{"id":"https://openalex.org/W4404047422","doi":"https://doi.org/10.1137/23m156642x","title":"Fredholm Integral Equations for Function Approximation and the Training of Neural Networks","display_name":"Fredholm Integral Equations for Function Approximation and the Training of Neural Networks","publication_year":2024,"publication_date":"2024-10-30","ids":{"openalex":"https://openalex.org/W4404047422","doi":"https://doi.org/10.1137/23m156642x"},"language":"en","primary_location":{"id":"doi:10.1137/23m156642x","is_oa":true,"landing_page_url":"https://doi.org/10.1137/23m156642x","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"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 Mathematics of Data Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.1137/23m156642x","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090892749","display_name":"Patrick Gel\u00df","orcid":"https://orcid.org/0000-0002-3645-9513"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Patrick Gel\u00df","raw_affiliation_strings":["AI in Society, Science, and Technology, Zuse Institute Berlin, 14195 Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"AI in Society, Science, and Technology, Zuse Institute Berlin, 14195 Berlin, Germany","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021729820","display_name":"Aizhan Issagali","orcid":null},"institutions":[{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Aizhan Issagali","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001615364","display_name":"Ralf Kornhuber","orcid":"https://orcid.org/0009-0006-3901-1745"},"institutions":[{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ralf Kornhuber","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5090892749"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6797,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.66028708,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"6","issue":"4","first_page":"1078","last_page":"1108"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9954000115394592,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.994700014591217,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6279389262199402},{"id":"https://openalex.org/keywords/fredholm-integral-equation","display_name":"Fredholm integral equation","score":0.603346586227417},{"id":"https://openalex.org/keywords/training","display_name":"Training (meteorology)","score":0.5853198766708374},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5121645927429199},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4821414649486542},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.47760555148124695},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47631654143333435},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.31949469447135925},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31885620951652527},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3121543526649475},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1449180245399475}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6279389262199402},{"id":"https://openalex.org/C89285879","wikidata":"https://www.wikidata.org/wiki/Q2991898","display_name":"Fredholm integral equation","level":3,"score":0.603346586227417},{"id":"https://openalex.org/C2777211547","wikidata":"https://www.wikidata.org/wiki/Q17141490","display_name":"Training (meteorology)","level":2,"score":0.5853198766708374},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5121645927429199},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4821414649486542},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.47760555148124695},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47631654143333435},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31949469447135925},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31885620951652527},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3121543526649475},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1449180245399475},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/23m156642x","is_oa":true,"landing_page_url":"https://doi.org/10.1137/23m156642x","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"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 Mathematics of Data Science","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1137/23m156642x","is_oa":true,"landing_page_url":"https://doi.org/10.1137/23m156642x","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"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 Mathematics of Data Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5271502856","display_name":null,"funder_award_id":"101017733","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"}],"funders":[{"id":"https://openalex.org/F4320332999","display_name":"Horizon 2020 Framework Programme","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W50417968","https://openalex.org/W114314968","https://openalex.org/W147998453","https://openalex.org/W1570089119","https://openalex.org/W1955857676","https://openalex.org/W1993482030","https://openalex.org/W1995406764","https://openalex.org/W1996869553","https://openalex.org/W1998598124","https://openalex.org/W2024165284","https://openalex.org/W2031216664","https://openalex.org/W2034996255","https://openalex.org/W2036133196","https://openalex.org/W2043680591","https://openalex.org/W2061933243","https://openalex.org/W2069225091","https://openalex.org/W2088522763","https://openalex.org/W2088739747","https://openalex.org/W2103496339","https://openalex.org/W2152799582","https://openalex.org/W2157890204","https://openalex.org/W2158581396","https://openalex.org/W2258054274","https://openalex.org/W2604332136","https://openalex.org/W2885052892","https://openalex.org/W2889716319","https://openalex.org/W2893769615","https://openalex.org/W2962947392","https://openalex.org/W2970843715","https://openalex.org/W2978683479","https://openalex.org/W3035038335","https://openalex.org/W3099398162","https://openalex.org/W3107512664","https://openalex.org/W3201276202","https://openalex.org/W4280556412","https://openalex.org/W4286717651","https://openalex.org/W4292361795"],"related_works":["https://openalex.org/W2972080159","https://openalex.org/W2017640945","https://openalex.org/W2031473926","https://openalex.org/W2386739836","https://openalex.org/W2493083010","https://openalex.org/W2021616187","https://openalex.org/W22811207","https://openalex.org/W4308895501","https://openalex.org/W2189527329","https://openalex.org/W2397046274"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2025-12-27T23:08:20.325037","created_date":"2025-10-10T00:00:00"}