{"id":"https://openalex.org/W4405903294","doi":"https://doi.org/10.1137/24m1721311","title":"L\u00e9vy Score Function and Score-Based Particle Algorithm for Nonlinear L\u00e9vy\u2013Fokker\u2013Planck Equations","display_name":"L\u00e9vy Score Function and Score-Based Particle Algorithm for Nonlinear L\u00e9vy\u2013Fokker\u2013Planck Equations","publication_year":2026,"publication_date":"2026-05-20","ids":{"openalex":"https://openalex.org/W4405903294","doi":"https://doi.org/10.1137/24m1721311"},"language":"en","primary_location":{"id":"doi:10.1137/24m1721311","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1721311","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","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2412.19520","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046353442","display_name":"Yuanfei Huang","orcid":"https://orcid.org/0000-0002-5242-9904"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]},{"id":"https://openalex.org/I2802603000","display_name":"Asia Pacific Center for Theoretical Physics","ror":"https://ror.org/011hxwn54","country_code":"KR","type":"facility","lineage":["https://openalex.org/I2802603000"]}],"countries":["HK","KR"],"is_corresponding":false,"raw_author_name":"Yuanfei Huang","raw_affiliation_strings":["Asia Pacific Center for Theoretical Physics, Pohang, 37673 Korea, and Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong SAR"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Asia Pacific Center for Theoretical Physics, Pohang, 37673 Korea, and Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong SAR","institution_ids":["https://openalex.org/I168719708","https://openalex.org/I2802603000"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061364557","display_name":"Chengyu Liu","orcid":"https://orcid.org/0000-0003-2140-2706"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Chengyu Liu","raw_affiliation_strings":["Department of Data Science, City University of Hong Kong, Kowloon, Hong Kong SAR"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Data Science, City University of Hong Kong, Kowloon, Hong Kong SAR","institution_ids":["https://openalex.org/I168719708"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068096714","display_name":"Xiang Zhou","orcid":"https://orcid.org/0000-0002-0400-766X"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Xiang Zhou","raw_affiliation_strings":["Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong SAR"],"raw_orcid":"https://orcid.org/0000-0002-3835-3894","affiliations":[{"raw_affiliation_string":"Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong SAR","institution_ids":["https://openalex.org/I168719708"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0097452,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"64","issue":"3","first_page":"656","last_page":"684"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9991999864578247,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9991999864578247,"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/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9930999875068665,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9921000003814697,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/fokker\u2013planck-equation","display_name":"Fokker\u2013Planck equation","score":0.6107620596885681},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.585640013217926},{"id":"https://openalex.org/keywords/score","display_name":"Score","score":0.5061251521110535},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4513600468635559},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3841140866279602},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37765634059906006},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3772767186164856},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.370873361825943},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3670349717140198},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23319268226623535},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.19428792595863342},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.11542049050331116},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.07316398620605469}],"concepts":[{"id":"https://openalex.org/C69123182","wikidata":"https://www.wikidata.org/wiki/Q891766","display_name":"Fokker\u2013Planck equation","level":3,"score":0.6107620596885681},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.585640013217926},{"id":"https://openalex.org/C65660741","wikidata":"https://www.wikidata.org/wiki/Q3952743","display_name":"Score","level":2,"score":0.5061251521110535},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4513600468635559},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3841140866279602},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37765634059906006},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3772767186164856},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.370873361825943},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3670349717140198},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23319268226623535},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.19428792595863342},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11542049050331116},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.07316398620605469}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/24m1721311","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1721311","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:2412.19520","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2412.19520","pdf_url":"https://arxiv.org/pdf/2412.19520","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":"doi:10.48550/arxiv.2412.19520","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2412.19520","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2412.19520","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2412.19520","pdf_url":"https://arxiv.org/pdf/2412.19520","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/G1950707144","display_name":null,"funder_award_id":"12061160462","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3333516775","display_name":null,"funder_award_id":"11308121","funder_id":"https://openalex.org/F4320309893","funder_display_name":"City University of Hong Kong"}],"funders":[{"id":"https://openalex.org/F4320309893","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2992409218","https://openalex.org/W1494630543","https://openalex.org/W4388044880","https://openalex.org/W2057022985","https://openalex.org/W2035936743","https://openalex.org/W4256389389","https://openalex.org/W4320514436","https://openalex.org/W2064571445","https://openalex.org/W2316454864","https://openalex.org/W1989512732"],"abstract_inverted_index":{"The":[0,172],"score":[1,49,71,90],"function":[2,50,72,91,113],"for":[3,51,92,151],"the":[4,10,13,21,28,34,43,47,52,69,82,88,110,118,121,137,152,156,165,169,177,182,191],"diffusion":[5,30],"process,":[6],"also":[7],"known":[8],"as":[9],"gradient":[11],"of":[12,36,120,195],"log-density,":[14],"is":[15,186],"a":[16,98,129],"basic":[17],"concept":[18],"to":[19,135],"characterize":[20],"probability":[22,44,122,160],"flow":[23,45,123],"with":[24,76,124,176],"important":[25],"applications":[26,201],"in":[27,73,168,202],"score-based":[29,131],"generative":[31],"modelling":[32],"and":[33,64,78,102,158,181,193,204],"simulation":[35],"It\u00f4":[37],"stochastic":[38,94,140],"differential":[39],"equations.":[40,85],"However,":[41],"neither":[42],"nor":[46],"corresponding":[48,70],"diffusion-jump":[53],"process":[54,141],"are":[55,206],"known.":[56],"This":[57],"paper":[58],"delivers":[59],"mathematical":[60],"derivation,":[61],"numerical":[62,157,198],"algorithm,":[63],"error":[65,149,174,180,185],"analysis":[66,175],"focusing":[67],"on":[68,117],"non-Gaussian":[74],"systems":[75],"jumps":[77],"discontinuities":[79],"represented":[80],"by":[81,108,163],"nonlinear":[83],"L\u00e9vy--Fokker--Planck":[84],"We":[86,147],"propose":[87],"L\u00e9vy":[89,139,170],"such":[93],"equations,":[95],"which":[96],"features":[97],"nonlocal":[99,166],"double-integral":[100],"term,":[101],"we":[103,127],"develop":[104,128],"its":[105],"training":[106],"algorithm":[107,134],"minimizing":[109],"proposed":[111],"loss":[112],"from":[114,200],"samples.":[115],"Based":[116],"equivalence":[119],"deterministic":[125],"dynamics,":[126],"self-consistent":[130],"transport":[132],"particle":[133],"sample":[136],"interactive":[138],"at":[142],"discrete":[143],"time":[144,183],"grid":[145],"points.":[146],"provide":[148],"bound":[150],"Kullback--Leibler":[153],"divergence":[154],"between":[155],"true":[159],"density":[161],"functions":[162],"overcoming":[164],"challenges":[167],"score.":[171],"full":[173],"Monte":[178],"Carlo":[179],"discretization":[184],"furthermore":[187],"established.":[188],"To":[189],"show":[190],"usefulness":[192],"efficiency":[194],"our":[196],"approach,":[197],"examples":[199],"biology":[203],"finance":[205],"tested.":[207]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2024-12-31T00:00:00"}