{"id":"https://openalex.org/W7162804778","doi":"https://doi.org/10.48550/arxiv.2605.29373","title":"Deep Adaptive Dimension Reduction for Bayesian Inference in Inverse Problems","display_name":"Deep Adaptive Dimension Reduction for Bayesian Inference in Inverse Problems","publication_year":2026,"publication_date":"2026-05-28","ids":{"openalex":"https://openalex.org/W7162804778","doi":"https://doi.org/10.48550/arxiv.2605.29373"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.29373","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.29373","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,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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.2605.29373","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137322486","display_name":"Yueyang Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Yueyang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137336250","display_name":"Xili Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Xili","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137388692","display_name":"Kejun Tang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tang, Kejun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137365889","display_name":"Xiaoliang Wan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wan, Xiaoliang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137368470","display_name":"Tao Zhou","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhou, Tao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5137393507","display_name":"Chao Yang","orcid":"https://orcid.org/0000-0001-6067-7505"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yang, Chao","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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.40540000796318054,"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"}},"topics":[{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.40540000796318054,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.3481999933719635,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.09200000017881393,"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/inverse-problem","display_name":"Inverse problem","score":0.5985999703407288},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.5059000253677368},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4729999899864197},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.4706999957561493},{"id":"https://openalex.org/keywords/prior-probability","display_name":"Prior probability","score":0.44209998846054077},{"id":"https://openalex.org/keywords/posterior-probability","display_name":"Posterior probability","score":0.42739999294281006},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.4259999990463257},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.42080000042915344},{"id":"https://openalex.org/keywords/bayesian-inference","display_name":"Bayesian inference","score":0.3962000012397766}],"concepts":[{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5985999703407288},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.5059000253677368},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47749999165534973},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4747999906539917},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4729999899864197},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.4706999957561493},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45719999074935913},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.44209998846054077},{"id":"https://openalex.org/C57830394","wikidata":"https://www.wikidata.org/wiki/Q278079","display_name":"Posterior probability","level":3,"score":0.42739999294281006},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.4259999990463257},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.42080000042915344},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.3962000012397766},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.39239999651908875},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38850000500679016},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.3831999897956848},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.37130001187324524},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.3580000102519989},{"id":"https://openalex.org/C131675550","wikidata":"https://www.wikidata.org/wiki/Q7646884","display_name":"Surrogate model","level":2,"score":0.3091000020503998},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.29660001397132874},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.2865000069141388},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.2818000018596649},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.2777999937534332},{"id":"https://openalex.org/C93959086","wikidata":"https://www.wikidata.org/wiki/Q6888345","display_name":"Model selection","level":2,"score":0.27619999647140503},{"id":"https://openalex.org/C115311070","wikidata":"https://www.wikidata.org/wiki/Q5347255","display_name":"Effective dimension","level":3,"score":0.2732999920845032},{"id":"https://openalex.org/C37903108","wikidata":"https://www.wikidata.org/wiki/Q4874474","display_name":"Bayesian linear regression","level":4,"score":0.2646999955177307},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2644999921321869},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.25850000977516174},{"id":"https://openalex.org/C68022304","wikidata":"https://www.wikidata.org/wiki/Q842217","display_name":"Bayes estimator","level":3,"score":0.25440001487731934}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.29373","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.29373","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,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.29373","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.29373","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,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":{"Solving":[0],"high-dimensional":[1,198],"PDE-governed":[2,161],"inverse":[3,162],"problems":[4,163],"is":[5],"often":[6],"challenging":[7,191],"due":[8],"to":[9,139],"complex":[10,93],"non-Gaussian":[11],"posterior":[12,94,112,149],"distributions,":[13],"expensive":[14],"forward":[15],"model":[16],"evaluations,":[17],"and":[18,51,74,87,158,177,197],"misspecified":[19],"prior":[20,73,101,108,116],"information.":[21],"To":[22],"address":[23],"these":[24],"issues,":[25],"we":[26],"propose":[27],"a":[28,79,121,154],"deep":[29],"adaptive":[30,123],"dimension-reduction":[31],"Bayesian":[32],"inference":[33],"framework":[34],"based":[35],"on":[36,153],"the":[37,71,107,141,144,185],"Variational":[38],"Flow":[39],"(VF)":[40],"model.":[41],"Since":[42],"standard":[43,160],"normalizing":[44,68],"flows":[45,69],"are":[46],"restricted":[47],"by":[48,60],"bijective":[49],"mappings":[50],"cannot":[52],"directly":[53],"reduce":[54],"dimensions,":[55],"VF":[56,135],"overcomes":[57],"this":[58],"limitation":[59],"integrating":[61],"VAE-based":[62],"nonlinear":[63],"dimension":[64],"reduction":[65],"with":[66,126,174,184],"dual":[67],"for":[70],"latent":[72],"encoder.":[75],"This":[76],"design":[77],"provides":[78],"strictly":[80],"higher":[81],"evidence":[82],"lower":[83],"bound":[84],"than":[85],"VAE":[86],"allows":[88],"more":[89],"flexible":[90],"approximation":[91],"of":[92],"distributions.":[95],"We":[96],"further":[97,147],"introduce":[98],"an":[99,127],"iterative":[100],"updating":[102],"strategy":[103],"that":[104,165],"gradually":[105],"moves":[106],"mean":[109],"toward":[110],"high-probability":[111],"regions,":[113],"avoiding":[114],"manual":[115],"tuning.":[117],"These":[118],"components":[119],"form":[120],"closed":[122],"loop":[124],"together":[125],"adaptively":[128],"fine-tuned":[129],"Fourier":[130],"Neural":[131],"Operator":[132],"(FNO)":[133],"surrogate:":[134],"generates":[136],"posterior-concentrated":[137],"samples":[138],"refine":[140],"surrogate,":[142],"while":[143],"updated":[145],"surrogate":[146],"improves":[148],"inference.":[150],"Numerical":[151],"experiments":[152],"100-dimensional":[155],"Rosenbrock":[156],"problem":[157],"three":[159],"show":[164],"our":[166],"method":[167],"delivers":[168],"competitive":[169],"or":[170],"superior":[171],"accuracy":[172],"compared":[173],"MCMC,":[175],"UKI,":[176],"SVGD":[178],"baselines":[179],"across":[180],"all":[181],"tested":[182],"configurations,":[183],"most":[186],"pronounced":[187],"advantages":[188],"emerging":[189],"in":[190],"scenarios":[192],"such":[193],"as":[194],"high-noise":[195],"observations":[196],"parameter":[199],"spaces.":[200]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-30T00:00:00"}