{"id":"https://openalex.org/W4402850604","doi":"https://doi.org/10.1137/23m1607799","title":"Nonlinear Embeddings for Conserving Hamiltonians and Other Quantities with Neural Galerkin Schemes","display_name":"Nonlinear Embeddings for Conserving Hamiltonians and Other Quantities with Neural Galerkin Schemes","publication_year":2024,"publication_date":"2024-09-25","ids":{"openalex":"https://openalex.org/W4402850604","doi":"https://doi.org/10.1137/23m1607799"},"language":"en","primary_location":{"id":"doi:10.1137/23m1607799","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1607799","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016263174","display_name":"Paul Schwerdtner","orcid":"https://orcid.org/0000-0001-8761-9217"},"institutions":[{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Paul Schwerdtner","raw_affiliation_strings":["Corresponding author. Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 USA"],"raw_orcid":"https://orcid.org/0000-0001-8761-9217","affiliations":[{"raw_affiliation_string":"Corresponding author. Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 USA","institution_ids":["https://openalex.org/I36672615"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006470906","display_name":"Philipp Schulze","orcid":"https://orcid.org/0000-0002-7299-4628"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Philipp Schulze","raw_affiliation_strings":["Technische Universit\u00e4t Berlin, 10623 Berlin, Germany"],"raw_orcid":"https://orcid.org/0000-0002-7299-4628","affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Berlin, 10623 Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064983883","display_name":"Jules J. Berman","orcid":null},"institutions":[{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jules Berman","raw_affiliation_strings":["Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 USA","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027402421","display_name":"Benjamin Peherstorfer","orcid":"https://orcid.org/0000-0002-1558-6775"},"institutions":[{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Benjamin Peherstorfer","raw_affiliation_strings":["Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 USA"],"raw_orcid":"https://orcid.org/0000-0002-1558-6775","affiliations":[{"raw_affiliation_string":"Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 USA","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5016263174"],"corresponding_institution_ids":["https://openalex.org/I36672615"],"apc_list":null,"apc_paid":null,"fwci":1.887,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.8580882,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"46","issue":"5","first_page":"C583","last_page":"C607"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7952933311462402},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.7210525870323181},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6977263689041138},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5529285073280334},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3709893226623535},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08093348145484924}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7952933311462402},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.7210525870323181},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6977263689041138},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5529285073280334},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3709893226623535},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08093348145484924},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/23m1607799","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1607799","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2859371015","display_name":null,"funder_award_id":"2046521","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6179710623","display_name":null,"funder_award_id":"N00014-22-1-2728","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G7583106547","display_name":null,"funder_award_id":"FA9550-21-1-0222","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":60,"referenced_works":["https://openalex.org/W1515678755","https://openalex.org/W1544770838","https://openalex.org/W1665592869","https://openalex.org/W1788163261","https://openalex.org/W1902394114","https://openalex.org/W1965357780","https://openalex.org/W1969824994","https://openalex.org/W1995504856","https://openalex.org/W2003468238","https://openalex.org/W2006042718","https://openalex.org/W2040642276","https://openalex.org/W2147414751","https://openalex.org/W2168386575","https://openalex.org/W2290725312","https://openalex.org/W2297679915","https://openalex.org/W2515869736","https://openalex.org/W2542306153","https://openalex.org/W2773572071","https://openalex.org/W2803629276","https://openalex.org/W2805132766","https://openalex.org/W2885643524","https://openalex.org/W2902774355","https://openalex.org/W2974671401","https://openalex.org/W2976100866","https://openalex.org/W2978339362","https://openalex.org/W2990138404","https://openalex.org/W3003292238","https://openalex.org/W3008005432","https://openalex.org/W3024413179","https://openalex.org/W3025765672","https://openalex.org/W3097181558","https://openalex.org/W3098680501","https://openalex.org/W3106790087","https://openalex.org/W3140960170","https://openalex.org/W3150423751","https://openalex.org/W3158004996","https://openalex.org/W3162324712","https://openalex.org/W3174510059","https://openalex.org/W3179076679","https://openalex.org/W3207960601","https://openalex.org/W4200357168","https://openalex.org/W4210995191","https://openalex.org/W4213321166","https://openalex.org/W4223983369","https://openalex.org/W4254671851","https://openalex.org/W4255754126","https://openalex.org/W4292170110","https://openalex.org/W4302564868","https://openalex.org/W4319263538","https://openalex.org/W4322742850","https://openalex.org/W4323669582","https://openalex.org/W4328051924","https://openalex.org/W4367054992","https://openalex.org/W4380878066","https://openalex.org/W4384008083","https://openalex.org/W4386236687","https://openalex.org/W4386534940","https://openalex.org/W4387910988","https://openalex.org/W4392699414","https://openalex.org/W4399125066"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W4235910846","https://openalex.org/W1986323742","https://openalex.org/W2943697195"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2}],"updated_date":"2025-12-23T23:11:35.936235","created_date":"2025-10-10T00:00:00"}