{"id":"https://openalex.org/W7083592592","doi":"https://doi.org/10.1016/j.jcp.2025.114408","title":"Sobolev training for operator learning","display_name":"Sobolev training for operator learning","publication_year":2025,"publication_date":"2025-09-27","ids":{"openalex":"https://openalex.org/W7083592592","doi":"https://doi.org/10.1016/j.jcp.2025.114408"},"language":"en","primary_location":{"id":"doi:10.1016/j.jcp.2025.114408","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.jcp.2025.114408","pdf_url":null,"source":{"id":"https://openalex.org/S148709879","display_name":"Journal of Computational Physics","issn_l":"0021-9991","issn":["0021-9991","1090-2716"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational Physics","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":null,"display_name":"Namkyeong Cho","orcid":"https://orcid.org/0000-0002-8232-437X"},"institutions":[{"id":"https://openalex.org/I12832649","display_name":"Gachon University","ror":"https://ror.org/03ryywt80","country_code":"KR","type":"education","lineage":["https://openalex.org/I12832649"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Namkyeong Cho","raw_affiliation_strings":["Department of Finance and Big Data, Gachon University, Sujeong-gu, Seongnamdaero, Gyeonggi-do, 1342, Republic of Korea"],"raw_orcid":"https://orcid.org/0000-0002-8232-437X","affiliations":[{"raw_affiliation_string":"Department of Finance and Big Data, Gachon University, Sujeong-gu, Seongnamdaero, Gyeonggi-do, 1342, Republic of Korea","institution_ids":["https://openalex.org/I12832649"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Junseung Ryu","orcid":null},"institutions":[{"id":"https://openalex.org/I123900574","display_name":"Pohang University of Science and Technology","ror":"https://ror.org/04xysgw12","country_code":"KR","type":"education","lineage":["https://openalex.org/I123900574"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Junseung Ryu","raw_affiliation_strings":["Department of Mathematics, POSTECH, Pohang, Gyeongsangbuk-do, 37673, Republic of Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, POSTECH, Pohang, Gyeongsangbuk-do, 37673, Republic of Korea","institution_ids":["https://openalex.org/I123900574"]}]},{"author_position":"last","author":{"id":null,"display_name":"Hyung Ju Hwang","orcid":null},"institutions":[{"id":"https://openalex.org/I123900574","display_name":"Pohang University of Science and Technology","ror":"https://ror.org/04xysgw12","country_code":"KR","type":"education","lineage":["https://openalex.org/I123900574"]},{"id":"https://openalex.org/I4210142886","display_name":"Pohang TechnoPark (South Korea)","ror":"https://ror.org/04t7p9y73","country_code":"KR","type":"company","lineage":["https://openalex.org/I4210142886"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Hyung Ju Hwang","raw_affiliation_strings":["AMSquare Corp., Pohang, Gyeongsangbuk-do, 37673, Republic of Korea","Center for Mathematical Machine Learning and its Applications, Pohang, Gyeongsangbuk-do, 37673, Republic of Korea","Department of Mathematics, POSTECH, Pohang, Gyeongsangbuk-do, 37673, Republic of Korea","Graduate School of Artificial Intelligence, POSTECH, Pohang, Gyeongsangbuk-do, 37673, Republic of Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"AMSquare Corp., Pohang, Gyeongsangbuk-do, 37673, Republic of Korea","institution_ids":["https://openalex.org/I123900574","https://openalex.org/I4210142886"]},{"raw_affiliation_string":"Center for Mathematical Machine Learning and its Applications, Pohang, Gyeongsangbuk-do, 37673, Republic of Korea","institution_ids":["https://openalex.org/I4210142886"]},{"raw_affiliation_string":"Department of Mathematics, POSTECH, Pohang, Gyeongsangbuk-do, 37673, Republic of Korea","institution_ids":["https://openalex.org/I123900574"]},{"raw_affiliation_string":"Graduate School of Artificial Intelligence, POSTECH, Pohang, Gyeongsangbuk-do, 37673, Republic of Korea","institution_ids":["https://openalex.org/I123900574"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I123900574","https://openalex.org/I4210142886"],"apc_list":{"value":3750,"currency":"USD","value_usd":3750},"apc_paid":null,"fwci":2.6057,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.93974539,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"543","issue":null,"first_page":"114408","last_page":"114408"},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T14400","display_name":"Medical Coding and Health Information","score":0.05090000107884407,"subfield":{"id":"https://openalex.org/subfields/3605","display_name":"Health Information Management"},"field":{"id":"https://openalex.org/fields/36","display_name":"Health Professions"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T14400","display_name":"Medical Coding and Health Information","score":0.05090000107884407,"subfield":{"id":"https://openalex.org/subfields/3605","display_name":"Health Information Management"},"field":{"id":"https://openalex.org/fields/36","display_name":"Health Professions"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11819","display_name":"Data-Driven Disease Surveillance","score":0.05000000074505806,"subfield":{"id":"https://openalex.org/subfields/2713","display_name":"Epidemiology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T12011","display_name":"Insurance, Mortality, Demography, Risk Management","score":0.04580000042915344,"subfield":{"id":"https://openalex.org/subfields/3317","display_name":"Demography"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.7003999948501587},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.6992999911308289},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6115000247955322},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5479999780654907},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.40299999713897705},{"id":"https://openalex.org/keywords/training","display_name":"Training (meteorology)","score":0.38989999890327454},{"id":"https://openalex.org/keywords/shift-operator","display_name":"Shift operator","score":0.3840000033378601}],"concepts":[{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.7003999948501587},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.6992999911308289},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6115000247955322},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5479999780654907},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5112000107765198},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49470001459121704},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4244000017642975},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41359999775886536},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.40299999713897705},{"id":"https://openalex.org/C2777211547","wikidata":"https://www.wikidata.org/wiki/Q17141490","display_name":"Training (meteorology)","level":2,"score":0.38989999890327454},{"id":"https://openalex.org/C65630602","wikidata":"https://www.wikidata.org/wiki/Q2278680","display_name":"Shift operator","level":4,"score":0.3840000033378601},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.323199987411499},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.321399986743927},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.3068999946117401},{"id":"https://openalex.org/C24902271","wikidata":"https://www.wikidata.org/wiki/Q7449297","display_name":"Semi-elliptic operator","level":3,"score":0.299699991941452},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.29739999771118164},{"id":"https://openalex.org/C185644265","wikidata":"https://www.wikidata.org/wiki/Q3711848","display_name":"Sobolev inequality","level":3,"score":0.2736000120639801},{"id":"https://openalex.org/C99392333","wikidata":"https://www.wikidata.org/wiki/Q5450385","display_name":"Finite-rank operator","level":3,"score":0.27140000462532043},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.2614000141620636}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.jcp.2025.114408","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.jcp.2025.114408","pdf_url":null,"source":{"id":"https://openalex.org/S148709879","display_name":"Journal of Computational Physics","issn_l":"0021-9991","issn":["0021-9991","1090-2716"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational Physics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1010832933","display_name":null,"funder_award_id":"RS-2023-00219980","funder_id":"https://openalex.org/F4320328359","funder_display_name":"Ministry of Science and ICT, South Korea"},{"id":"https://openalex.org/G2309250114","display_name":null,"funder_award_id":"2019-0-01906","funder_id":"https://openalex.org/F4320322030","funder_display_name":"Ministry of Science, ICT and Future Planning"},{"id":"https://openalex.org/G494944064","display_name":null,"funder_award_id":"2023RIS-009","funder_id":"https://openalex.org/F4320321408","funder_display_name":"Ministry of Education"},{"id":"https://openalex.org/G7124767135","display_name":null,"funder_award_id":"RS-2022-00165268","funder_id":"https://openalex.org/F4320328359","funder_display_name":"Ministry of Science and ICT, South Korea"},{"id":"https://openalex.org/G8835405211","display_name":null,"funder_award_id":"GCU-202502800001","funder_id":"https://openalex.org/F4320321366","funder_display_name":"Gachon University"}],"funders":[{"id":"https://openalex.org/F4320321282","display_name":"Pohang University of Science and Technology","ror":"https://ror.org/04xysgw12"},{"id":"https://openalex.org/F4320321366","display_name":"Gachon University","ror":"https://ror.org/03ryywt80"},{"id":"https://openalex.org/F4320321408","display_name":"Ministry of Education","ror":"https://ror.org/01p262204"},{"id":"https://openalex.org/F4320322030","display_name":"Ministry of Science, ICT and Future Planning","ror":"https://ror.org/032e49973"},{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"},{"id":"https://openalex.org/F4320328359","display_name":"Ministry of Science and ICT, South Korea","ror":"https://ror.org/01wpjm123"},{"id":"https://openalex.org/F4320335489","display_name":"Institute for Information and Communications Technology Promotion","ror":"https://ror.org/01g0hqq23"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W2012255853","https://openalex.org/W2122224951","https://openalex.org/W2137983211","https://openalex.org/W2899283552","https://openalex.org/W2979786244","https://openalex.org/W3034999214","https://openalex.org/W4386955678","https://openalex.org/W4391848179"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}