{"id":"https://openalex.org/W4416615263","doi":"https://doi.org/10.1137/23m1579091","title":"Bounded KRnet and Its Applications to Density Estimation and Approximation","display_name":"Bounded KRnet and Its Applications to Density Estimation and Approximation","publication_year":2025,"publication_date":"2025-11-25","ids":{"openalex":"https://openalex.org/W4416615263","doi":"https://doi.org/10.1137/23m1579091"},"language":"en","primary_location":{"id":"doi:10.1137/23m1579091","doi":"https://doi.org/10.1137/23m1579091","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1579091","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,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-140","russia-white-list-1"],"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"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2305.09063","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005460546","display_name":"Li Zeng","orcid":"https://orcid.org/0000-0002-1201-064X","observed_orcids":["https://orcid.org/0000-0002-1201-064X"]},"institutions":[{"id":"https://openalex.org/I80947539","display_name":"Fuzhou University","ror":"https://ror.org/011xvna82","country_code":"CN","type":"education","lineage":["https://openalex.org/I80947539"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li Zeng","raw_affiliation_strings":["School of Mathematics and Statistics, Fuzhou University, Fuzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Fuzhou University, Fuzhou, China","institution_ids":["https://openalex.org/I80947539"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112618541","display_name":"Xiaoliang Wan","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I121820613","display_name":"Louisiana State University","ror":"https://ror.org/05ect4e57","country_code":"US","type":"education","lineage":["https://openalex.org/I121820613"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xiaoliang Wan","raw_affiliation_strings":["Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, LA 70803 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, LA 70803 USA","institution_ids":["https://openalex.org/I121820613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004294250","display_name":"Tao Zhou","orcid":"https://orcid.org/0000-0001-5040-8571","observed_orcids":["https://orcid.org/0000-0001-5040-8571"]},"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":"Tao Zhou","raw_affiliation_strings":["Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8577,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.66097754,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"47","issue":"6","first_page":"C1294","last_page":"C1318"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9750999808311462,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9750999808311462,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.009399999864399433,"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/T10320","display_name":"Neural Networks and Applications","score":0.008999999612569809,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/invertible-mappings","display_name":"invertible mappings","score":0.6940000057220459},{"id":"https://openalex.org/keywords/transport-maps","display_name":"transport maps","score":0.6420000195503235},{"id":"https://openalex.org/keywords/density-estimation","display_name":"density estimation","score":0.9200000166893005},{"id":"https://openalex.org/keywords/deep-generative-models","display_name":"deep generative models","score":0.7429999709129333},{"id":"https://openalex.org/keywords/fokker-planck-equation","display_name":"Fokker-Planck equation","score":0.8790000081062317},{"id":"https://openalex.org/keywords/keller-segel-equation","display_name":"Keller-Segel equation","score":0.8510000109672546},{"id":"https://openalex.org/keywords/kinetic-equations","display_name":"kinetic equations","score":0.4189999997615814},{"id":"https://openalex.org/keywords/adaptive-learning","display_name":"adaptive learning","score":0.45100000500679016}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7854999899864197},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6668000221252441},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5167999863624573},{"id":"https://openalex.org/C189508267","wikidata":"https://www.wikidata.org/wiki/Q17088227","display_name":"Density estimation","level":3,"score":0.38589999079704285},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36739999055862427},{"id":"https://openalex.org/C96250715","wikidata":"https://www.wikidata.org/wiki/Q965330","display_name":"Estimation","level":2,"score":0.3174999952316284},{"id":"https://openalex.org/C27851653","wikidata":"https://www.wikidata.org/wiki/Q829653","display_name":"Bounded variation","level":2,"score":0.29899999499320984},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.29789999127388},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.2946999967098236},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2906000018119812},{"id":"https://openalex.org/C2986878899","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical approximation","level":3,"score":0.28529998660087585},{"id":"https://openalex.org/C92928283","wikidata":"https://www.wikidata.org/wiki/Q4949981","display_name":"Bounded deformation","level":4,"score":0.26930001378059387},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2678000032901764},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.2628999948501587},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.2596000134944916},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.25609999895095825}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/23m1579091","doi":"https://doi.org/10.1137/23m1579091","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1579091","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,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-140","russia-white-list-1"],"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"},{"id":"pmh:oai:arXiv.org:2305.09063","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2305.09063","pdf_url":"https://arxiv.org/pdf/2305.09063","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.2305.09063","doi":"https://doi.org/10.48550/arxiv.2305.09063","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2305.09063","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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2305.09063","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2305.09063","pdf_url":"https://arxiv.org/pdf/2305.09063","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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1574759293","display_name":"Efficient Algorithms Related to and Beyond the Large Deviation Technique","funder_award_id":"1913163","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1881597498","display_name":null,"funder_award_id":"XDA25010404","funder_id":"https://openalex.org/F4320321133","funder_display_name":"Chinese Academy of Sciences"},{"id":"https://openalex.org/G2506195653","display_name":null,"funder_award_id":"12288201","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2856102575","display_name":null,"funder_award_id":"12288201","funder_id":"https://openalex.org/F4320321133","funder_display_name":"Chinese Academy of Sciences"},{"id":"https://openalex.org/G2948815092","display_name":"Adaptive sampling for scientific machine learning: algorithms and applications","funder_award_id":"2513234","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3506334458","display_name":null,"funder_award_id":"12461160275","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8019429922","display_name":null,"funder_award_id":"12401566","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8533620077","display_name":null,"funder_award_id":"12288201","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/F4320321133","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4416615263.pdf","grobid_xml":"https://content.openalex.org/works/W4416615263.grobid-xml"},"referenced_works_count":49,"referenced_works":["https://openalex.org/W1583912456","https://openalex.org/W1959608418","https://openalex.org/W1978135292","https://openalex.org/W1982366717","https://openalex.org/W1997225897","https://openalex.org/W2002363668","https://openalex.org/W2029698240","https://openalex.org/W2042892258","https://openalex.org/W2067673508","https://openalex.org/W2105613866","https://openalex.org/W2129905273","https://openalex.org/W2238007812","https://openalex.org/W2409550820","https://openalex.org/W2760972773","https://openalex.org/W2774736168","https://openalex.org/W2810998233","https://openalex.org/W2885324189","https://openalex.org/W2898540847","https://openalex.org/W2899283552","https://openalex.org/W2900369848","https://openalex.org/W2913510728","https://openalex.org/W2963647337","https://openalex.org/W2964110066","https://openalex.org/W2964121744","https://openalex.org/W3004450693","https://openalex.org/W3016703299","https://openalex.org/W3035647965","https://openalex.org/W3092321786","https://openalex.org/W3096831136","https://openalex.org/W3137229187","https://openalex.org/W3138583834","https://openalex.org/W3165444044","https://openalex.org/W3183498204","https://openalex.org/W3212612922","https://openalex.org/W4210363725","https://openalex.org/W4220785892","https://openalex.org/W4220851692","https://openalex.org/W4220936630","https://openalex.org/W4223440841","https://openalex.org/W4255839052","https://openalex.org/W4286751013","https://openalex.org/W4293659830","https://openalex.org/W4310446950","https://openalex.org/W4312324509","https://openalex.org/W4313419889","https://openalex.org/W4322824984","https://openalex.org/W4388304013","https://openalex.org/W4394652738","https://openalex.org/W4402217122"],"related_works":["https://openalex.org/W3165444044","https://openalex.org/W3092321786","https://openalex.org/W3137229187","https://openalex.org/W4322824984","https://openalex.org/W4323557397","https://openalex.org/W4391335165","https://openalex.org/W4406599158","https://openalex.org/W3117545831","https://openalex.org/W3154367844","https://openalex.org/W7159637423"],"abstract_inverted_index":{"Abstract.":[0],"In":[1],"this":[2],"paper,":[3],"we":[4,108,148,191],"develop":[5,192],"an":[6,110,193],"invertible":[7],"mapping,":[8],"called":[9],"B-KRnet,":[10,147,190],"on":[11,76,83,127,154,189],"a":[12,43,77,90,105,123,150,155,182],"bounded":[13,162],"domain":[14,157],"and":[15,33,69,146,163,186],"apply":[16],"it":[17],"to":[18,38,97,119,135,197,219],"density":[19,113,136],"estimation/approximation":[20],"for":[21],"data":[22,140],"or":[23,206],"the":[24,30,34,56,60,84,99,120,128,172,175,221],"solutions":[25,203],"of":[26,42,45,59,122,174,184,214,223],"PDEs":[27],"such":[28],"as":[29,104,210],"Fokker\u2013Planck":[31,178],"equation":[32],"Keller\u2013Segel":[35],"equation.":[36],"Similar":[37],"KRnet,":[39],"B-KRnet":[40,68,73,96,103],"consists":[41],"series":[44],"coupling":[46,144],"layers":[47],"with":[48],"progressively":[49],"fewer":[50],"active":[51],"transformation":[52],"dimensions,":[53],"inspired":[54],"by":[55],"triangular":[57],"structure":[58],"Knothe\u2013Rosenblatt":[61],"(KR)":[62],"rearrangement.":[63],"The":[64],"main":[65],"difference":[66],"between":[67],"KRnet":[70,80,145],"is":[71,74,81,93,171,181,217],"that":[72,117],"defined":[75,82],"hypercube":[78],"while":[79],"whole":[85],"space;":[86],"in":[87,95],"other":[88,164],"words,":[89],"new":[91],"mechanism":[92],"introduced":[94],"maintain":[98],"exact":[100],"invertibility.":[101],"Using":[102],"transport":[106],"map,":[107],"obtain":[109],"explicit":[111],"probability":[112],"function":[114],"(PDF)":[115],"model":[116,153],"corresponds":[118],"pushforward":[121],"base":[124],"(uniform)":[125],"distribution":[126],"hypercube.":[129],"It":[130],"can":[131,207],"be":[132,208],"directly":[133],"applied":[134],"estimation":[137],"when":[138],"only":[139],"are":[141,161,166,204],"available.":[142],"By":[143],"define":[149],"deep":[151],"generative":[152],"high-dimensional":[156],"where":[158],"some":[159],"dimensions":[160,165],"unbounded.":[167],"A":[168,212],"typical":[169],"case":[170],"solution":[173],"stationary":[176],"kinetic":[177],"equation,":[179],"which":[180],"PDF":[183],"position":[185],"momentum.":[187],"Based":[188],"adaptive":[194],"learning":[195],"approach":[196],"approximate":[198],"partial":[199],"differential":[200],"equations":[201],"whose":[202],"PDFs":[205],"treated":[209],"PDFs.":[211],"variety":[213],"numerical":[215],"experiments":[216],"presented":[218],"demonstrate":[220],"effectiveness":[222],"B-KRnet.":[224]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1}],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2025-11-25T00:00:00"}