{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T23:59:11Z","timestamp":1762300751105,"version":"3.40.5"},"reference-count":40,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12171466"],"award-info":[{"award-number":["12171466"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2024,10,31]]},"DOI":"10.1137\/22m152373x","type":"journal-article","created":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T13:52:51Z","timestamp":1725457971000},"page":"2087-2120","source":"Crossref","is-referenced-by-count":1,"title":["Error Analysis Based on Inverse Modified Differential Equations for Discovery of Dynamics Using Linear Multistep Methods and Deep Learning"],"prefix":"10.1137","volume":"62","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7473-9604","authenticated-orcid":true,"given":"Aiqing","family":"Zhu","sequence":"first","affiliation":[{"name":"LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China."}]},{"given":"Sidi","family":"Wu","sequence":"additional","affiliation":[{"name":"LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China."}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3301-3487","authenticated-orcid":true,"given":"Yifa","family":"Tang","sequence":"additional","affiliation":[{"name":"LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China."}]}],"member":"351","published-online":{"date-parts":[[2024,9,4]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1016\/0098-1354(96)00133-0"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02188219"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1063\/1.5128231"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0609476104"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-017-00030-8"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1017\/9781108380690"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1517384113"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1007\/BF02551274"},{"key":"ref12","doi-asserted-by":"crossref","first-page":"e0119821","DOI":"10.1371\/journal.pone.0119821","volume":"10","author":"Daniels B. C.","year":"2014","journal-title":"PloS One"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2021.08.015"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492921000052"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1137\/21M140691X"},{"key":"ref17","first-page":"1","volume":"4","author":"Feng K.","year":"1993","journal-title":"Ser. Appl. Math."},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1016\/S0098-1354(98)00191-4"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1007\/s002110050469"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1007\/s002110050271"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142999353594"},{"key":"ref23","series-title":"Springer Ser. Comput. Math. 31","volume-title":"Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations","author":"Hairer E.","year":"2006"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-05221-7"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2008.2006703"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1016\/0893-6080(90)90005-6"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2022.111203"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1137\/19M130981X"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1080\/13873950500068567"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0469(1963)020<0130:DNF>2.0.CO;2"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1137\/20M134695X"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1137\/19M1274067"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2019.06.042"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2017.07.050"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142997329797"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.1602614"},{"volume-title":"Introduction to Complex Analysis in Several Variables","year":"2005","author":"Scheidemann V.","key":"ref48"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1126\/science.1165893"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107298019"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1162\/neco_a_01364"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.4208\/cicp.OA-2020-0193"},{"key":"ref53","series-title":"Appl. Math. Sci. 41","volume-title":"The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors","author":"Sparrow C.","year":"2012"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.3390\/math7080757"},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevFluids.6.114402"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2021.0207"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","deposited":{"date-parts":[[2024,9,24]],"date-time":"2024-09-24T19:37:27Z","timestamp":1727206647000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/22M152373X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,4]]},"references-count":40,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2024,10,31]]}},"alternative-id":["10.1137\/22M152373X"],"URL":"https:\/\/doi.org\/10.1137\/22m152373x","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"type":"print","value":"0036-1429"},{"type":"electronic","value":"1095-7170"}],"subject":[],"published":{"date-parts":[[2024,9,4]]}}}