2020.3022072"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2019.2913022"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v38i10.29016"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1016\/j.patcog.2023.109836"},{"key":"ref56","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2023.119622"},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1002\/widm.32"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.1515\/9781400873173"},{"key":"ref59","doi-asserted-by":"publisher","DOI":"10.1561\/2200000016"},{"key":"ref60","doi-asserted-by":"publisher","DOI":"10.1007\/s11263-007-0109-1"},{"key":"ref61","doi-asserted-by":"publisher","DOI":"10.1109\/ACV.1994.341300"},{"key":"ref62","doi-asserted-by":"publisher","DOI":"10.18772\/10539\/20690"},{"key":"ref63","article-title":"Columbia object image library (coil-20)","author":"Nene","year":"1996"},{"key":"ref64","doi-asserted-by":"publisher","DOI":"10.1109\/34.291440"},{"key":"ref65","doi-asserted-by":"publisher","DOI":"10.1038\/415530a"},{"key":"ref66","doi-asserted-by":"publisher","DOI":"10.1038\/nm0102-68"},{"key":"ref67","doi-asserted-by":"publisher","DOI":"10.1038\/ng765"},{"key":"ref68","doi-asserted-by":"publisher","DOI":"10.1093\/bioinformatics\/bti033"}],"container-title":["IEEE Transactions on Pattern Analysis and Machine Intelligence"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx8\/34\/11372200\/11278613.pdf?arnumber=11278613","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,9]],"date-time":"2026-02-09T21:06:20Z","timestamp":1770671180000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/11278613\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3]]},"references-count":68,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.1109\/tpami.2025.3640844","relation":{},"ISSN":["0162-8828","2160-9292","1939-3539"],"issn-type":[{"value":"0162-8828","type":"print"},{"value":"2160-9292","type":"electronic"},{"value":"1939-3539","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3]]}}}