{"id":"https://openalex.org/W2995438359","doi":"https://doi.org/10.1109/tnnls.2021.3049719","title":"Efficient Approximation of High-Dimensional Functions With Neural Networks","display_name":"Efficient Approximation of High-Dimensional Functions With Neural Networks","publication_year":2021,"publication_date":"2021-01-29","ids":{"openalex":"https://openalex.org/W2995438359","doi":"https://doi.org/10.1109/tnnls.2021.3049719","mag":"2995438359","pmid":"https://pubmed.ncbi.nlm.nih.gov/33513112"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2021.3049719","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tnnls.2021.3049719","pdf_url":"https://ieeexplore.ieee.org/ielx7/5962385/9816060/09340559.pdf","source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite","pubmed"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://ieeexplore.ieee.org/ielx7/5962385/9816060/09340559.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002005113","display_name":"Patrick Cheridito","orcid":"https://orcid.org/0000-0001-9074-7295"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Patrick Cheridito","raw_affiliation_strings":["Department of Mathematics, ETH Zurich, Zurich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, ETH Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074382323","display_name":"Arnulf Jentzen","orcid":"https://orcid.org/0000-0002-9840-3339"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Arnulf Jentzen","raw_affiliation_strings":["Department of Mathematics, ETH Zurich, Zurich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, ETH Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001762952","display_name":"Florian Rossmannek","orcid":"https://orcid.org/0000-0001-5772-5086"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Florian Rossmannek","raw_affiliation_strings":["Department of Mathematics, ETH Zurich, Zurich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, ETH Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5002005113"],"corresponding_institution_ids":["https://openalex.org/I35440088"],"apc_list":null,"apc_paid":null,"fwci":2.8162,"has_fulltext":true,"cited_by_count":34,"citation_normalized_percentile":{"value":0.91802499,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":"33","issue":"7","first_page":"3079","last_page":"3093"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9998999834060669,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9957000017166138,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9930999875068665,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.8785882592201233},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.7705634236335754},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6996944546699524},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5842982530593872},{"id":"https://openalex.org/keywords/function-approximation","display_name":"Function approximation","score":0.540589451789856},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.524843692779541},{"id":"https://openalex.org/keywords/activation-function","display_name":"Activation function","score":0.4543225169181824},{"id":"https://openalex.org/keywords/linear-approximation","display_name":"Linear approximation","score":0.4289938807487488},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3615269660949707},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3607133626937866},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3595694899559021},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.32869356870651245},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3126121759414673},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07606416940689087}],"concepts":[{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.8785882592201233},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.7705634236335754},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6996944546699524},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5842982530593872},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.540589451789856},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.524843692779541},{"id":"https://openalex.org/C38365724","wikidata":"https://www.wikidata.org/wiki/Q4677469","display_name":"Activation function","level":3,"score":0.4543225169181824},{"id":"https://openalex.org/C160824197","wikidata":"https://www.wikidata.org/wiki/Q2071054","display_name":"Linear approximation","level":3,"score":0.4289938807487488},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3615269660949707},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3607133626937866},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3595694899559021},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.32869356870651245},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3126121759414673},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07606416940689087},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":5,"locations":[{"id":"doi:10.1109/tnnls.2021.3049719","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tnnls.2021.3049719","pdf_url":"https://ieeexplore.ieee.org/ielx7/5962385/9816060/09340559.pdf","source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:33513112","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33513112","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":"IEEE transactions on neural networks and learning systems","raw_type":null},{"id":"pmh:oai:arXiv.org:1912.04310","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1912.04310","pdf_url":"https://arxiv.org/pdf/1912.04310","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:www.research-collection.ethz.ch:20.500.11850/522331","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11850/522331","pdf_url":null,"source":{"id":"https://openalex.org/S4306402302","display_name":"Repository for Publications and Research Data (ETH Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I35440088","host_organization_name":"ETH Zurich","host_organization_lineage":["https://openalex.org/I35440088"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems, 33 (7)","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"doi:10.3929/ethz-b-000522331","is_oa":true,"landing_page_url":"https://doi.org/10.3929/ethz-b-000522331","pdf_url":null,"source":{"id":"https://openalex.org/S7407051236","display_name":"ETH Z\u00fcrich Research Collection","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1109/tnnls.2021.3049719","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tnnls.2021.3049719","pdf_url":"https://ieeexplore.ieee.org/ielx7/5962385/9816060/09340559.pdf","source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1177974802","display_name":null,"funder_award_id":"EXC 2044-390685587","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G1652504919","display_name":null,"funder_award_id":"EXC 2044","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G1962423931","display_name":null,"funder_award_id":"175699","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G2110285270","display_name":null,"funder_award_id":"2044-390685587","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G2817606592","display_name":null,"funder_award_id":"390685587","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G3237484952","display_name":null,"funder_award_id":"Germany's Excellence Strategy EXC 2044-390685587","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5074471488","display_name":null,"funder_award_id":"Excellence Strategy EXC 2044-390685587","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5106512922","display_name":null,"funder_award_id":"Deutsche Forschungsgemeinschaft (DFG","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8055832297","display_name":null,"funder_award_id":"EXC 2044-390685587, Mathematics M\u00fcnster: Dynamics-Geometry-Structure","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G870869636","display_name":null,"funder_award_id":"EXC 2044-39068558","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2995438359.pdf","grobid_xml":"https://content.openalex.org/works/W2995438359.grobid-xml"},"referenced_works_count":53,"referenced_works":["https://openalex.org/W566184825","https://openalex.org/W1971735090","https://openalex.org/W1973631422","https://openalex.org/W1979554434","https://openalex.org/W1988115241","https://openalex.org/W1994108380","https://openalex.org/W2006240266","https://openalex.org/W2034551836","https://openalex.org/W2044828368","https://openalex.org/W2074381721","https://openalex.org/W2075407161","https://openalex.org/W2085310530","https://openalex.org/W2099706683","https://openalex.org/W2103496339","https://openalex.org/W2113990981","https://openalex.org/W2137983211","https://openalex.org/W2152593035","https://openalex.org/W2153714959","https://openalex.org/W2158581396","https://openalex.org/W2166116275","https://openalex.org/W2511261638","https://openalex.org/W2528305538","https://openalex.org/W2593965610","https://openalex.org/W2595713799","https://openalex.org/W2747971139","https://openalex.org/W2803636134","https://openalex.org/W2883486956","https://openalex.org/W2885273747","https://openalex.org/W2890889625","https://openalex.org/W2891311596","https://openalex.org/W2910155483","https://openalex.org/W2919115771","https://openalex.org/W2923153053","https://openalex.org/W2938185552","https://openalex.org/W2962742960","https://openalex.org/W2962761333","https://openalex.org/W2963146412","https://openalex.org/W2964153674","https://openalex.org/W2967394275","https://openalex.org/W3000236721","https://openalex.org/W3012168927","https://openalex.org/W3023241366","https://openalex.org/W3105432754","https://openalex.org/W3125537303","https://openalex.org/W3133816032","https://openalex.org/W3146803896","https://openalex.org/W3180808552","https://openalex.org/W3204236384","https://openalex.org/W4236966694","https://openalex.org/W6691187937","https://openalex.org/W6733962499","https://openalex.org/W6734407986","https://openalex.org/W6734616715"],"related_works":["https://openalex.org/W4322615556","https://openalex.org/W3133651710","https://openalex.org/W4287555349","https://openalex.org/W4313559025","https://openalex.org/W2007295947","https://openalex.org/W3113111988","https://openalex.org/W2138382551","https://openalex.org/W2040708657","https://openalex.org/W2096285364","https://openalex.org/W3136275618"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"we":[3,120],"develop":[4],"a":[5,31,36,39,62,72,109],"framework":[6],"for":[7,108],"showing":[8],"that":[9,80,126],"neural":[10,41],"networks":[11,70,88,97,134],"can":[12,49,89,127],"overcome":[13],"the":[14,28,45,85,103,117,136],"curse":[15,137],"of":[16,30,38,65,75,105,116,124,138],"dimensionality":[17],"in":[18,43],"different":[19,122],"high-dimensional":[20],"approximation":[21,111],"problems.":[22],"Our":[23],"approach":[24],"is":[25,35],"based":[26],"on":[27,84,102],"notion":[29],"catalog":[32,64,69,87],"network,":[33],"which":[34,44],"generalization":[37],"standard":[40],"network":[42],"nonlinear":[46],"activation":[47],"functions":[48,125],"vary":[50],"from":[51,61],"layer":[52,54],"to":[53],"as":[55,57],"long":[56],"they":[58],"are":[59],"chosen":[60],"predefined":[63],"functions.":[66,77],"As":[67,113],"such,":[68],"constitute":[71],"rich":[73],"family":[74],"continuous":[76],"We":[78],"show":[79],"under":[81],"appropriate":[82],"conditions":[83],"catalog,":[86],"efficiently":[90],"be":[91,128],"approximated":[92,129],"with":[93,130],"rectified":[94],"linear":[95,132],"unit-type":[96],"and":[98],"provide":[99],"precise":[100],"estimates":[101],"number":[104],"parameters":[106],"needed":[107],"given":[110],"accuracy.":[112],"special":[114],"cases":[115],"general":[118],"results,":[119],"obtain":[121],"classes":[123],"recitifed":[131],"unit":[133],"without":[135],"dimensionality.":[139]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3}],"updated_date":"2026-04-03T22:45:19.894376","created_date":"2025-10-10T00:00:00"}
