{"id":"https://openalex.org/W7208744757","doi":"https://doi.org/10.48550/arxiv.2609.03343","title":"Learning Informative Prior with Infinite-Dimensional Continuous Normalizing Flow for Bayesian Inverse Problem","display_name":"Learning Informative Prior with Infinite-Dimensional Continuous Normalizing Flow for Bayesian Inverse Problem","publication_year":2026,"publication_date":"2026-09-03","ids":{"openalex":"https://openalex.org/W7208744757","doi":"https://doi.org/10.48550/arxiv.2609.03343"},"language":null,"primary_location":{"id":"pmh:oai:arXiv.org:2609.03343","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.03343","pdf_url":"https://arxiv.org/pdf/2609.03343","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/2609.03343","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5150056035","display_name":"Yang Zhao","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhao, Yang","raw_affiliation_strings":["School of Mathematics and Statistics , Xi'an Jiaotong University , Xi'an 710049 , China;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Xi'an Jiaotong University , Xi'an 710049 , China;","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014948446","display_name":"Junxiong Jia","orcid":"https://orcid.org/0000-0002-0917-2381","observed_orcids":["https://orcid.org/0000-0002-0917-2381"]},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jia, Junxiong","raw_affiliation_strings":["School of Mathematics and Statistics , Xi'an Jiaotong University , Xi'an 710049 , China;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Xi'an Jiaotong University , Xi'an 710049 , China;","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5150030990","display_name":"Tao Zhou","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhou, Tao","raw_affiliation_strings":["Academy of Mathematics and Systems Sciences , Chinese Academy of Sciences , Beijing , 100190 , China;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Academy of Mathematics and Systems Sciences , Chinese Academy of Sciences , Beijing , 100190 , China;","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.29589998722076416,"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":0.29589998722076416,"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":0.2754000127315521,"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":0.17069999873638153,"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/bayesian-inversion","display_name":"Bayesian inversion","score":0.9190000295639038},{"id":"https://openalex.org/keywords/continuous-normalizing-flows","display_name":"continuous normalizing flows","score":0.9390000104904175},{"id":"https://openalex.org/keywords/neural-odes","display_name":"neural ordinary differential equations","score":0.9160000085830688},{"id":"https://openalex.org/keywords/partial-differential-equations","display_name":"partial differential equations","score":0.7570000290870667},{"id":"https://openalex.org/keywords/inverse-scattering","display_name":"inverse scattering","score":0.7009999752044678},{"id":"https://openalex.org/keywords/inverse-heat-conduction-problem","display_name":"inverse heat conduction problem","score":0.8799999952316284},{"id":"https://openalex.org/keywords/posterior-sampling","display_name":"posterior sampling","score":0.546999990940094}],"concepts":[{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.6657000184059143},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.604200005531311},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.5582000017166138},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5447999835014343},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.499099999666214},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.48910000920295715},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48069998621940613},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.460999995470047},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.43799999356269836},{"id":"https://openalex.org/C136628613","wikidata":"https://www.wikidata.org/wiki/Q17098188","display_name":"Inverse scattering transform","level":4,"score":0.43380001187324524},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41679999232292175},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.41659998893737793},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39469999074935913},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.37959998846054077},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3628000020980835},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.3418000042438507},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.3384000062942505},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.3215000033378601},{"id":"https://openalex.org/C174558057","wikidata":"https://www.wikidata.org/wiki/Q11639409","display_name":"Inverse scattering problem","level":3,"score":0.3192000091075897},{"id":"https://openalex.org/C101112237","wikidata":"https://www.wikidata.org/wiki/Q4874481","display_name":"Bayesian statistics","level":4,"score":0.3183000087738037},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.3077000081539154},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.2985000014305115},{"id":"https://openalex.org/C207201462","wikidata":"https://www.wikidata.org/wiki/Q182505","display_name":"Bayes' theorem","level":3,"score":0.2806999981403351},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.26429998874664307}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.03343","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.03343","pdf_url":"https://arxiv.org/pdf/2609.03343","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.2609.03343","doi":"https://doi.org/10.48550/arxiv.2609.03343","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.03343","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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.03343","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.03343","pdf_url":"https://arxiv.org/pdf/2609.03343","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":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1575459986","display_name":null,"funder_award_id":"12322116","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3794296119","display_name":null,"funder_award_id":"12271428","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7208744757.pdf","grobid_xml":"https://content.openalex.org/works/W7208744757.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"addresses":[2],"infinite-dimensional":[3,17,33,45,80],"Bayesian":[4,77,103],"inference":[5],"for":[6,90,100],"inverse":[7,113,118,120,125],"problem":[8],"of":[9,74,87,139],"partial":[10],"differential":[11,42],"equations":[12],"with":[13,96],"model":[14],"parameters":[15],"in":[16,44,79],"Hilbert":[18],"space.":[19,81],"To":[20],"effectively":[21],"incorporate":[22],"prior":[23,62,78,89],"information,":[24],"we":[25],"propose":[26],"a":[27,38,47,55],"novel":[28],"continuous":[29],"normalizing":[30],"flows":[31],"based":[32],"model.":[34],"Specifically,":[35],"by":[36],"introducing":[37],"well-defined":[39],"neural":[40],"ordinary":[41],"equation":[43],"space,":[46],"simple":[48,116],"reference":[49],"measure":[50,58],"can":[51],"be":[52],"transformed":[53],"into":[54],"more":[56],"complex":[57],"which":[59],"encodes":[60],"the":[61,72,88,101,115,124,132,137,140],"information.":[63],"A":[64],"corresponding":[65],"theoretical":[66,133],"framework":[67,107],"is":[68,108],"established":[69],"to":[70,110],"ensure":[71],"well-posedness":[73],"our":[75],"proposed":[76,106,141],"We":[82],"also":[83],"provide":[84],"training":[85],"methods":[86],"two":[91,97],"distinct":[92],"data":[93],"settings,":[94],"along":[95],"sampling":[98],"algorithms":[99],"resulting":[102],"posterior.":[104],"The":[105],"applied":[109],"three":[111],"representative":[112],"problems:":[114],"smooth":[117],"problem,":[119,122],"scattering":[121],"and":[123,135],"heat":[126],"conduction":[127],"problem.":[128],"Numerical":[129],"experiments":[130],"support":[131],"analysis":[134],"demonstrate":[136],"efficiency":[138],"algorithms.":[142]},"counts_by_year":[],"updated_date":"2026-10-13T10:08:12.033832","created_date":"2026-09-05T00:00:00"}
