{"id":"https://openalex.org/W3130552779","doi":"https://doi.org/10.1137/21m1440773","title":"Stein Variational Gradient Descent on Infinite-Dimensional Space and Applications to Statistical Inverse Problems","display_name":"Stein Variational Gradient Descent on Infinite-Dimensional Space and Applications to Statistical Inverse Problems","publication_year":2022,"publication_date":"2022-08-01","ids":{"openalex":"https://openalex.org/W3130552779","doi":"https://doi.org/10.1137/21m1440773","mag":"3130552779"},"language":"en","primary_location":{"id":"doi:10.1137/21m1440773","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1440773","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2102.09741","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014948446","display_name":"Junxiong Jia","orcid":"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":"Junxiong Jia","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/A5100742532","display_name":"Peijun Li","orcid":"https://orcid.org/0000-0001-5119-6435"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Peijun Li","raw_affiliation_strings":["Department of Mathematics, Purdue University, West Lafayette, Indiana, 47907, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Purdue University, West Lafayette, Indiana, 47907, USA","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091017287","display_name":"Deyu Meng","orcid":"https://orcid.org/0000-0002-1294-8283"},"institutions":[{"id":"https://openalex.org/I111950717","display_name":"Macau University of Science and Technology","ror":"https://ror.org/03jqs2n27","country_code":"MO","type":"education","lineage":["https://openalex.org/I111950717","https://openalex.org/I4391767947"]},{"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","MO"],"is_corresponding":true,"raw_author_name":"Deyu Meng","raw_affiliation_strings":["Macau University of Science and Technology, Taipa, Macau","School of Mathematics and Statistics and Ministry of Education Key Lab of Intelligent Networks and Network Security, Xi'an Jiaotong University, Xi'an, 710049, China, and Macau Institute of Systems Engineering,"],"raw_orcid":"https://orcid.org/0000-0002-1294-8283","affiliations":[{"raw_affiliation_string":"Macau University of Science and Technology, Taipa, Macau","institution_ids":["https://openalex.org/I111950717"]},{"raw_affiliation_string":"School of Mathematics and Statistics and Ministry of Education Key Lab of Intelligent Networks and Network Security, Xi'an Jiaotong University, Xi'an, 710049, China, and Macau Institute of Systems Engineering,","institution_ids":["https://openalex.org/I87445476"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5091017287"],"corresponding_institution_ids":["https://openalex.org/I111950717","https://openalex.org/I87445476"],"apc_list":null,"apc_paid":null,"fwci":2.7366,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.89273863,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"60","issue":"4","first_page":"2225","last_page":"2252"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9995999932289124,"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/T10894","display_name":"Groundwater flow and contamination studies","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10271","display_name":"Seismic Imaging and Inversion Techniques","score":0.9887999892234802,"subfield":{"id":"https://openalex.org/subfields/1908","display_name":"Geophysics"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8351877331733704},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.6201640963554382},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.596274733543396},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5581406950950623},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5487620234489441},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.4977298080921173},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.47179096937179565},{"id":"https://openalex.org/keywords/balanced-flow","display_name":"Balanced flow","score":0.43994659185409546},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4369547367095947},{"id":"https://openalex.org/keywords/reproducing-kernel-hilbert-space","display_name":"Reproducing kernel Hilbert space","score":0.416714608669281},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3826889991760254},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3229821026325226},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12798812985420227},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.12265470623970032},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11873623728752136}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8351877331733704},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.6201640963554382},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.596274733543396},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5581406950950623},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5487620234489441},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.4977298080921173},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.47179096937179565},{"id":"https://openalex.org/C167879884","wikidata":"https://www.wikidata.org/wiki/Q727568","display_name":"Balanced flow","level":2,"score":0.43994659185409546},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4369547367095947},{"id":"https://openalex.org/C80884492","wikidata":"https://www.wikidata.org/wiki/Q3345678","display_name":"Reproducing kernel Hilbert space","level":3,"score":0.416714608669281},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3826889991760254},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3229821026325226},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12798812985420227},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.12265470623970032},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11873623728752136},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/21m1440773","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1440773","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2102.09741","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2102.09741","pdf_url":"https://arxiv.org/pdf/2102.09741","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:doi:10.48550/arxiv.2102.09741","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2102.09741","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2102.09741","pdf_url":"https://arxiv.org/pdf/2102.09741","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G168428553","display_name":null,"funder_award_id":"PCL2021A12","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G243730240","display_name":null,"funder_award_id":"2020YFA0713403","funder_id":"https://openalex.org/F4320321540","funder_display_name":"Ministry of Science and Technology of the People's Republic of China"},{"id":"https://openalex.org/G309346365","display_name":null,"funder_award_id":"DMS-1912704","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3155074394","display_name":null,"funder_award_id":"12090020","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5230869291","display_name":null,"funder_award_id":"061/2020/A2","funder_id":"https://openalex.org/F4320323893","funder_display_name":"Fundo para o Desenvolvimento das Ci\u00eancias e da Tecnologia"},{"id":"https://openalex.org/G5234250448","display_name":null,"funder_award_id":"11690011","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5372072380","display_name":null,"funder_award_id":"U1811461","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6387986177","display_name":null,"funder_award_id":"61721002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7156104877","display_name":null,"funder_award_id":"11871392","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G824516698","display_name":null,"funder_award_id":"12090021","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321540","display_name":"Ministry of Science and Technology of the People's Republic of China","ror":"https://ror.org/027s68j25"},{"id":"https://openalex.org/F4320323893","display_name":"Fundo para o Desenvolvimento das Ci\u00eancias e da Tecnologia","ror":"https://ror.org/05vna4324"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3130552779.pdf"},"referenced_works_count":73,"referenced_works":["https://openalex.org/W73123583","https://openalex.org/W260216039","https://openalex.org/W335436902","https://openalex.org/W596189563","https://openalex.org/W1074099955","https://openalex.org/W1512208174","https://openalex.org/W1523113578","https://openalex.org/W1531455566","https://openalex.org/W1540232275","https://openalex.org/W1570089119","https://openalex.org/W1581736319","https://openalex.org/W1600293573","https://openalex.org/W1663973292","https://openalex.org/W2008439960","https://openalex.org/W2009503811","https://openalex.org/W2046973159","https://openalex.org/W2064991026","https://openalex.org/W2066012686","https://openalex.org/W2084962682","https://openalex.org/W2126304434","https://openalex.org/W2133027741","https://openalex.org/W2142737094","https://openalex.org/W2149498546","https://openalex.org/W2152657433","https://openalex.org/W2153678797","https://openalex.org/W2158446701","https://openalex.org/W2165867509","https://openalex.org/W2268335277","https://openalex.org/W2398886555","https://openalex.org/W2539071726","https://openalex.org/W2545806747","https://openalex.org/W2558810859","https://openalex.org/W2798836194","https://openalex.org/W2802580048","https://openalex.org/W2806674516","https://openalex.org/W2884453666","https://openalex.org/W2885549115","https://openalex.org/W2895340627","https://openalex.org/W2909021043","https://openalex.org/W2915292366","https://openalex.org/W2952020389","https://openalex.org/W2952625664","https://openalex.org/W2961415614","https://openalex.org/W2962707560","https://openalex.org/W2962851448","https://openalex.org/W2963388623","https://openalex.org/W2963746556","https://openalex.org/W2963956018","https://openalex.org/W2963964397","https://openalex.org/W2963973173","https://openalex.org/W2964015695","https://openalex.org/W2970378037","https://openalex.org/W2970698058","https://openalex.org/W2971906246","https://openalex.org/W2999784105","https://openalex.org/W3005085468","https://openalex.org/W3013057283","https://openalex.org/W3029861853","https://openalex.org/W3035387695","https://openalex.org/W3093052988","https://openalex.org/W3101357194","https://openalex.org/W3101511580","https://openalex.org/W3105773709","https://openalex.org/W3105948459","https://openalex.org/W3123754959","https://openalex.org/W3134669147","https://openalex.org/W3135985701","https://openalex.org/W4212863985","https://openalex.org/W4214686751","https://openalex.org/W4242259929","https://openalex.org/W4245654886","https://openalex.org/W4292156489","https://openalex.org/W4300475775"],"related_works":["https://openalex.org/W4287028882","https://openalex.org/W3192094705","https://openalex.org/W4234882900","https://openalex.org/W2891466145","https://openalex.org/W2970719462","https://openalex.org/W2952110137","https://openalex.org/W4387349426","https://openalex.org/W4309201680","https://openalex.org/W4381797995","https://openalex.org/W2940361845"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"propose":[4],"an":[5,94],"infinite-dimensional":[6,50],"version":[7],"of":[8,34,63,80,97,115,123],"the":[9,32,49,53,61,78,98,112,116,120],"Stein":[10,54],"variational":[11],"gradient":[12],"descent":[13],"(iSVGD)":[14],"method":[15,22],"for":[16,48],"solving":[17],"Bayesian":[18],"inverse":[19,95,127],"problems.":[20,128],"The":[21,88],"can":[23],"generate":[24],"approximate":[25],"samples":[26],"from":[27],"posteriors":[28],"efficiently.":[29],"Based":[30],"on":[31],"concepts":[33],"operator-valued":[35],"kernels":[36],"and":[37,83,110],"vector-valued":[38],"reproducing":[39],"kernel":[40],"Hilbert":[41],"spaces,":[42],"a":[43,67,85],"rigorous":[44],"definition":[45],"is":[46,74],"given":[47],"objects,":[51],"e.g.,":[52],"operator,":[55],"which":[56],"are":[57,91],"proved":[58],"to":[59,93],"be":[60],"limit":[62],"finite-dimensional":[64],"ones.":[65],"Moreover,":[66],"more":[68],"efficient":[69],"iSVGD":[70],"with":[71],"preconditioning":[72],"operators":[73],"constructed":[75],"by":[76],"generalizing":[77],"change":[79],"variables":[81],"formula":[82],"introducing":[84],"regularity":[86],"parameter.":[87],"proposed":[89,117],"algorithms":[90],"applied":[92],"problem":[96],"steady":[99],"state":[100],"Darcy":[101],"flow":[102],"equation.":[103],"Numerical":[104],"results":[105],"confirm":[106],"our":[107],"theoretical":[108],"findings":[109],"demonstrate":[111],"potential":[113],"applications":[114],"approach":[118],"in":[119],"posterior":[121],"sampling":[122],"large-scale":[124],"nonlinear":[125],"statistical":[126]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}