{"id":"https://openalex.org/W4403491647","doi":"https://doi.org/10.1038/s42256-024-00910-x","title":"Blending neural operators and relaxation methods in PDE numerical solvers","display_name":"Blending neural operators and relaxation methods in PDE numerical solvers","publication_year":2024,"publication_date":"2024-10-17","ids":{"openalex":"https://openalex.org/W4403491647","doi":"https://doi.org/10.1038/s42256-024-00910-x"},"language":"en","primary_location":{"id":"doi:10.1038/s42256-024-00910-x","is_oa":false,"landing_page_url":"https://doi.org/10.1038/s42256-024-00910-x","pdf_url":null,"source":{"id":"https://openalex.org/S2912241403","display_name":"Nature Machine Intelligence","issn_l":"2522-5839","issn":["2522-5839"],"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 Machine Intelligence","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/A5061668124","display_name":"Enrui Zhang","orcid":"https://orcid.org/0000-0001-6955-1124"},"institutions":[{"id":"https://openalex.org/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Enrui Zhang","raw_affiliation_strings":["Division of Applied Mathematics, Brown University, Providence, RI, USA"],"affiliations":[{"raw_affiliation_string":"Division of Applied Mathematics, Brown University, Providence, RI, USA","institution_ids":["https://openalex.org/I27804330"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007794414","display_name":"Adar Kahana","orcid":"https://orcid.org/0000-0003-4889-5037"},"institutions":[{"id":"https://openalex.org/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Adar Kahana","raw_affiliation_strings":["Division of Applied Mathematics, Brown University, Providence, RI, USA"],"affiliations":[{"raw_affiliation_string":"Division of Applied Mathematics, Brown University, Providence, RI, USA","institution_ids":["https://openalex.org/I27804330"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080114950","display_name":"Alena Kopani\u010d\u00e1kov\u00e1","orcid":null},"institutions":[{"id":"https://openalex.org/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alena Kopani\u010d\u00e1kov\u00e1","raw_affiliation_strings":["Division of Applied Mathematics, Brown University, Providence, RI, USA"],"affiliations":[{"raw_affiliation_string":"Division of Applied Mathematics, Brown University, Providence, RI, USA","institution_ids":["https://openalex.org/I27804330"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011112251","display_name":"Eli Turkel","orcid":"https://orcid.org/0000-0003-4273-0303"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Eli Turkel","raw_affiliation_strings":["Department of Applied Mathematics, Tel Aviv University, Tel Aviv, Israel"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Tel Aviv University, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018561547","display_name":"Rishikesh Ranade","orcid":"https://orcid.org/0000-0002-7692-7502"},"institutions":[{"id":"https://openalex.org/I21160419","display_name":"Ansys (United States)","ror":"https://ror.org/05cf5b117","country_code":"US","type":"company","lineage":["https://openalex.org/I21160419"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rishikesh Ranade","raw_affiliation_strings":["CTO Office, Ansys Inc, Canonsburg, PA, USA"],"affiliations":[{"raw_affiliation_string":"CTO Office, Ansys Inc, Canonsburg, PA, USA","institution_ids":["https://openalex.org/I21160419"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114303417","display_name":"Jay Pathak","orcid":"https://orcid.org/0000-0002-2942-2771"},"institutions":[{"id":"https://openalex.org/I21160419","display_name":"Ansys (United States)","ror":"https://ror.org/05cf5b117","country_code":"US","type":"company","lineage":["https://openalex.org/I21160419"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jay Pathak","raw_affiliation_strings":["CTO Office, Ansys Inc, Canonsburg, PA, USA"],"affiliations":[{"raw_affiliation_string":"CTO Office, Ansys Inc, Canonsburg, PA, USA","institution_ids":["https://openalex.org/I21160419"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009658255","display_name":"George Em Karniadakis","orcid":"https://orcid.org/0000-0002-9713-7120"},"institutions":[{"id":"https://openalex.org/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"George Em Karniadakis","raw_affiliation_strings":["Division of Applied Mathematics, Brown University, Providence, RI, USA","School of Engineering, Brown University, Providence, RI, USA"],"affiliations":[{"raw_affiliation_string":"Division of Applied Mathematics, Brown University, Providence, RI, USA","institution_ids":["https://openalex.org/I27804330"]},{"raw_affiliation_string":"School of Engineering, Brown University, Providence, RI, USA","institution_ids":["https://openalex.org/I27804330"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5009658255"],"corresponding_institution_ids":["https://openalex.org/I27804330"],"apc_list":{"value":9750,"currency":"EUR","value_usd":11690},"apc_paid":null,"fwci":5.2239,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.96310231,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"6","issue":"11","first_page":"1303","last_page":"1313"},"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/T10320","display_name":"Neural Networks and Applications","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9929999709129333,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5207598209381104},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5203441977500916},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32172131538391113},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.21619459986686707},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.18076470494270325},{"id":"https://openalex.org/keywords/internal-medicine","display_name":"Internal medicine","score":0.077538400888443}],"concepts":[{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5207598209381104},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5203441977500916},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32172131538391113},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.21619459986686707},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.18076470494270325},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.077538400888443}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1038/s42256-024-00910-x","is_oa":false,"landing_page_url":"https://doi.org/10.1038/s42256-024-00910-x","pdf_url":null,"source":{"id":"https://openalex.org/S2912241403","display_name":"Nature Machine Intelligence","issn_l":"2522-5839","issn":["2522-5839"],"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 Machine Intelligence","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6708679598","display_name":null,"funder_award_id":"N00014-22-1-2795","funder_id":"https://openalex.org/F4320337477","funder_display_name":"Naval Nuclear Propulsion Program (Naval Reactors)"},{"id":"https://openalex.org/G8717535088","display_name":null,"funder_award_id":"206745","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"},{"id":"https://openalex.org/F4320337477","display_name":"Naval Nuclear Propulsion Program (Naval Reactors)","ror":"https://ror.org/03sk1we31"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":73,"referenced_works":["https://openalex.org/W321261355","https://openalex.org/W654805605","https://openalex.org/W1506342804","https://openalex.org/W1519370937","https://openalex.org/W1525132831","https://openalex.org/W1615140576","https://openalex.org/W1997831216","https://openalex.org/W2000425991","https://openalex.org/W2014065899","https://openalex.org/W2017085690","https://openalex.org/W2032222091","https://openalex.org/W2037879537","https://openalex.org/W2041876368","https://openalex.org/W2047352485","https://openalex.org/W2075218807","https://openalex.org/W2100204691","https://openalex.org/W2131537960","https://openalex.org/W2139923370","https://openalex.org/W2140153041","https://openalex.org/W2151478420","https://openalex.org/W2159338095","https://openalex.org/W2171303908","https://openalex.org/W2468193039","https://openalex.org/W2482071863","https://openalex.org/W2635312788","https://openalex.org/W2749028154","https://openalex.org/W2891039272","https://openalex.org/W2899283552","https://openalex.org/W2912389156","https://openalex.org/W2963527086","https://openalex.org/W2978175238","https://openalex.org/W2979786244","https://openalex.org/W2993158195","https://openalex.org/W3003922491","https://openalex.org/W3015209189","https://openalex.org/W3037588546","https://openalex.org/W3087889215","https://openalex.org/W3092923133","https://openalex.org/W3099057226","https://openalex.org/W3102569296","https://openalex.org/W3115418185","https://openalex.org/W3134515731","https://openalex.org/W3135067840","https://openalex.org/W3137240924","https://openalex.org/W3161200675","https://openalex.org/W3168635287","https://openalex.org/W3201666041","https://openalex.org/W4205624883","https://openalex.org/W4210423197","https://openalex.org/W4210826095","https://openalex.org/W4210888884","https://openalex.org/W4213199992","https://openalex.org/W4220717841","https://openalex.org/W4221019179","https://openalex.org/W4221152086","https://openalex.org/W4226429807","https://openalex.org/W4237224039","https://openalex.org/W4242769917","https://openalex.org/W4246757711","https://openalex.org/W4294170298","https://openalex.org/W4300666158","https://openalex.org/W4307744072","https://openalex.org/W4310291155","https://openalex.org/W4310497802","https://openalex.org/W4319042408","https://openalex.org/W4366351147","https://openalex.org/W4386930657","https://openalex.org/W4399675984","https://openalex.org/W6755308174","https://openalex.org/W6810693006","https://openalex.org/W6930076921","https://openalex.org/W6947755855","https://openalex.org/W6967780016"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2412311587"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":18}],"updated_date":"2026-04-13T07:58:08.660418","created_date":"2025-10-10T00:00:00"}