{"id":"https://openalex.org/W7163379615","doi":"https://doi.org/10.48550/arxiv.2606.03469","title":"Physics-guided correction for operator learning under model misspecification","display_name":"Physics-guided correction for operator learning under model misspecification","publication_year":2026,"publication_date":"2026-06-02","ids":{"openalex":"https://openalex.org/W7163379615","doi":"https://doi.org/10.48550/arxiv.2606.03469"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.03469","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.03469","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.2606.03469","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137757698","display_name":"Lei Ma","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ma, Lei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012268400","display_name":"Nicolas Boull\u00e9","orcid":"https://orcid.org/0000-0002-1425-8307"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Boull\u00e9, Nicolas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102685950","display_name":"Yusen Yang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yang, Yu-Sen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137798009","display_name":"Hao Wu","orcid":"https://orcid.org/0000-0002-5213-2959"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wu, Hao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5137804977","display_name":"Ling Guo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guo, Ling","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":0.9975000023841858,"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":0.9975000023841858,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.0006000000284984708,"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"}},{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.00019999999494757503,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.6797999739646912},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.6442000269889832},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.5386999845504761},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4212000072002411},{"id":"https://openalex.org/keywords/missing-data","display_name":"Missing data","score":0.4104999899864197},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.3517000079154968},{"id":"https://openalex.org/keywords/observational-error","display_name":"Observational error","score":0.3027999997138977}],"concepts":[{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6797999739646912},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6442000269889832},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.5386999845504761},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4862000048160553},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4657000005245209},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45320001244544983},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.435699999332428},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4212000072002411},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4140999913215637},{"id":"https://openalex.org/C9357733","wikidata":"https://www.wikidata.org/wiki/Q6878417","display_name":"Missing data","level":2,"score":0.4104999899864197},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3517000079154968},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3345000147819519},{"id":"https://openalex.org/C19619285","wikidata":"https://www.wikidata.org/wiki/Q196372","display_name":"Observational error","level":2,"score":0.3027999997138977},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.2987000048160553},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.29589998722076416},{"id":"https://openalex.org/C116672817","wikidata":"https://www.wikidata.org/wiki/Q1454986","display_name":"Physical system","level":2,"score":0.2883000075817108},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.2872999906539917},{"id":"https://openalex.org/C103088060","wikidata":"https://www.wikidata.org/wiki/Q1062839","display_name":"Error detection and correction","level":2,"score":0.2689000070095062},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.03469","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.03469","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.2606.03469","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.03469","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Physics-informed":[0],"operator":[1,67,80,90,101],"learning":[2,71],"provides":[3,126],"an":[4,93,135],"efficient":[5],"framework":[6,69,212],"for":[7,70,104],"approximating":[8],"solution":[9,72],"operators":[10,73],"of":[11,210],"partial":[12],"differential":[13],"equations":[14],"by":[15,92,196],"combining":[16],"observational":[17],"data":[18],"with":[19,160],"governing":[20,32,76,175],"physical":[21,47,95,169],"laws.":[22],"However,":[23],"most":[24],"existing":[25],"methods":[26],"implicitly":[27],"assume":[28],"that":[29,102,188],"the":[30,79,82,105,109,123,131,141,145,154,164,189,208,211],"prescribed":[31],"equation":[33],"is":[34,85,111,151],"accurate.":[35],"This":[36],"assumption":[37],"may":[38],"fail":[39],"in":[40],"practical":[41],"applications,":[42],"where":[43,122],"model":[44,58,96,165],"simplifications,":[45],"missing":[46],"effects,":[48],"parameter":[49],"drift,":[50],"or":[51],"incomplete":[52],"constitutive":[53],"relations":[54],"can":[55],"lead":[56],"to":[57,166,173,216],"misspecification.":[59],"In":[60],"this":[61],"work,":[62],"we":[63,114],"propose":[64],"a":[65,88,98,118,127],"physics-guided":[66],"correction":[68,100,137,150],"under":[74,201],"misspecified":[75,197],"equations.":[77,176],"At":[78],"level,":[81],"target":[83],"mapping":[84],"decomposed":[86],"into":[87,153],"prior":[89,128,146],"induced":[91,195],"approximate":[94],"and":[97,130,144,157,184,203,213],"learnable":[99],"accounts":[103],"remaining":[106],"discrepancy.":[107],"Although":[108],"formulation":[110],"architecture":[112],"independent,":[113],"realize":[115],"it":[116],"using":[117],"serial":[119],"DeepONet":[120,125,133],"architecture,":[121],"first":[124],"prediction":[129],"second":[132],"learns":[134],"additive":[136],"conditioned":[138],"on":[139,179],"both":[140],"input":[142],"function":[143],"prediction.":[147],"The":[148],"learned":[149],"incorporated":[152],"physics":[155],"residual":[156],"trained":[158],"together":[159],"data-consistency":[161],"constraints,":[162],"allowing":[163],"retain":[167],"useful":[168],"structure":[170],"while":[171],"adapting":[172],"inaccurate":[174],"Numerical":[177],"experiments":[178],"diffusion-reaction,":[180],"Burgers,":[181],"cavity":[182],"flow,":[183],"hyperelastic":[185],"problems":[186],"show":[187],"proposed":[190],"method":[191],"substantially":[192],"reduces":[193],"errors":[194],"physics.":[198],"Additional":[199],"tests":[200],"sparse":[202],"noisy":[204],"observations":[205],"further":[206],"demonstrate":[207],"robustness":[209],"its":[214],"ability":[215],"provide":[217],"informative":[218],"uncertainty":[219],"estimates":[220],"through":[221],"deep":[222],"ensembles.":[223]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-04T00:00:00"}
