{"id":"https://openalex.org/W7213587772","doi":"https://doi.org/10.48550/arxiv.2609.20794","title":"PosteriorBench: From Point Estimates to Posterior Matching in Evaluating Generative Inverse Solvers","display_name":"PosteriorBench: From Point Estimates to Posterior Matching in Evaluating Generative Inverse Solvers","publication_year":2026,"publication_date":"2026-09-17","ids":{"openalex":"https://openalex.org/W7213587772","doi":"https://doi.org/10.48550/arxiv.2609.20794"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.20794","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20794","pdf_url":"https://arxiv.org/pdf/2609.20794","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.20794","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019802589","display_name":"Jiachen Yao","orcid":"https://orcid.org/0000-0002-1575-891X","observed_orcids":["https://orcid.org/0000-0002-1575-891X"]},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yao, Jiachen","raw_affiliation_strings":["California Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"California Institute of Technology","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5152139789","display_name":"Zi-Siang Hsu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I16733864","display_name":"National Taiwan University","ror":"https://ror.org/05bqach95","country_code":"TW","type":"education","lineage":["https://openalex.org/I16733864"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Hsu, Zi-Siang","raw_affiliation_strings":["National Taiwan University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Taiwan University","institution_ids":["https://openalex.org/I16733864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5152134753","display_name":"Xi Deng","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Deng, Xi","raw_affiliation_strings":["California Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"California Institute of Technology","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5152136128","display_name":"Aditi Gupta","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I148283060","display_name":"Lawrence Berkeley National Laboratory","ror":"https://ror.org/02jbv0t02","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I148283060","https://openalex.org/I39565521"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gupta, Aditi","raw_affiliation_strings":["Lawrence Berkeley National Laboratory"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lawrence Berkeley National Laboratory","institution_ids":["https://openalex.org/I148283060"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036781407","display_name":"Xin Ju","orcid":"https://orcid.org/0000-0003-4110-7472","observed_orcids":["https://orcid.org/0000-0003-4110-7472"]},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ju, Xin","raw_affiliation_strings":["Department of Energy Science and Engineering , Stanford University","EarthFlow AI , Inc "],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Energy Science and Engineering , Stanford University","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"EarthFlow AI , Inc ","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054164034","display_name":"Sally M. Benson","orcid":"https://orcid.org/0000-0002-3733-4296","observed_orcids":["https://orcid.org/0000-0002-3733-4296","https://orcid.org/0000-0003-1947-3118"]},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Benson, Sally M","raw_affiliation_strings":["Department of Energy Science and Engineering , Stanford University","EarthFlow AI , Inc "],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Energy Science and Engineering , Stanford University","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"EarthFlow AI , Inc ","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007168661","display_name":"Gege Wen","orcid":"https://orcid.org/0000-0003-1668-3777","observed_orcids":["https://orcid.org/0000-0003-1668-3777"]},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Wen, Gege","raw_affiliation_strings":["Department of Earth Sciences and Engineering , Imperial College London","EarthFlow AI , Inc "],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Earth Sciences and Engineering , Imperial College London","institution_ids":["https://openalex.org/I47508984"]},{"raw_affiliation_string":"EarthFlow AI , Inc ","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023215207","display_name":"Animashree Anandkumar","orcid":"https://orcid.org/0000-0002-6974-6797","observed_orcids":["https://orcid.org/0000-0002-6974-6797"]},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anandkumar, Anima","raw_affiliation_strings":["California Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"California Institute of Technology","institution_ids":["https://openalex.org/I122411786"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.8666999936103821,"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":0.8666999936103821,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.05620000138878822,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"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":0.013700000010430813,"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/posterior-matching","display_name":"posterior matching","score":0.8349999785423279},{"id":"https://openalex.org/keywords/benchmarking","display_name":"benchmarking","score":0.36000001430511475},{"id":"https://openalex.org/keywords/ill-posed-inverse-problems","display_name":"ill-posed inverse problems","score":0.8410000205039978},{"id":"https://openalex.org/keywords/uncertainty-quantification","display_name":"uncertainty quantification","score":0.8859999775886536},{"id":"https://openalex.org/keywords/mode-collapse","display_name":"mode collapse","score":0.8009999990463257},{"id":"https://openalex.org/keywords/carbon-capture-and-storage","display_name":"carbon capture and storage","score":0.9810000061988831},{"id":"https://openalex.org/keywords/light-transport","display_name":"light transport","score":0.8009999990463257},{"id":"https://openalex.org/keywords/neural-operators","display_name":"neural operators","score":0.9350000023841858},{"id":"https://openalex.org/keywords/wasserstein-distance","display_name":"Wasserstein distance","score":0.7120000123977661},{"id":"https://openalex.org/keywords/maximum-mean-discrepancy","display_name":"maximum mean discrepancy","score":0.7649999856948853},{"id":"https://openalex.org/keywords/sparse-sensing","display_name":"sparse sensing","score":0.5370000004768372}],"concepts":[{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.853600025177002},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.5723999738693237},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5392000079154968},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.520799994468689},{"id":"https://openalex.org/C57830394","wikidata":"https://www.wikidata.org/wiki/Q278079","display_name":"Posterior probability","level":3,"score":0.5076000094413757},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4952999949455261},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.4668000042438507},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4666000008583069},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.44179999828338623},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4404999911785126},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4339999854564667},{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.4050000011920929},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.39160001277923584},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.38769999146461487},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3785000145435333},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.36340001225471497},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.35749998688697815},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.31459999084472656},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.31360000371932983},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.3125},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.31060001254081726},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3061999976634979},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.30399999022483826},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.2874000072479248},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.27649998664855957},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.2685999870300293},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.265500009059906},{"id":"https://openalex.org/C43521106","wikidata":"https://www.wikidata.org/wiki/Q2165493","display_name":"Pipeline (software)","level":2,"score":0.251800000667572}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.20794","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20794","pdf_url":"https://arxiv.org/pdf/2609.20794","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.2609.20794","doi":"https://doi.org/10.48550/arxiv.2609.20794","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.20794","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:2609.20794","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20794","pdf_url":"https://arxiv.org/pdf/2609.20794","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/G1013331665","display_name":null,"funder_award_id":"N00014-23-1-2654","funder_id":"https://openalex.org/F4320333591","funder_display_name":"Multidisciplinary University Research Initiative"},{"id":"https://openalex.org/G2582167037","display_name":null,"funder_award_id":"N00014-23-1-2654","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320333591","display_name":"Multidisciplinary University Research Initiative","ror":null},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213587772.pdf","grobid_xml":"https://content.openalex.org/works/W7213587772.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7127943859","https://openalex.org/W4413104748","https://openalex.org/W6929563116","https://openalex.org/W7214243312","https://openalex.org/W7162308911","https://openalex.org/W7165812628","https://openalex.org/W4415317053","https://openalex.org/W7127175287","https://openalex.org/W4415117786","https://openalex.org/W4414577602"],"abstract_inverted_index":{"Generative":[0],"models":[1],"are":[2,235],"increasingly":[3],"used":[4],"to":[5,58,237],"solve":[6],"scientific":[7],"inverse":[8,84,90],"problems,":[9,31],"but":[10,118],"existing":[11],"evaluations":[12],"still":[13,56],"focus":[14],"primarily":[15],"on":[16],"whether":[17,134],"a":[18,22,48,75,153,203],"method":[19,49],"can":[20,50],"produce":[21],"single":[23,145],"plausible":[24],"reconstruction.":[25],"This":[26],"is":[27],"insufficient":[28],"for":[29,77,206],"ill-posed":[30],"where":[32],"multiple":[33],"solutions":[34,141],"may":[35],"be":[36],"consistent":[37],"with":[38,152,202],"the":[39,60,79,137,144],"same":[40],"sparse":[41,189],"or":[42,68],"noisy":[43],"observations.":[44],"In":[45],"these":[46,150],"settings,":[47],"achieve":[51],"strong":[52],"pointwise":[53,176],"accuracy":[54,81],"while":[55,221],"failing":[57],"capture":[59,99],"true":[61],"posterior":[62,155],"through":[63],"mode":[64],"collapse,":[65],"overconfident":[66],"uncertainty,":[67,179],"averaging":[69],"incompatible":[70],"solutions.":[71],"We":[72,148],"introduce":[73],"PosteriorBench,":[74],"benchmark":[76,187],"evaluating":[78],"distributional":[80,180],"of":[82,133,140],"generative":[83],"solvers.":[85],"PosteriorBench":[86],"evaluates":[87],"four":[88],"physics-based":[89],"problems:":[91],"Darcy":[92],"flow":[93],"inversion,":[94],"Poisson":[95],"source":[96],"recovery,":[97],"carbon":[98],"and":[100,102,125,168,182,199,209,229,232],"storage,":[101],"light":[103],"transport":[104],"material":[105],"inference.":[106],"For":[107],"each":[108],"task,":[109],"we":[110],"construct":[111],"high-fidelity":[112],"reference":[113],"posteriors":[114],"using":[115],"computationally":[116],"heavy":[117],"established":[119],"procedures":[120],"such":[121],"as":[122],"rejection":[123],"sampling":[124],"Markov":[126],"chain":[127],"Monte":[128],"Carlo,":[129],"enabling":[130],"direct":[131],"assessment":[132],"solvers":[135],"recover":[136],"full":[138],"set":[139],"rather":[142],"than":[143],"best":[146],"sample.":[147],"pair":[149],"references":[151],"five-metric":[154],"evaluation":[156],"suite:":[157],"posterior-mean":[158],"error,":[159,161],"posterior-standard-deviation":[160],"maximum":[162],"mean":[163],"discrepancy,":[164],"sliced":[165],"Wasserstein":[166],"distance,":[167],"radially":[169],"averaged":[170],"power-spectrum":[171],"error.":[172],"These":[173],"metrics":[174],"assess":[175],"accuracy,":[177],"marginal":[178],"alignment,":[181],"global":[183],"frequency":[184],"fidelity.":[185],"The":[186],"spans":[188],"sensing,":[190],"low-resolution":[191],"observations,":[192],"nonlinear":[193],"forward":[194],"models,":[195],"varying":[196],"noise":[197,234],"levels,":[198],"multimodal":[200],"priors,":[201],"unified":[204],"pipeline":[205],"distribution":[207],"matching":[208],"uncertainty":[210],"quantification.":[211],"Our":[212],"experiments":[213],"reveal":[214],"substantial":[215],"distribution-matching":[216],"gaps":[217],"across":[218],"current":[219],"solvers,":[220],"showing":[222],"that":[223],"neural":[224],"operators":[225],"improve":[226],"resolution":[227],"robustness,":[228],"guidance":[230],"weights":[231],"generation":[233],"key":[236],"posterior-variance":[238],"calibration.":[239]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-19T00:00:00"}
