{"id":"https://openalex.org/W7157071593","doi":"https://doi.org/10.1038/s43588-026-00974-2","title":"NOEM: efficient and scalable finite element method enabled by reusable neural operators","display_name":"NOEM: efficient and scalable finite element method enabled by reusable neural operators","publication_year":2026,"publication_date":"2026-04-28","ids":{"openalex":"https://openalex.org/W7157071593","doi":"https://doi.org/10.1038/s43588-026-00974-2","pmid":"https://pubmed.ncbi.nlm.nih.gov/42050047"},"language":"en","primary_location":{"id":"doi:10.1038/s43588-026-00974-2","is_oa":false,"landing_page_url":"https://doi.org/10.1038/s43588-026-00974-2","pdf_url":null,"source":{"id":"https://openalex.org/S4210228084","display_name":"Nature Computational Science","issn_l":"2662-8457","issn":["2662-8457"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nature Computational Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5031017069","display_name":"Weihang Ouyang","orcid":null},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]},{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["HK","US"],"is_corresponding":false,"raw_author_name":"Weihang Ouyang","raw_affiliation_strings":["Department of Civil and Environmental Engineering, Hong Kong Polytechnic University, Hong Kong, China","Department of Statistics and Data Science, Yale University, New Haven, CT, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Civil and Environmental Engineering, Hong Kong Polytechnic University, Hong Kong, China","institution_ids":["https://openalex.org/I14243506"]},{"raw_affiliation_string":"Department of Statistics and Data Science, Yale University, New Haven, CT, USA","institution_ids":["https://openalex.org/I32971472"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023632213","display_name":"Yeonjong Shin","orcid":"https://orcid.org/0000-0003-4577-1979"},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yeonjong Shin","raw_affiliation_strings":["Department of Mathematics, North Carolina State University, Raleigh, NC, USA"],"raw_orcid":"https://orcid.org/0000-0003-4577-1979","affiliations":[{"raw_affiliation_string":"Department of Mathematics, North Carolina State University, Raleigh, NC, USA","institution_ids":["https://openalex.org/I137902535"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134760881","display_name":"Si-Wei Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Si-Wei Liu","raw_affiliation_strings":["Department of Civil and Environmental Engineering, Hong Kong Polytechnic University, Hong Kong, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Civil and Environmental Engineering, Hong Kong Polytechnic University, Hong Kong, China","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5134816563","display_name":"Lu Lu","orcid":"https://orcid.org/0000-0002-5476-5768"},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Lu Lu","raw_affiliation_strings":["Department of Chemical and Environmental Engineering, Yale University, New Haven, CT, USA. lu.lu@yale.edu","Department of Statistics and Data Science, Yale University, New Haven, CT, USA. lu.lu@yale.edu"],"raw_orcid":"https://orcid.org/0000-0002-5476-5768","affiliations":[{"raw_affiliation_string":"Department of Chemical and Environmental Engineering, Yale University, New Haven, CT, USA. lu.lu@yale.edu","institution_ids":["https://openalex.org/I32971472"]},{"raw_affiliation_string":"Department of Statistics and Data Science, Yale University, New Haven, CT, USA. lu.lu@yale.edu","institution_ids":["https://openalex.org/I32971472"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5134816563"],"corresponding_institution_ids":["https://openalex.org/I32971472"],"apc_list":{"value":9750,"currency":"EUR","value_usd":11690},"apc_paid":null,"fwci":25.0303,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.994106,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"6","issue":"4","first_page":"417","last_page":"429"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.8465999960899353,"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":0.8465999960899353,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.05270000174641609,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"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":0.03189999982714653,"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/finite-element-method","display_name":"Finite element method","score":0.8072999715805054},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.7439000010490417},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.6171000003814697},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5659999847412109},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5465999841690063},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5315999984741211},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4555000066757202},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.38109999895095825}],"concepts":[{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.8072999715805054},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.7439000010490417},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.635699987411499},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.6171000003814697},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5659999847412109},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5465999841690063},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5315999984741211},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4555000066757202},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3917999863624573},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.38690000772476196},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.38109999895095825},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3686999976634979},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35370001196861267},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.33570000529289246},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3312999904155731},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.32030001282691956},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.3070000112056732},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.3046000003814697},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.29899999499320984},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.2849999964237213},{"id":"https://openalex.org/C177605945","wikidata":"https://www.wikidata.org/wiki/Q11007230","display_name":"Smoothed finite element method","level":5,"score":0.27880001068115234},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.2538999915122986},{"id":"https://openalex.org/C181145010","wikidata":"https://www.wikidata.org/wiki/Q4418033","display_name":"Mesh generation","level":3,"score":0.2535000145435333}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1038/s43588-026-00974-2","is_oa":false,"landing_page_url":"https://doi.org/10.1038/s43588-026-00974-2","pdf_url":null,"source":{"id":"https://openalex.org/S4210228084","display_name":"Nature Computational Science","issn_l":"2662-8457","issn":["2662-8457"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nature Computational Science","raw_type":"journal-article"},{"id":"pmid:42050047","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/42050047","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nature computational science","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W4509327","https://openalex.org/W2092398714","https://openalex.org/W2131057369","https://openalex.org/W2139923370","https://openalex.org/W2429115365","https://openalex.org/W2575296977","https://openalex.org/W2975503980","https://openalex.org/W2979786244","https://openalex.org/W3014009018","https://openalex.org/W3107259331","https://openalex.org/W3109749236","https://openalex.org/W3119381932","https://openalex.org/W3163993681","https://openalex.org/W3200268147","https://openalex.org/W3200673624","https://openalex.org/W3204708751","https://openalex.org/W3205073660","https://openalex.org/W3206427994","https://openalex.org/W4221019179","https://openalex.org/W4221152086","https://openalex.org/W4224089288","https://openalex.org/W4230048260","https://openalex.org/W4244063180","https://openalex.org/W4308731656","https://openalex.org/W4361205706","https://openalex.org/W4367674997","https://openalex.org/W4385370256","https://openalex.org/W4389898131","https://openalex.org/W4396941397","https://openalex.org/W4396943721","https://openalex.org/W4398563583","https://openalex.org/W4399254499","https://openalex.org/W4400883379","https://openalex.org/W4402675562","https://openalex.org/W4405194331","https://openalex.org/W4405215895","https://openalex.org/W4411725628","https://openalex.org/W4412381934","https://openalex.org/W4412877047","https://openalex.org/W4413384924","https://openalex.org/W4414514064","https://openalex.org/W7130860228","https://openalex.org/W7131210358","https://openalex.org/W7134172769","https://openalex.org/W7150742179"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":3}],"updated_date":"2026-04-30T06:05:26.967640","created_date":"2026-04-29T00:00:00"}