{"id":"https://openalex.org/W2964015695","doi":"https://doi.org/10.1137/18m1187611","title":"Scaling Limit of the Stein Variational Gradient Descent: The Mean Field Regime","display_name":"Scaling Limit of the Stein Variational Gradient Descent: The Mean Field Regime","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2964015695","doi":"https://doi.org/10.1137/18m1187611","mag":"2964015695"},"language":"en","primary_location":{"id":"doi:10.1137/18m1187611","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1187611","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","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/A5061472917","display_name":"Jianfeng Lu","orcid":"https://orcid.org/0000-0001-6255-5165"},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jianfeng Lu","raw_affiliation_strings":["Department of Mathematics, Duke University, Durham NC 27708, USA"],"raw_orcid":"https://orcid.org/0000-0001-6255-5165","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Duke University, Durham NC 27708, USA","institution_ids":["https://openalex.org/I170897317"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080770658","display_name":"Yulong Lu","orcid":"https://orcid.org/0000-0003-2914-414X"},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yulong Lu","raw_affiliation_strings":["Department of Mathematics, Duke University, Durham NC 27708, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Duke University, Durham NC 27708, USA","institution_ids":["https://openalex.org/I170897317"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012884872","display_name":"James Nolen","orcid":"https://orcid.org/0000-0003-4630-2293"},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"James Nolen","raw_affiliation_strings":["Department of Mathematics, Duke University, Durham NC 27708, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Duke University, Durham NC 27708, USA","institution_ids":["https://openalex.org/I170897317"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I170897317"],"apc_list":null,"apc_paid":null,"fwci":8.5959,"has_fulltext":false,"cited_by_count":59,"citation_normalized_percentile":{"value":0.98364008,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"51","issue":"2","first_page":"648","last_page":"671"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9958999752998352,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.855373740196228},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7393560409545898},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.6102439165115356},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.6055940389633179},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5589103698730469},{"id":"https://openalex.org/keywords/normalization","display_name":"Normalization (sociology)","score":0.5181378126144409},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5180835723876953},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.49991321563720703},{"id":"https://openalex.org/keywords/particle-system","display_name":"Particle system","score":0.484973669052124},{"id":"https://openalex.org/keywords/scaling-limit","display_name":"Scaling limit","score":0.47064846754074097},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.4435258209705353},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4039596915245056},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.30230480432510376},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08580797910690308}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.855373740196228},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7393560409545898},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.6102439165115356},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.6055940389633179},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5589103698730469},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.5181378126144409},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5180835723876953},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.49991321563720703},{"id":"https://openalex.org/C179003449","wikidata":"https://www.wikidata.org/wiki/Q1757458","display_name":"Particle system","level":2,"score":0.484973669052124},{"id":"https://openalex.org/C24084028","wikidata":"https://www.wikidata.org/wiki/Q7429781","display_name":"Scaling limit","level":3,"score":0.47064846754074097},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.4435258209705353},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4039596915245056},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.30230480432510376},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08580797910690308},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C19165224","wikidata":"https://www.wikidata.org/wiki/Q23404","display_name":"Anthropology","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/18m1187611","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1187611","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4099999964237213,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G1204787863","display_name":"CAREER: Research and training in advanced computational methods for quantum and statistical mechanics","funder_award_id":"1454939","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4081752835","display_name":"CAREER: Research and training in stochastic dynamics","funder_award_id":"1351653","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6965837496","display_name":null,"funder_award_id":"DMS-1351653","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7534110628","display_name":null,"funder_award_id":"DMS-1454939","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1954227087","https://openalex.org/W1968835931","https://openalex.org/W1983452151","https://openalex.org/W1984878971","https://openalex.org/W1992957154","https://openalex.org/W2001536020","https://openalex.org/W2012405657","https://openalex.org/W2042892258","https://openalex.org/W2054723044","https://openalex.org/W2071048859","https://openalex.org/W2074043571","https://openalex.org/W2144787610","https://openalex.org/W2171306535","https://openalex.org/W2222154095","https://openalex.org/W2559655401","https://openalex.org/W2612690371","https://openalex.org/W2963134136","https://openalex.org/W2963388623","https://openalex.org/W2963964450","https://openalex.org/W4254086930"],"related_works":["https://openalex.org/W2591697403","https://openalex.org/W2953716828","https://openalex.org/W2904857019","https://openalex.org/W2944728705","https://openalex.org/W3011538607","https://openalex.org/W2904022177","https://openalex.org/W4321441197","https://openalex.org/W2359348847","https://openalex.org/W4294432981","https://openalex.org/W1553706835"],"abstract_inverted_index":{"We":[0,38,63],"study":[1],"an":[2],"interacting":[3],"particle":[4,44,51],"system":[5,52],"in":[6,41,94],"$R^d$":[7],"motivated":[8],"by":[9],"Stein":[10],"variational":[11],"gradient":[12],"descent":[13],"[Q.":[14],"Liu":[15],"and":[16,60,70],"D.":[17],"Wang,":[18],"Proceedings":[19],"of":[20,49,57,72],"NIPS,":[21],"2016],":[22],"a":[23,28,55,58,95],"deterministic":[24],"algorithm":[25],"for":[26],"approximating":[27],"given":[29],"probability":[30],"density":[31],"with":[32],"unknown":[33],"normalization":[34],"based":[35],"on":[36],"particles.":[37],"prove":[39,65,81],"that":[40,82],"the":[42,46,50,66,73,76,83,86,90],"large":[43],"limit":[45],"empirical":[47],"measure":[48],"converges":[53,88],"to":[54,75,85,89],"solution":[56,74,84,93],"nonlocal":[59],"nonlinear":[61],"PDE.":[62,78],"also":[64],"global":[67],"existence,":[68],"uniqueness,":[69],"regularity":[71],"limiting":[77],"Finally,":[79],"we":[80],"PDE":[87],"unique":[91],"invariant":[92],"long":[96],"time":[97],"limit.":[98]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":13},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":8}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
