{"id":"https://openalex.org/W4391353536","doi":"https://doi.org/10.1137/23m1560574","title":"Bayesian Deep Learning Framework for Uncertainty Quantification in Stochastic Partial Differential Equations","display_name":"Bayesian Deep Learning Framework for Uncertainty Quantification in Stochastic Partial Differential Equations","publication_year":2024,"publication_date":"2024-01-30","ids":{"openalex":"https://openalex.org/W4391353536","doi":"https://doi.org/10.1137/23m1560574"},"language":"en","primary_location":{"id":"doi:10.1137/23m1560574","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1560574","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001704071","display_name":"Jeahan Jung","orcid":null},"institutions":[{"id":"https://openalex.org/I123900574","display_name":"Pohang University of Science and Technology","ror":"https://ror.org/04xysgw12","country_code":"KR","type":"education","lineage":["https://openalex.org/I123900574"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Jeahan Jung","raw_affiliation_strings":["Department of Mathematics, Pohang University of Science and Technology (POSTECH), Pohang, 37673, Republic of Korea"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Pohang University of Science and Technology (POSTECH), Pohang, 37673, Republic of Korea","institution_ids":["https://openalex.org/I123900574"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010450182","display_name":"Hyomin Shin","orcid":null},"institutions":[{"id":"https://openalex.org/I123900574","display_name":"Pohang University of Science and Technology","ror":"https://ror.org/04xysgw12","country_code":"KR","type":"education","lineage":["https://openalex.org/I123900574"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Hyomin Shin","raw_affiliation_strings":["Department of Mathematics, Pohang University of Science and Technology (POSTECH), Pohang, 37673, Republic of Korea"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Pohang University of Science and Technology (POSTECH), Pohang, 37673, Republic of Korea","institution_ids":["https://openalex.org/I123900574"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101396625","display_name":"Minseok Choi","orcid":"https://orcid.org/0000-0002-7245-0823"},"institutions":[{"id":"https://openalex.org/I123900574","display_name":"Pohang University of Science and Technology","ror":"https://ror.org/04xysgw12","country_code":"KR","type":"education","lineage":["https://openalex.org/I123900574"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Minseok Choi","raw_affiliation_strings":["Corresponding author. Department of Mathematics, Pohang University of Science and Technology (POSTECH), Pohang, 37673, Republic of Korea"],"affiliations":[{"raw_affiliation_string":"Corresponding author. Department of Mathematics, Pohang University of Science and Technology (POSTECH), Pohang, 37673, Republic of Korea","institution_ids":["https://openalex.org/I123900574"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5001704071"],"corresponding_institution_ids":["https://openalex.org/I123900574"],"apc_list":null,"apc_paid":null,"fwci":4.5608,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.94539908,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"46","issue":"1","first_page":"C57","last_page":"C76"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9988999962806702,"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/T12560","display_name":"Nuclear Engineering Thermal-Hydraulics","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.73508620262146},{"id":"https://openalex.org/keywords/uncertainty-quantification","display_name":"Uncertainty quantification","score":0.727622389793396},{"id":"https://openalex.org/keywords/stochastic-partial-differential-equation","display_name":"Stochastic partial differential equation","score":0.642541766166687},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5918501615524292},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.5271498560905457},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5200474262237549},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.46897420287132263},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33454954624176025},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.23967018723487854},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18400835990905762}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.73508620262146},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.727622389793396},{"id":"https://openalex.org/C84629840","wikidata":"https://www.wikidata.org/wiki/Q16979017","display_name":"Stochastic partial differential equation","level":3,"score":0.642541766166687},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5918501615524292},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.5271498560905457},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5200474262237549},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.46897420287132263},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33454954624176025},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.23967018723487854},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18400835990905762}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/23m1560574","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1560574","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4640205972","display_name":null,"funder_award_id":"2021R1C1C1007875","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"}],"funders":[{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1545319692","https://openalex.org/W1880751280","https://openalex.org/W2018159038","https://openalex.org/W2030308624","https://openalex.org/W2059448777","https://openalex.org/W2060182887","https://openalex.org/W2099192586","https://openalex.org/W2604272474","https://openalex.org/W2781856433","https://openalex.org/W2784733489","https://openalex.org/W2786232134","https://openalex.org/W2811208018","https://openalex.org/W2890968382","https://openalex.org/W2899283552","https://openalex.org/W2900369848","https://openalex.org/W2906236663","https://openalex.org/W2908541468","https://openalex.org/W2912649832","https://openalex.org/W3004450693","https://openalex.org/W3010849941","https://openalex.org/W3011147100","https://openalex.org/W3092231855","https://openalex.org/W3100968477","https://openalex.org/W3116268267","https://openalex.org/W4223440841","https://openalex.org/W4245654886","https://openalex.org/W4293775970","https://openalex.org/W4307296250","https://openalex.org/W4312572415","https://openalex.org/W4367185933"],"related_works":["https://openalex.org/W620239920","https://openalex.org/W109055908","https://openalex.org/W1546584948","https://openalex.org/W2060658157","https://openalex.org/W2972896374","https://openalex.org/W4237379163","https://openalex.org/W2164842548","https://openalex.org/W3125773376","https://openalex.org/W2085400897","https://openalex.org/W3150981116"],"abstract_inverted_index":{".Bayesian":[0],"physics-informed":[1],"neural":[2,76,208],"networks":[3],"(B-PINNs)":[4],"have":[5],"emerged":[6],"as":[7],"an":[8,71,129],"efficient":[9,130],"tool":[10],"for":[11,27,60,132,160,175],"uncertainty":[12,36,61,176],"quantification":[13,62,177],"in":[14,44,63,178],"partial":[15,212],"differential":[16,213],"equations":[17],"(PDEs).":[18],"However,":[19],"their":[20],"applicability":[21],"has":[22],"been":[23],"limited":[24],"to":[25,32,140,167],"accounting":[26],"noisy":[28],"data.":[29],"They":[30],"fail":[31],"effectively":[33,114],"address":[34],"the":[35,39,68,80,84,93,98,106,116,142,148,169,185,192,198,202],"arising":[37],"from":[38],"randomness":[40],"of":[41,70,83,119,171,194,201],"physical":[42,95],"parameters":[43,85,196],"stochastic":[45],"PDEs":[46],"(SPDEs).":[47],"To":[48,113],"this":[49],"end,":[50],"we":[51,122],"propose":[52,136],"a":[53,74,109,124,137],"novel":[54],"Bayesian":[55,75],"deep":[56],"learning":[57],"framework":[58],"designed":[59],"SPDE":[64,72,165],"problems.":[65],"We":[66,91,135,156],"model":[67],"solution":[69],"using":[73,108],"network":[77],"(BNN),":[78],"where":[79],"posterior":[81,117],"distribution":[82,100,118],"is":[86,182,188],"constructed":[87],"by":[88,191],"Bayes'":[89],"rule.":[90],"incorporate":[92],"governing":[94],"laws":[96],"into":[97],"likelihood":[99,107],"through":[101],"automatic":[102],"differentiation":[103],"and":[104,163,197],"estimate":[105],"Gaussian":[110],"mixture":[111],"model.":[112],"learn":[115],"BNN":[120,195],"parameters,":[121],"employ":[123],"Hamiltonian":[125,149],"Monte":[126,150,210],"Carlo":[127],"method,":[128],"method":[131,174],"high-dimensional":[133],"sampling.":[134],"parallel":[138],"algorithm":[139],"mitigate":[141],"high":[143],"computational":[144,186,206],"cost":[145,187],"associated":[146],"with":[147],"Carlo,":[151],"thereby":[152],"enhancing":[153],"its":[154,205],"efficiency.":[155],"provide":[157],"numerical":[158],"examples":[159],"both":[161],"forward":[162],"inverse":[164],"problems":[166],"demonstrate":[168],"effectiveness":[170],"our":[172],"proposed":[173],"SPDEs.":[179],"Notably,":[180],"it":[181],"demonstrated":[183],"that":[184],"almost":[189],"unaffected":[190],"number":[193],"random":[199],"dimension":[200],"problem,":[203],"underscoring":[204],"efficiency.KeywordsBayesian":[207],"networkHamiltonian":[209],"Carlostochastic":[211],"equationuncertainty":[214],"quantificationMSC":[215],"codes60H3535R6062M45":[216]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3}],"updated_date":"2026-04-03T22:45:19.894376","created_date":"2025-10-10T00:00:00"}