{"id":"https://openalex.org/W7224135018","doi":"https://doi.org/10.48550/arxiv.2610.37359","title":"Multifidelity variational inference for derivative-free PDE-constrained inverse problems","display_name":"Multifidelity variational inference for derivative-free PDE-constrained inverse problems","publication_year":2026,"publication_date":"2026-10-27","ids":{"openalex":"https://openalex.org/W7224135018","doi":"https://doi.org/10.48550/arxiv.2610.37359"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.37359","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.37359","pdf_url":"https://arxiv.org/pdf/2610.37359","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.37359","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015313443","display_name":"Eric Parish","orcid":"https://orcid.org/0000-0002-5478-2998","observed_orcids":["https://orcid.org/0000-0002-5478-2998"]},"institutions":[{"id":"https://openalex.org/I192454743","display_name":"Sandia National Laboratories California","ror":"https://ror.org/058m7ey48","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I192454743","https://openalex.org/I198811213","https://openalex.org/I4210104735"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Parish, Eric J.","raw_affiliation_strings":["Sandia National Laboratories , Livermore , CA , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sandia National Laboratories , Livermore , CA , USA","institution_ids":["https://openalex.org/I192454743"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5015313443"],"corresponding_institution_ids":["https://openalex.org/I192454743"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.3127000033855438,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.3127000033855438,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.3093000054359436,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.24869999289512634,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/derivative-free-optimization","display_name":"derivative-free optimization","score":0.8669999837875366},{"id":"https://openalex.org/keywords/evidence-lower-bound","display_name":"evidence lower bound","score":0.8299999833106995},{"id":"https://openalex.org/keywords/variance-reduction","display_name":"variance reduction","score":0.7509999871253967},{"id":"https://openalex.org/keywords/model-reduction","display_name":"model reduction","score":0.8730000257492065},{"id":"https://openalex.org/keywords/second-order-optimization","display_name":"second-order optimization","score":0.7149999737739563},{"id":"https://openalex.org/keywords/adaptive-model-updating","display_name":"adaptive model updating","score":0.4350000023841858}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6966999769210815},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.6575999855995178},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.6201000213623047},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5996999740600586},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5981000065803528},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.5325999855995178},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.5192999839782715},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49320000410079956},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.4860000014305115},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.4846999943256378},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.448199987411499},{"id":"https://openalex.org/C2777472644","wikidata":"https://www.wikidata.org/wiki/Q16968992","display_name":"Approximate inference","level":3,"score":0.42399999499320984},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.40139999985694885},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.3504999876022339},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.3483000099658966},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.3407000005245209},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3393000066280365},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.33880001306533813},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32600000500679016},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.3240000009536743},{"id":"https://openalex.org/C57830394","wikidata":"https://www.wikidata.org/wiki/Q278079","display_name":"Posterior probability","level":3,"score":0.32109999656677246},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.3188000023365021},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.30970001220703125},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3093999922275543},{"id":"https://openalex.org/C62644790","wikidata":"https://www.wikidata.org/wiki/Q3454689","display_name":"Variance reduction","level":3,"score":0.30230000615119934},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.2791000008583069},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.2743000090122223},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.2685000002384186},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.25529998540878296},{"id":"https://openalex.org/C162376815","wikidata":"https://www.wikidata.org/wiki/Q2158281","display_name":"Frequentist inference","level":4,"score":0.25450000166893005}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.37359","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.37359","pdf_url":"https://arxiv.org/pdf/2610.37359","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2610.37359","doi":"https://doi.org/10.48550/arxiv.2610.37359","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.37359","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.37359","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.37359","pdf_url":"https://arxiv.org/pdf/2610.37359","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G11630931","display_name":null,"funder_award_id":"DENA0003525","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G2214935549","display_name":null,"funder_award_id":"NA0003525","funder_id":"https://openalex.org/F4320338291","funder_display_name":"Sandia National Laboratories"},{"id":"https://openalex.org/G413247060","display_name":null,"funder_award_id":"DE\u2010NA,0003525","funder_id":"https://openalex.org/F4320338291","funder_display_name":"Sandia National Laboratories"},{"id":"https://openalex.org/G4903105778","display_name":null,"funder_award_id":"NA0003525","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G5339743583","display_name":null,"funder_award_id":"NA0003525","funder_id":"https://openalex.org/F4320332369","funder_display_name":"National Nuclear Security Administration"},{"id":"https://openalex.org/G855168022","display_name":null,"funder_award_id":"DENA-0003525","funder_id":"https://openalex.org/F4320332369","funder_display_name":"National Nuclear Security Administration"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320332369","display_name":"National Nuclear Security Administration","ror":"https://ror.org/03sk1we31"},{"id":"https://openalex.org/F4320338291","display_name":"Sandia National Laboratories","ror":"https://ror.org/01apwpt12"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7224135018.pdf","grobid_xml":"https://content.openalex.org/works/W7224135018.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7161544201","https://openalex.org/W4406231171","https://openalex.org/W7102797938","https://openalex.org/W4415053851","https://openalex.org/W4221167292","https://openalex.org/W3210999712","https://openalex.org/W3135985701","https://openalex.org/W2755770519","https://openalex.org/W4388898500","https://openalex.org/W7172416709"],"abstract_inverted_index":{"We":[0,92,134,175],"develop":[1,94],"a":[2,66,73,95,122,169,183],"multifidelity":[3,60],"black-box":[4],"variational":[5,128,162],"inference":[6,163],"(MF-BBVI)":[7],"approach":[8,159],"for":[9,32,90,137,164],"PDE-constrained":[10,192],"Bayesian":[11],"inverse":[12,166,193],"problems":[13,167],"in":[14,171],"which":[15,38],"forward":[16],"solves":[17],"are":[18,23,46],"expensive":[19],"and":[20,83,104,119,141,154,190],"PDE":[21,43],"gradients":[22],"unavailable.":[24],"The":[25,157],"method":[26,178],"is":[27],"built":[28],"on":[29,101,179],"score-function":[30,106],"estimators":[31,63],"the":[33,42,84,127,132,139,143,177],"evidence":[34],"lower":[35],"bound":[36],"(ELBO),":[37],"avoid":[39],"differentiation":[40],"through":[41,168],"model":[44,110,124],"but":[45],"known":[47],"to":[48,79],"suffer":[49],"from":[50],"high":[51,56],"variance.":[52],"To":[53],"address":[54],"this":[55],"variance,":[57],"we":[58,112],"employ":[59],"approximate":[61,144],"control-variate":[62,145],"that":[64,117],"combine":[65],"small":[67],"number":[68,75,85],"of":[69,76,86],"high-fidelity":[70,87],"samples":[71,78],"with":[72,186],"larger":[74],"low-fidelity":[77,109],"reduce":[80],"estimator":[81,150],"variance":[82,152],"evaluations":[88],"required":[89],"optimization.":[91,133],"further":[93],"PDE-derivative-free":[96],"second-order":[97],"optimization":[98],"strategy":[99,116],"based":[100],"both":[102],"gradient":[103],"Hessian":[105],"estimators.":[107],"For":[108],"generation,":[111],"propose":[113],"an":[114,187],"on-the-fly":[115],"builds":[118],"adaptively":[120],"updates":[121],"reduced-order":[123],"(ROM)":[125],"as":[126],"distribution":[129],"evolves":[130],"throughout":[131],"investigate":[135],"strategies":[136],"adapting":[138],"ROM":[140],"estimating":[142],"gains,":[146],"examining":[147],"tradeoffs":[148],"between":[149],"bias,":[151],"reduction,":[153],"computational":[155,173],"cost.":[156,174],"resulting":[158],"facilitates":[160],"derivative-free":[161],"large-scale":[165],"reduction":[170],"overall":[172],"demonstrate":[176],"four":[180],"numerical":[181],"examples:":[182],"linear":[184],"benchmark":[185],"exact":[188],"posterior":[189],"three":[191],"problems.":[194]},"counts_by_year":[],"updated_date":"2026-11-01T11:40:01.658920","created_date":"2026-10-29T00:00:00"}