{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T20:03:47Z","timestamp":1778097827696,"version":"3.51.4"},"reference-count":22,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/501100013287","name":"Science Challenge Project","doi-asserted-by":"publisher","award":["TZ2018001"],"award-info":[{"award-number":["TZ2018001"]}],"id":[{"id":"10.13039\/501100013287","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11671265"],"award-info":[{"award-number":["11671265"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","award":["DE-SC0019453"],"award-info":[{"award-number":["DE-SC0019453"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","award":["100028801-BROWN-APP"],"award-info":[{"award-number":["100028801-BROWN-APP"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2020,1]]},"DOI":"10.1137\/19m1260141","type":"journal-article","created":{"date-parts":[[2020,3,16]],"date-time":"2020-03-16T15:49:32Z","timestamp":1584373772000},"page":"A639-A665","source":"Crossref","is-referenced-by-count":241,"title":["Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks"],"prefix":"10.1137","volume":"42","author":[{"given":"Dongkun","family":"Zhang","sequence":"first","affiliation":[]},{"given":"Ling","family":"Guo","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9713-7120","authenticated-orcid":true,"given":"George Em","family":"Karniadakis","sequence":"additional","affiliation":[]}],"member":"351","published-online":{"date-parts":[[2020,3,16]]},"reference":[{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2017.04.057"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1109\/72.286886"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1109\/72.392253"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2013.02.033"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2013.02.020"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2013.02.047"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2014.03.050"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1007\/BF02551274"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1109\/72.712178"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1109\/72.870037"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1016\/S0764-4442(00)01793-6"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1137\/140967787"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.4208\/cicp.020215.070515a"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2017.11.039"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1017\/jfm.2018.872"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2009.09.017"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2011.10.001"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1016\/j.ocemod.2016.01.006"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2012.08.041"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1137\/040615201"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827501387826"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2019.07.048"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/19M1260141","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,30]],"date-time":"2020-04-30T17:20:20Z","timestamp":1588267220000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/19M1260141"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1]]},"references-count":22,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2020,1]]}},"alternative-id":["10.1137\/19M1260141"],"URL":"https:\/\/doi.org\/10.1137\/19m1260141","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1]]}}}