{"id":"https://openalex.org/W3020191331","doi":"https://doi.org/10.1007/s10915-021-01532-w","title":"Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks","display_name":"Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks","publication_year":2021,"publication_date":"2021-06-05","ids":{"openalex":"https://openalex.org/W3020191331","doi":"https://doi.org/10.1007/s10915-021-01532-w","mag":"3020191331"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-021-01532-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-021-01532-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-021-01532-w.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10915-021-01532-w.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019220707","display_name":"Moritz Geist","orcid":null},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Moritz Geist","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Technische Universit\u00e4t Berlin, Stra\u00dfe des 17.\u00a0Juni 136, 10623, Berlin, Germany","Institut f\u00fcr Mathematik , Technische Universit\u00e4t Berlin , Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Technische Universit\u00e4t Berlin, Stra\u00dfe des 17.\u00a0Juni 136, 10623, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]},{"raw_affiliation_string":"Institut f\u00fcr Mathematik , Technische Universit\u00e4t Berlin , Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041074956","display_name":"Philipp Petersen","orcid":"https://orcid.org/0000-0003-3566-1020"},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Philipp Petersen","raw_affiliation_strings":["Faculty of Mathematics and Research Plattform Data Science @ Uni Vienna, University of Vienna, Oskar Morgenstern Platz 1, 1090, Vienna, Austria","Faculty of Mathematics and Research Plattform Data Science @ Uni Vienna, University of Vienna, Vienna, Austria"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Research Plattform Data Science @ Uni Vienna, University of Vienna, Oskar Morgenstern Platz 1, 1090, Vienna, Austria","institution_ids":["https://openalex.org/I129774422"]},{"raw_affiliation_string":"Faculty of Mathematics and Research Plattform Data Science @ Uni Vienna, University of Vienna, Vienna, Austria","institution_ids":["https://openalex.org/I129774422"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008776954","display_name":"Mones Raslan","orcid":"https://orcid.org/0000-0003-1014-7383"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Mones Raslan","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Technische Universit\u00e4t Berlin, Stra\u00dfe des 17.\u00a0Juni 136, 10623, Berlin, Germany","Institut f\u00fcr Mathematik , Technische Universit\u00e4t Berlin , Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Technische Universit\u00e4t Berlin, Stra\u00dfe des 17.\u00a0Juni 136, 10623, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]},{"raw_affiliation_string":"Institut f\u00fcr Mathematik , Technische Universit\u00e4t Berlin , Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102878006","display_name":"Reinhold Schneider","orcid":"https://orcid.org/0000-0003-0529-7467"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Reinhold Schneider","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Technische Universit\u00e4t Berlin, Stra\u00dfe des 17.\u00a0Juni 136, 10623, Berlin, Germany","Institut f\u00fcr Mathematik , Technische Universit\u00e4t Berlin , Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Technische Universit\u00e4t Berlin, Stra\u00dfe des 17.\u00a0Juni 136, 10623, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]},{"raw_affiliation_string":"Institut f\u00fcr Mathematik , Technische Universit\u00e4t Berlin , Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090767423","display_name":"Gitta Kutyniok","orcid":"https://orcid.org/0000-0001-9738-2487"},"institutions":[{"id":"https://openalex.org/I78037679","display_name":"UiT The Arctic University of Norway","ror":"https://ror.org/00wge5k78","country_code":"NO","type":"education","lineage":["https://openalex.org/I78037679"]},{"id":"https://openalex.org/I8204097","display_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/05591te55","country_code":"DE","type":"education","lineage":["https://openalex.org/I8204097"]}],"countries":["DE","NO"],"is_corresponding":false,"raw_author_name":"Gitta Kutyniok","raw_affiliation_strings":["Department of Physics and Technology, University of Troms\u00f8, Troms\u00f8, Norway","Mathematisches Institut, Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen, Theresienstr. 39, 80333, Munich, Germany","Mathematisches Institut, Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen, Munich, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Physics and Technology, University of Troms\u00f8, Troms\u00f8, Norway","institution_ids":["https://openalex.org/I78037679"]},{"raw_affiliation_string":"Mathematisches Institut, Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen, Theresienstr. 39, 80333, Munich, Germany","institution_ids":["https://openalex.org/I8204097"]},{"raw_affiliation_string":"Mathematisches Institut, Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen, Munich, Germany","institution_ids":["https://openalex.org/I8204097"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5019220707"],"corresponding_institution_ids":["https://openalex.org/I4577782"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":2.2361,"has_fulltext":true,"cited_by_count":20,"citation_normalized_percentile":{"value":0.88091566,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"88","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998000264167786,"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":0.9998000264167786,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9839000105857849,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.983299970626831,"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/intrinsic-dimension","display_name":"Intrinsic dimension","score":0.6670207977294922},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.6178860068321228},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5773608684539795},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5640081763267517},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.551239013671875},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5394035577774048},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45782431960105896},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44589921832084656},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43809887766838074},{"id":"https://openalex.org/keywords/comparability","display_name":"Comparability","score":0.41570937633514404},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3910137116909027},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.27774322032928467},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19638919830322266},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09485834836959839}],"concepts":[{"id":"https://openalex.org/C30732413","wikidata":"https://www.wikidata.org/wiki/Q17092636","display_name":"Intrinsic dimension","level":3,"score":0.6670207977294922},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.6178860068321228},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5773608684539795},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5640081763267517},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.551239013671875},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5394035577774048},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45782431960105896},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44589921832084656},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43809887766838074},{"id":"https://openalex.org/C197947376","wikidata":"https://www.wikidata.org/wiki/Q5155608","display_name":"Comparability","level":2,"score":0.41570937633514404},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3910137116909027},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.27774322032928467},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19638919830322266},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09485834836959839},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1007/s10915-021-01532-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-021-01532-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-021-01532-w.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:epub.ub.uni-muenchen.de:126389","is_oa":false,"landing_page_url":"http://nbn-resolving.de/urn:nbn:de:bvb:19-epub-126389-8","pdf_url":null,"source":{"id":"https://openalex.org/S4306401845","display_name":"Open access LMU (Ludwid Maxmilian's Universitat Munchen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I8204097","host_organization_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","host_organization_lineage":["https://openalex.org/I8204097"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Journal of Scientific Computing","raw_type":"NonPeerReviewed"},{"id":"pmh:oai:arXiv.org:2004.12131","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2004.12131","pdf_url":"https://arxiv.org/pdf/2004.12131","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":"mag:3020191331","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/2004.12131","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:munin.uit.no:10037/24272","is_oa":true,"landing_page_url":"https://hdl.handle.net/10037/24272","pdf_url":null,"source":{"id":"https://openalex.org/S4306400066","display_name":"Munin Open Research Archive (The Arctic University of Norway)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I78037679","host_organization_name":"UiT The Arctic University of Norway","host_organization_lineage":["https://openalex.org/I78037679"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.2004.12131","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2004.12131","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s10915-021-01532-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-021-01532-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-021-01532-w.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3031800739","display_name":null,"funder_award_id":"BIFOLD","funder_id":"https://openalex.org/F4320321114","funder_display_name":"Bundesministerium f\u00fcr Bildung und Forschung"},{"id":"https://openalex.org/G352791218","display_name":null,"funder_award_id":"(BMBF)","funder_id":"https://openalex.org/F4320321114","funder_display_name":"Bundesministerium f\u00fcr Bildung und Forschung"},{"id":"https://openalex.org/G5168466499","display_name":null,"funder_award_id":"Project","funder_id":"https://openalex.org/F4320321114","funder_display_name":"Bundesministerium f\u00fcr Bildung und Forschung"},{"id":"https://openalex.org/G5256195679","display_name":null,"funder_award_id":"Project AP4","funder_id":"https://openalex.org/F4320321114","funder_display_name":"Bundesministerium f\u00fcr Bildung und Forschung"},{"id":"https://openalex.org/G7142560593","display_name":null,"funder_award_id":"Berlin Institute for the Foundations of Learning a","funder_id":"https://openalex.org/F4320321114","funder_display_name":"Bundesministerium f\u00fcr Bildung und Forschung"},{"id":"https://openalex.org/G7225624288","display_name":null,"funder_award_id":"This work was","funder_id":"https://openalex.org/F4320321114","funder_display_name":"Bundesministerium f\u00fcr Bildung und Forschung"},{"id":"https://openalex.org/G8878106147","display_name":null,"funder_award_id":"Projects EF1-1 and EF1-4","funder_id":"https://openalex.org/F4320330291","funder_display_name":"Berlin Mathematics Research Center MATH+"}],"funders":[{"id":"https://openalex.org/F4320321114","display_name":"Bundesministerium f\u00fcr Bildung und Forschung","ror":"https://ror.org/04pz7b180"},{"id":"https://openalex.org/F4320321691","display_name":"Universit\u00e4t Wien","ror":"https://ror.org/03prydq77"},{"id":"https://openalex.org/F4320324094","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40"},{"id":"https://openalex.org/F4320330291","display_name":"Berlin Mathematics Research Center MATH+","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3020191331.pdf","grobid_xml":"https://content.openalex.org/works/W3020191331.grobid-xml"},"referenced_works_count":89,"referenced_works":["https://openalex.org/W595079961","https://openalex.org/W597932189","https://openalex.org/W1522301498","https://openalex.org/W1605528072","https://openalex.org/W2047278710","https://openalex.org/W2052690618","https://openalex.org/W2056653303","https://openalex.org/W2070980742","https://openalex.org/W2075646404","https://openalex.org/W2079224763","https://openalex.org/W2112796928","https://openalex.org/W2117302185","https://openalex.org/W2133041109","https://openalex.org/W2158985775","https://openalex.org/W2165695298","https://openalex.org/W2166116275","https://openalex.org/W2212370034","https://openalex.org/W2267573953","https://openalex.org/W2267743026","https://openalex.org/W2295099209","https://openalex.org/W2515829451","https://openalex.org/W2528305538","https://openalex.org/W2550848904","https://openalex.org/W2625995436","https://openalex.org/W2734689136","https://openalex.org/W2745110207","https://openalex.org/W2749028154","https://openalex.org/W2753962198","https://openalex.org/W2754833785","https://openalex.org/W2760972773","https://openalex.org/W2761704992","https://openalex.org/W2766298346","https://openalex.org/W2772097715","https://openalex.org/W2778051509","https://openalex.org/W2786232134","https://openalex.org/W2787302432","https://openalex.org/W2788980797","https://openalex.org/W2803629276","https://openalex.org/W2805915852","https://openalex.org/W2883486956","https://openalex.org/W2889523591","https://openalex.org/W2890291741","https://openalex.org/W2890889625","https://openalex.org/W2895471748","https://openalex.org/W2903926864","https://openalex.org/W2904885366","https://openalex.org/W2923153053","https://openalex.org/W2930017973","https://openalex.org/W2933916181","https://openalex.org/W2962761333","https://openalex.org/W2963112935","https://openalex.org/W2963146412","https://openalex.org/W2963798430","https://openalex.org/W2966419255","https://openalex.org/W2973805762","https://openalex.org/W2974910615","https://openalex.org/W2981405625","https://openalex.org/W2982376398","https://openalex.org/W2986795381","https://openalex.org/W2990653417","https://openalex.org/W2998107928","https://openalex.org/W2998847955","https://openalex.org/W2998882635","https://openalex.org/W3000236721","https://openalex.org/W3002335888","https://openalex.org/W3002607072","https://openalex.org/W3011579803","https://openalex.org/W3014009018","https://openalex.org/W3023241366","https://openalex.org/W3047451562","https://openalex.org/W3049518590","https://openalex.org/W3098175809","https://openalex.org/W3101260193","https://openalex.org/W3101643101","https://openalex.org/W3103239355","https://openalex.org/W3104183394","https://openalex.org/W3126658681","https://openalex.org/W3167031531","https://openalex.org/W3180808552","https://openalex.org/W3200336025","https://openalex.org/W4240395309","https://openalex.org/W4245558064","https://openalex.org/W6600135713","https://openalex.org/W6600159499","https://openalex.org/W6600474023","https://openalex.org/W6601430172","https://openalex.org/W6603255028","https://openalex.org/W6603336431","https://openalex.org/W6821340083"],"related_works":["https://openalex.org/W2933916181","https://openalex.org/W2883486956","https://openalex.org/W2528305538","https://openalex.org/W2963146412","https://openalex.org/W2986795381","https://openalex.org/W2962761333","https://openalex.org/W2899283552","https://openalex.org/W2760972773","https://openalex.org/W2749028154","https://openalex.org/W2625995436","https://openalex.org/W2103496339","https://openalex.org/W2890889625","https://openalex.org/W2803629276","https://openalex.org/W3135895479","https://openalex.org/W3021748939","https://openalex.org/W3101260193","https://openalex.org/W3098175809","https://openalex.org/W2194775991","https://openalex.org/W2152593035","https://openalex.org/W2079224763"],"abstract_inverted_index":{"Abstract":[0],"We":[1,83,111],"perform":[2],"a":[3],"comprehensive":[4],"numerical":[5,24,130],"study":[6,31,145],"of":[7,10,23,35,51,62,73,77,96,99,107,126,143],"the":[8,21,27,32,49,52,60,63,70,74,78,94,97,102,108,116,123,141],"effect":[9,95],"approximation-theoretical":[11,119],"results":[12],"for":[13,43,115],"neural":[14,45,155],"networks":[15,46],"on":[16,59,101,153],"practical":[17,124],"learning":[18,109,127],"problems":[19,128],"in":[20,129],"context":[22],"analysis.":[25,131],"As":[26],"underlying":[28],"model,":[29],"we":[30,146],"machine-learning-based":[33],"solution":[34,75],"parametric":[36,79],"partial":[37,80],"differential":[38,81],"equations.":[39],"Here,":[40],"approximation":[41],"theory":[42],"fully-connected":[44],"predicts":[47],"that":[48,118],"performance":[50],"model":[53],"should":[54],"depend":[55],"only":[56],"very":[57],"mildly":[58],"dimension":[61,72],"parameter":[64],"space":[65],"and":[66,104,137],"is":[67],"determined":[68],"by":[69,92,151],"intrinsic":[71],"manifold":[76],"equation.":[82],"use":[84],"various":[85],"methods":[86],"to":[87,133],"establish":[88],"comparability":[89],"between":[90],"test-cases":[91,100],"minimizing":[93],"choice":[98],"optimization":[103],"sampling":[105],"aspects":[106],"problem.":[110],"find":[112],"strong":[113],"support":[114],"hypothesis":[117],"effects":[120],"heavily":[121],"influence":[122],"behavior":[125],"Turning":[132],"practically":[134],"more":[135],"successful":[136],"modern":[138],"architectures,":[139],"at":[140],"end":[142],"this":[144],"derive":[147],"improved":[148],"error":[149],"bounds":[150],"focusing":[152],"convolutional":[154],"networks.":[156]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
