{"id":"https://openalex.org/W7133346090","doi":"https://doi.org/10.48550/arxiv.2603.01420","title":"Tackling multiphysics problems via finite element-guided physics-informed operator learning","display_name":"Tackling multiphysics problems via finite element-guided physics-informed operator learning","publication_year":2026,"publication_date":"2026-03-02","ids":{"openalex":"https://openalex.org/W7133346090","doi":"https://doi.org/10.48550/arxiv.2603.01420"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.01420","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.01420","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":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.01420","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044024598","display_name":"Yusuke Yamazaki","orcid":"https://orcid.org/0009-0001-4104-9228"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yamazaki, Yusuke","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048938990","display_name":"Reza Najian Asl","orcid":"https://orcid.org/0000-0002-6657-888X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Asl, Reza Najian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5121275639","display_name":"Markus Apel","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Apel, Markus","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5127934770","display_name":"Mayu Muramatsu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Muramatsu, Mayu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5127983434","display_name":"Shahed Rezaei","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rezaei, Shahed","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.9301000237464905,"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":0.9301000237464905,"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/T11948","display_name":"Machine Learning in Materials Science","score":0.04309999942779541,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"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/T10514","display_name":"Numerical methods in engineering","score":0.0019000000320374966,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/multiphysics","display_name":"Multiphysics","score":0.715399980545044},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5838000178337097},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5055000185966492},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.45570001006126404},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.43810001015663147},{"id":"https://openalex.org/keywords/rotation-formalisms-in-three-dimensions","display_name":"Rotation formalisms in three dimensions","score":0.3968999981880188},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.3887999951839447},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.3610000014305115}],"concepts":[{"id":"https://openalex.org/C46435376","wikidata":"https://www.wikidata.org/wiki/Q1829750","display_name":"Multiphysics","level":3,"score":0.715399980545044},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5838000178337097},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5724999904632568},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5055000185966492},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.45570001006126404},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.43810001015663147},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.41280001401901245},{"id":"https://openalex.org/C171018156","wikidata":"https://www.wikidata.org/wiki/Q7370306","display_name":"Rotation formalisms in three dimensions","level":2,"score":0.3968999981880188},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3887999951839447},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3610000014305115},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.35989999771118164},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32910001277923584},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.31869998574256897},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.31299999356269836},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.3122999966144562},{"id":"https://openalex.org/C22367795","wikidata":"https://www.wikidata.org/wiki/Q7625208","display_name":"Structured prediction","level":2,"score":0.30239999294281006},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2863999903202057},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.2842000126838684},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.28209999203681946},{"id":"https://openalex.org/C159674985","wikidata":"https://www.wikidata.org/wiki/Q6823718","display_name":"Method of mean weighted residuals","level":4,"score":0.2791999876499176},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2705000042915344},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.26930001378059387},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.26010000705718994},{"id":"https://openalex.org/C136389625","wikidata":"https://www.wikidata.org/wiki/Q334384","display_name":"Supervised learning","level":3,"score":0.25920000672340393},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.25600001215934753},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.2533000111579895}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.01420","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.01420","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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.01420","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.01420","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":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"work":[1],"presents":[2],"a":[3,37,70,94,134,199,204,231,236],"finite":[4,44,121,138,232],"element-guided":[5,122],"physics-informed":[6,227],"operator":[7,27,72,130,139,178,228],"learning":[8,73,140,179,229],"framework":[9,24,62],"for":[10,63,181,209,241],"multiphysics":[11,64,243],"problems":[12,65],"with":[13,36,89,118,230],"coupled":[14,80,242],"partial":[15],"differential":[16],"equations":[17],"(PDEs)":[18],"on":[19,42,56,78,144,158,188],"arbitrary":[20],"domains.":[21],"The":[22,60,148],"proposed":[23,120,136],"learns":[25],"an":[26],"from":[28],"the":[29,33,43,51,106,111,119,162,170,220,224],"input":[30],"space":[31,35],"to":[32],"solution":[34,156],"weighted":[38],"residual":[39],"formulation":[40],"based":[41,143],"element":[45],"method,":[46],"enabling":[47],"discretization-independent":[48],"prediction":[49],"beyond":[50],"training":[52,189,194,201,213],"resolution":[53],"without":[54],"relying":[55],"labeled":[57],"simulation":[58],"data.":[59],"present":[61,221],"is":[66,76,207],"implemented":[67],"in":[68,169],"Folax,":[69],"JAX-based":[71],"platform,":[74],"and":[75,84,93,133,173,183,193,238],"verified":[77],"nonlinear":[79],"thermo-mechanical":[81],"problems.":[82,108],"Two-":[83],"three-dimensional":[85],"representative":[86],"volume":[87],"elements":[88],"varying":[90,100],"heterogeneous":[91],"microstructures,":[92],"close-to-reality":[95],"industrial":[96],"casting":[97],"example":[98,107],"under":[99],"boundary":[101],"conditions":[102],"are":[103],"investigated":[104],"as":[105,235],"We":[109],"investigate":[110],"potential":[112,225],"of":[113,226],"several":[114],"neural":[115,126,146],"operators":[116,127,157],"combined":[117],"approach,":[123],"including":[124],"Fourier":[125],"(FNOs),":[128],"deep":[129],"networks":[131],"(DeepONets),":[132],"newly":[135],"implicit":[137],"(iFOL)":[141],"approach":[142,222,240],"conditional":[145],"fields.":[147],"results":[149],"demonstrate":[150],"that":[151,198],"FNOs":[152],"yield":[153],"highly":[154],"accurate":[155,210],"regular":[159],"domains,":[160],"where":[161],"global":[163],"features":[164],"can":[165],"be":[166],"efficiently":[167],"learned":[168],"spectral":[171],"domain,":[172],"iFOL":[174],"offers":[175],"efficient":[176],"parametric":[177],"capabilities":[180],"complex":[182],"irregular":[184],"geometries.":[185],"Furthermore,":[186],"studies":[187],"strategies,":[190],"network":[191,206],"decomposition,":[192],"sample":[195,214],"quality":[196,215],"reveal":[197],"monolithic":[200],"strategy":[202],"using":[203],"single":[205],"sufficient":[208],"predictions,":[211],"while":[212],"strongly":[216],"influences":[217],"performance.":[218],"Overall,":[219],"highlights":[223],"element-based":[233],"loss":[234],"unified":[237],"scalable":[239],"simulations.":[244]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-03-04T00:00:00"}