{"id":"https://openalex.org/W4367059178","doi":"https://doi.org/10.1088/2632-2153/acd0a1","title":"Spectrally adapted physics-informed neural networks for solving unbounded domain problems","display_name":"Spectrally adapted physics-informed neural networks for solving unbounded domain problems","publication_year":2023,"publication_date":"2023-04-26","ids":{"openalex":"https://openalex.org/W4367059178","doi":"https://doi.org/10.1088/2632-2153/acd0a1"},"language":"en","primary_location":{"id":"doi:10.1088/2632-2153/acd0a1","is_oa":true,"landing_page_url":"https://doi.org/10.1088/2632-2153/acd0a1","pdf_url":"https://iopscience.iop.org/article/10.1088/2632-2153/acd0a1/pdf","source":{"id":"https://openalex.org/S4210200687","display_name":"Machine Learning Science and Technology","issn_l":"2632-2153","issn":["2632-2153"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning: Science and Technology","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://iopscience.iop.org/article/10.1088/2632-2153/acd0a1/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088069608","display_name":"Mingtao Xia","orcid":"https://orcid.org/0000-0002-2116-4712"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mingtao Xia","raw_affiliation_strings":["Mathematics, University of California Los Angeles, Department of Mathematics, UCLA, Los Angeles, California, 90095, UNITED STATES"],"raw_orcid":"https://orcid.org/0000-0002-2116-4712","affiliations":[{"raw_affiliation_string":"Mathematics, University of California Los Angeles, Department of Mathematics, UCLA, Los Angeles, California, 90095, UNITED STATES","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088737112","display_name":"Lucas B\u00f6ttcher","orcid":"https://orcid.org/0000-0003-1700-1897"},"institutions":[{"id":"https://openalex.org/I71675930","display_name":"Frankfurt School of Finance & Management","ror":"https://ror.org/05gxyna29","country_code":"DE","type":"education","lineage":["https://openalex.org/I71675930"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Lucas B\u00f6ttcher","raw_affiliation_strings":["Frankfurt School of Finance & Management gGmbH, Frankfurt School of Finance and Management, Frankfurt am Main, 60322, GERMANY"],"raw_orcid":"https://orcid.org/0000-0003-1700-1897","affiliations":[{"raw_affiliation_string":"Frankfurt School of Finance & Management gGmbH, Frankfurt School of Finance and Management, Frankfurt am Main, 60322, GERMANY","institution_ids":["https://openalex.org/I71675930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044310323","display_name":"Tom Chou","orcid":"https://orcid.org/0000-0003-0785-6349"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Tom Chou","raw_affiliation_strings":["Department of Mathematics, University of California - Los Angeles, Los Angeles, CA 90095-1555, USA, Los Angeles, California, 90095-1766, UNITED STATES"],"raw_orcid":"https://orcid.org/0000-0003-0785-6349","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California - Los Angeles, Los Angeles, CA 90095-1555, USA, Los Angeles, California, 90095-1766, UNITED STATES","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5044310323"],"corresponding_institution_ids":["https://openalex.org/I161318765"],"apc_list":{"value":1600,"currency":"GBP","value_usd":1962},"apc_paid":{"value":1600,"currency":"GBP","value_usd":1962},"fwci":1.891,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.84319657,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"4","issue":"2","first_page":"025024","last_page":"025024"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998999834060669,"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":0.9998999834060669,"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/T11222","display_name":"Magnetic Properties and Applications","score":0.9678999781608582,"subfield":{"id":"https://openalex.org/subfields/2504","display_name":"Electronic, Optical and Magnetic Materials"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9677000045776367,"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/partial-differential-equation","display_name":"Partial differential equation","score":0.6637381315231323},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.6108110547065735},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5481359362602234},{"id":"https://openalex.org/keywords/semi-infinite","display_name":"Semi-infinite","score":0.544130802154541},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5166409611701965},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5114380121231079},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4750392735004425},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4417574405670166},{"id":"https://openalex.org/keywords/spectral-method","display_name":"Spectral method","score":0.4370720386505127},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.41162675619125366},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40746602416038513},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33845412731170654},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2200939953327179},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15757524967193604},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09130486845970154}],"concepts":[{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6637381315231323},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.6108110547065735},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5481359362602234},{"id":"https://openalex.org/C194571181","wikidata":"https://www.wikidata.org/wiki/Q7449306","display_name":"Semi-infinite","level":2,"score":0.544130802154541},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5166409611701965},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5114380121231079},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4750392735004425},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4417574405670166},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.4370720386505127},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.41162675619125366},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40746602416038513},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33845412731170654},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2200939953327179},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15757524967193604},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09130486845970154}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1088/2632-2153/acd0a1","is_oa":true,"landing_page_url":"https://doi.org/10.1088/2632-2153/acd0a1","pdf_url":"https://iopscience.iop.org/article/10.1088/2632-2153/acd0a1/pdf","source":{"id":"https://openalex.org/S4210200687","display_name":"Machine Learning Science and Technology","issn_l":"2632-2153","issn":["2632-2153"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning: Science and Technology","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:18c160c2081a40e7ba4d48fc7d71047e","is_oa":true,"landing_page_url":"https://doaj.org/article/18c160c2081a40e7ba4d48fc7d71047e","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Machine Learning: Science and Technology, Vol 4, Iss 2, p 025024 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1088/2632-2153/acd0a1","is_oa":true,"landing_page_url":"https://doi.org/10.1088/2632-2153/acd0a1","pdf_url":"https://iopscience.iop.org/article/10.1088/2632-2153/acd0a1/pdf","source":{"id":"https://openalex.org/S4210200687","display_name":"Machine Learning Science and Technology","issn_l":"2632-2153","issn":["2632-2153"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning: Science and Technology","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4549092555","display_name":null,"funder_award_id":"W911NF-18-1-0345","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G7597751644","display_name":null,"funder_award_id":"DMS-1814364","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"}],"funders":[{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":80,"referenced_works":["https://openalex.org/W1836465849","https://openalex.org/W1972766745","https://openalex.org/W1988115241","https://openalex.org/W2018041415","https://openalex.org/W2018435387","https://openalex.org/W2031848051","https://openalex.org/W2044231677","https://openalex.org/W2075210326","https://openalex.org/W2076479791","https://openalex.org/W2103641845","https://openalex.org/W2131263864","https://openalex.org/W2137983211","https://openalex.org/W2164971396","https://openalex.org/W2165083863","https://openalex.org/W2165281880","https://openalex.org/W2765872171","https://openalex.org/W2766151966","https://openalex.org/W2785024182","https://openalex.org/W2896377340","https://openalex.org/W2899283552","https://openalex.org/W2899771611","https://openalex.org/W2903849629","https://openalex.org/W2944878488","https://openalex.org/W2962727772","https://openalex.org/W2962730452","https://openalex.org/W2963376662","https://openalex.org/W2975293371","https://openalex.org/W2979786244","https://openalex.org/W2989551852","https://openalex.org/W2991550674","https://openalex.org/W2997588930","https://openalex.org/W2998366519","https://openalex.org/W3008118574","https://openalex.org/W3010849941","https://openalex.org/W3011053680","https://openalex.org/W3026782428","https://openalex.org/W3029817982","https://openalex.org/W3083106948","https://openalex.org/W3086358797","https://openalex.org/W3092923133","https://openalex.org/W3098546160","https://openalex.org/W3101826276","https://openalex.org/W3104592699","https://openalex.org/W3114000978","https://openalex.org/W3118628401","https://openalex.org/W3119206788","https://openalex.org/W3122402965","https://openalex.org/W3124006463","https://openalex.org/W3153522897","https://openalex.org/W3157506487","https://openalex.org/W3163993681","https://openalex.org/W3195988074","https://openalex.org/W3199727000","https://openalex.org/W3201666041","https://openalex.org/W3214496267","https://openalex.org/W4206582666","https://openalex.org/W4212954647","https://openalex.org/W4224882380","https://openalex.org/W4225717750","https://openalex.org/W4283381398","https://openalex.org/W4283712797","https://openalex.org/W4299590935","https://openalex.org/W4315477618","https://openalex.org/W4316926549","https://openalex.org/W4321328685","https://openalex.org/W6638667902","https://openalex.org/W6638908295","https://openalex.org/W6746017139","https://openalex.org/W6748177122","https://openalex.org/W6748581759","https://openalex.org/W6756040250","https://openalex.org/W6758539823","https://openalex.org/W6770495777","https://openalex.org/W6770852944","https://openalex.org/W6771456444","https://openalex.org/W6779567887","https://openalex.org/W6784227514","https://openalex.org/W6794429221","https://openalex.org/W6804467878","https://openalex.org/W6810803390"],"related_works":["https://openalex.org/W2386387936","https://openalex.org/W2623347760","https://openalex.org/W2140087070","https://openalex.org/W3034138874","https://openalex.org/W2964100222","https://openalex.org/W2796094661","https://openalex.org/W2505215844","https://openalex.org/W1014722270","https://openalex.org/W4226005585","https://openalex.org/W4367059178"],"abstract_inverted_index":{"Abstract":[0],"Solving":[1],"analytically":[2],"intractable":[3],"partial":[4],"differential":[5],"equations":[6],"(PDEs)":[7],"that":[8,33,79,136],"involve":[9],"at":[10,46,103],"least":[11,47],"one":[12],"variable":[13,44],"defined":[14],"on":[15,41],"an":[16],"unbounded":[17,26,43,133,170],"domain":[18,27,134],"arises":[19],"in":[20,106,159,169],"numerous":[21],"physical":[22],"applications.":[23],"Accurately":[24],"solving":[25,160],"PDEs":[28,98,161],"requires":[29],"efficient":[30],"numerical":[31,64,77,93,101,130],"methods":[32,69,120],"can":[34,121],"resolve":[35],"the":[36,39,42,85,151,154],"dependence":[37],"of":[38,50,63,84,87,132,147,153],"PDE":[40,126],"over":[45],"several":[48],"orders":[49],"magnitude.":[51],"We":[52,110],"propose":[53],"a":[54,145],"solution":[55],"to":[56,89,95,128],"such":[57],"problems":[58,135],"by":[59,141],"combining":[60],"two":[61],"classes":[62],"methods:":[65],"(i)":[66],"adaptive":[67,116],"spectral":[68,119],"and":[70,99,108,162],"(ii)":[71],"physics-informed":[72],"neural":[73],"networks":[74],"(PINNs).":[75],"The":[76],"approach":[78],"we":[80,149],"develop":[81],"takes":[82],"advantage":[83],"ability":[86],"PINNs":[88,158],"easily":[90],"implement":[91],"high-order":[92],"schemes":[94],"efficiently":[96,139],"solve":[97],"extrapolate":[100],"solutions":[102,131],"any":[104],"point":[105],"space":[107],"time.":[109],"then":[111],"show":[112],"how":[113],"recently":[114],"introduced":[115],"techniques":[117],"for":[118],"be":[122,138],"integrated":[123],"into":[124],"PINN-based":[125],"solvers":[127],"obtain":[129],"cannot":[137],"approximated":[140],"standard":[142],"PINNs.":[143],"Through":[144],"number":[146],"examples,":[148],"demonstrate":[150],"advantages":[152],"proposed":[155],"spectrally":[156],"adapted":[157],"estimating":[163],"model":[164],"parameters":[165],"from":[166],"noisy":[167],"observations":[168],"domains.":[171]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":7}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
