{"id":"https://openalex.org/W4412386030","doi":"https://doi.org/10.1137/23m1621356","title":"Bias-Variance Trade-Off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs","display_name":"Bias-Variance Trade-Off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs","publication_year":2025,"publication_date":"2025-07-14","ids":{"openalex":"https://openalex.org/W4412386030","doi":"https://doi.org/10.1137/23m1621356"},"language":"en","primary_location":{"id":"doi:10.1137/23m1621356","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1621356","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"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 Scientific Computing","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/A5090943765","display_name":"Zheyuan Hu","orcid":null},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":true,"raw_author_name":"Zheyuan Hu","raw_affiliation_strings":["Department of Computer Science, National University of Singapore, Singapore, 119077. The first three authors contributed equally"],"raw_orcid":"https://orcid.org/0000-0002-0116-9874","affiliations":[{"raw_affiliation_string":"Department of Computer Science, National University of Singapore, Singapore, 119077. The first three authors contributed equally","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114220120","display_name":"Zhouhao Yang","orcid":null},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Zhouhao Yang","raw_affiliation_strings":["Department of Computer Science, National University of Singapore, Singapore, 119077. The first three authors contributed equally"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, National University of Singapore, Singapore, 119077. The first three authors contributed equally","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018723326","display_name":"Yezhen Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Yezhen Wang","raw_affiliation_strings":["Department of Computer Science, National University of Singapore, Singapore, 119077. The first three authors contributed equally"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, National University of Singapore, Singapore, 119077. The first three authors contributed equally","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009658255","display_name":"George Em Karniadakis","orcid":"https://orcid.org/0000-0002-9713-7120"},"institutions":[{"id":"https://openalex.org/I142606810","display_name":"Pacific Northwest National Laboratory","ror":"https://ror.org/05h992307","country_code":"US","type":"facility","lineage":["https://openalex.org/I1325736334","https://openalex.org/I1330989302","https://openalex.org/I142606810","https://openalex.org/I39565521"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"George E. Karniadakis","raw_affiliation_strings":["Division of Applied Mathematics, Brown University, Providence, RI 02912 USA, and Advanced Computing, Mathematics and Data Division, Pacific Northwest National Laboratory, Richland, WA 99352 USA"],"raw_orcid":"https://orcid.org/0000-0002-9713-7120","affiliations":[{"raw_affiliation_string":"Division of Applied Mathematics, Brown University, Providence, RI 02912 USA, and Advanced Computing, Mathematics and Data Division, Pacific Northwest National Laboratory, Richland, WA 99352 USA","institution_ids":["https://openalex.org/I142606810"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102725006","display_name":"Kenji Kawaguchi","orcid":"https://orcid.org/0000-0002-8883-9040"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Kenji Kawaguchi","raw_affiliation_strings":["Department of Computer Science, National University of Singapore, Singapore, 119077. The first three authors contributed equally"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, National University of Singapore, Singapore, 119077. The first three authors contributed equally","institution_ids":["https://openalex.org/I165932596"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5090943765"],"corresponding_institution_ids":["https://openalex.org/I165932596"],"apc_list":null,"apc_paid":null,"fwci":6.9467,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.97050745,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"47","issue":"4","first_page":"C846","last_page":"C872"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":1.0,"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":1.0,"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/T10597","display_name":"Nuclear reactor physics and engineering","score":0.9916999936103821,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10558","display_name":"Advancements in Semiconductor Devices and Circuit Design","score":0.9907000064849854,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/smoothing","display_name":"Smoothing","score":0.6685096621513367},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6387853026390076},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5796683430671692},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.5554194450378418},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4440743029117584},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3966883718967438},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33490675687789917},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2568287253379822},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.25144821405410767},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2298092246055603},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.164948970079422}],"concepts":[{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.6685096621513367},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6387853026390076},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5796683430671692},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.5554194450378418},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4440743029117584},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3966883718967438},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33490675687789917},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2568287253379822},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.25144821405410767},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2298092246055603},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.164948970079422},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/23m1621356","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1621356","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"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 Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2740495549","display_name":null,"funder_award_id":"FA2386-24-1-4011","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G6231692990","display_name":null,"funder_award_id":"AISG2-TC-2023-010-SGIL","funder_id":"https://openalex.org/F4320320709","funder_display_name":"National Research Foundation Singapore"}],"funders":[{"id":"https://openalex.org/F4320320709","display_name":"National Research Foundation Singapore","ror":"https://ror.org/03cpyc314"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W2625995436","https://openalex.org/W2749028154","https://openalex.org/W2754833785","https://openalex.org/W2797393904","https://openalex.org/W2803629276","https://openalex.org/W2899283552","https://openalex.org/W2948551291","https://openalex.org/W2954388788","https://openalex.org/W2958410505","https://openalex.org/W2964016242","https://openalex.org/W2969381807","https://openalex.org/W2993551995","https://openalex.org/W3004573026","https://openalex.org/W3028295718","https://openalex.org/W3081577261","https://openalex.org/W3093786597","https://openalex.org/W3098790586","https://openalex.org/W3098844932","https://openalex.org/W3099661895","https://openalex.org/W3104718096","https://openalex.org/W3128157635","https://openalex.org/W3163993681","https://openalex.org/W3180106877","https://openalex.org/W3199775905","https://openalex.org/W3208953217","https://openalex.org/W3213841907","https://openalex.org/W4212988227","https://openalex.org/W4310166644","https://openalex.org/W4310348270","https://openalex.org/W4389301323","https://openalex.org/W4396690897","https://openalex.org/W4411104046"],"related_works":["https://openalex.org/W1978572805","https://openalex.org/W2383807498","https://openalex.org/W1997992934","https://openalex.org/W1987225439","https://openalex.org/W4238188170","https://openalex.org/W2125114371","https://openalex.org/W2019977573","https://openalex.org/W2149980199","https://openalex.org/W3125766170","https://openalex.org/W2040641410"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":3}],"updated_date":"2026-05-02T08:42:23.175194","created_date":"2025-10-10T00:00:00"}