{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T04:05:13Z","timestamp":1771905913954,"version":"3.50.1"},"reference-count":46,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"name":"PRIN 2017"},{"DOI":"10.13039\/100010661","name":"Horizon 2020 Framework Programme","doi-asserted-by":"publisher","award":["681447"],"award-info":[{"award-number":["681447"]}],"id":[{"id":"10.13039\/100010661","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2025,4,30]]},"DOI":"10.1137\/23m1604680","type":"journal-article","created":{"date-parts":[[2025,3,3]],"date-time":"2025-03-03T09:31:38Z","timestamp":1740994298000},"page":"C235-C264","source":"Crossref","is-referenced-by-count":4,"title":["Optimal Transport\u2013Inspired Deep Learning Framework for Slow-Decaying Kolmogorov \\({n}\\)-Width Problems: Exploiting Sinkhorn Loss and Wasserstein Kernel"],"prefix":"10.1137","volume":"47","author":[{"given":"Moaad","family":"Khamlich","sequence":"first","affiliation":[{"name":"mathLab, Mathematics Area, SISSA, I-34136 Trieste, Italy."}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1163-3386","authenticated-orcid":true,"given":"Federico","family":"Pichi","sequence":"additional","affiliation":[{"name":"mathLab, Mathematics Area, SISSA, I-34136 Trieste, Italy, and Chair of Computational Mathematics and Simulation Science, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, 1015 Lausanne, Switzerland."}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0810-8812","authenticated-orcid":true,"given":"Gianluigi","family":"Rozza","sequence":"additional","affiliation":[{"name":"mathLab, Mathematics Area, SISSA, I-34136 Trieste, Italy."}]}],"member":"351","published-online":{"date-parts":[[2025,3,3]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1137\/100805741"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611974829"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1515\/9783110498967"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2018.07.001"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1007\/BF00247653"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1016\/0893-9659(89)90079-7"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1017\/9781108380690"},{"key":"ref12","first-page":"808","volume":"78","author":"Chatterjee A.","year":"2000","journal-title":"Curr. Sci. India"},{"key":"ref13","volume-title":"Advances in Neural Information Processing Systems 22","author":"Cho Y.","year":"2009"},{"key":"ref14","volume-title":"Advances in Neural Information Processing Systems 26","author":"Cuturi M.","year":"2013"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1002\/nme.6831"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2020013"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.3.1.24"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-021-01462-7"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2021.114181"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1016\/j.comcom.2020.10.024"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2015.01.020"},{"key":"ref27","volume-title":"Deep Learning","author":"Goodfellow I.","year":"2016"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1051\/m2an:2007031"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2018.02.037"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2022.111671"},{"key":"ref31","volume-title":"Recurrent Neural Networks: Design and Applications","author":"Jain L. C.","year":"1999"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1038\/s42254-021-00314-5"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1142\/S012906570000034X"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2019.108973"},{"key":"ref35","doi-asserted-by":"crossref","unstructured":"T. M. Mitchell, J. G. Carbonell, and R. S. Michalski, Machine Learning, Springer Internat. Ser. Engrg. Comput. Sci. 12, McGraw-Hill, New York, 2007, https:\/\/doi.org\/10.1007\/978-1-4613-2279-5.","DOI":"10.1007\/978-1-4613-2279-5"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1016\/j.jocs.2021.101408"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-024-02694-z"},{"key":"ref39","first-page":"8024","volume-title":"Advances in Neural Information Processing Systems 32","author":"Paszke A.","year":"2019"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1561\/2200000073"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1016\/j.compfluid.2023.105813"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2024.112762"},{"key":"ref43","first-page":"1","author":"Plaen H. D.","year":"2020","journal-title":"2020 International Joint Conference on Neural Networks (IJCNN)"},{"key":"ref44","first-page":"932","volume":"19","author":"Raissi M.","year":"2018","journal-title":"J. Mach. Learn. Res."},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2018.10.045"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.3390\/e19020047"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1515\/9781400873173"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-023-02128-2"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2021.11.001"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-20828-2"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-78841-6"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1967.21.343"},{"key":"ref54","first-page":"1","volume":"20","author":"Sommerfeld M.","year":"2019","journal-title":"J. Mach. Learn. Res."},{"key":"ref56","doi-asserted-by":"publisher","DOI":"10.1137\/19M1271270"},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2021.11.010"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2019.01.031"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","deposited":{"date-parts":[[2025,3,3]],"date-time":"2025-03-03T09:31:54Z","timestamp":1740994314000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/23M1604680"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,3]]},"references-count":46,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,4,30]]}},"alternative-id":["10.1137\/23M1604680"],"URL":"https:\/\/doi.org\/10.1137\/23m1604680","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,3]]}}}