{"id":"https://openalex.org/W3177956798","doi":"https://doi.org/10.1007/s10208-021-09521-z","title":"Learning Interaction Kernels in Stochastic Systems of Interacting Particles from Multiple Trajectories","display_name":"Learning Interaction Kernels in Stochastic Systems of Interacting Particles from Multiple Trajectories","publication_year":2021,"publication_date":"2021-07-13","ids":{"openalex":"https://openalex.org/W3177956798","doi":"https://doi.org/10.1007/s10208-021-09521-z","mag":"3177956798"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-021-09521-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-021-09521-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-021-09521-z.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10208-021-09521-z.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070405591","display_name":"Fei Lu","orcid":"https://orcid.org/0000-0001-6842-7922"},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Fei Lu","raw_affiliation_strings":["Department of Mathematics, Johns Hopkins University, Baltimore, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Johns Hopkins University, Baltimore, USA","institution_ids":["https://openalex.org/I145311948"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089371996","display_name":"Mauro Maggioni","orcid":"https://orcid.org/0000-0003-3258-9297"},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mauro Maggioni","raw_affiliation_strings":["Department of Mathematics, Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, USA","institution_ids":["https://openalex.org/I145311948"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078840209","display_name":"Sui Tang","orcid":"https://orcid.org/0000-0003-3284-5123"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Sui Tang","raw_affiliation_strings":["Department of Mathematics, University of California, Santa Barbara, Santa Barbara, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Santa Barbara, Santa Barbara, USA","institution_ids":["https://openalex.org/I154570441"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5078840209"],"corresponding_institution_ids":["https://openalex.org/I154570441"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":3.4124,"has_fulltext":true,"cited_by_count":36,"citation_normalized_percentile":{"value":0.93329497,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"22","issue":"4","first_page":"1013","last_page":"1067"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":1.0,"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/T12592","display_name":"Opinion Dynamics and Social Influence","score":1.0,"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.9987000226974487,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/mathematics","display_name":"Mathematics","score":0.7394462823867798},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6989695429801941},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5530310273170471},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5526191592216492},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5211815237998962},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5166680812835693},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4978649616241455},{"id":"https://openalex.org/keywords/stochastic-approximation","display_name":"Stochastic approximation","score":0.45030108094215393},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3999132513999939},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19206121563911438},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17761364579200745},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.144565612077713},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.09906241297721863},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.09125480055809021}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7394462823867798},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6989695429801941},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5530310273170471},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5526191592216492},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5211815237998962},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5166680812835693},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4978649616241455},{"id":"https://openalex.org/C55479107","wikidata":"https://www.wikidata.org/wiki/Q97663916","display_name":"Stochastic approximation","level":3,"score":0.45030108094215393},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3999132513999939},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19206121563911438},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17761364579200745},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.144565612077713},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.09906241297721863},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.09125480055809021},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10208-021-09521-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-021-09521-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-021-09521-z.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10208-021-09521-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-021-09521-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-021-09521-z.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1072749480","display_name":null,"funder_award_id":"FA9550-17","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G1427164230","display_name":null,"funder_award_id":"1837991","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1523888516","display_name":null,"funder_award_id":"FA9550-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G1963708402","display_name":null,"funder_award_id":"NSF-1913243","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G260750634","display_name":null,"funder_award_id":"FA9550-17-1","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G352931048","display_name":null,"funder_award_id":"AFOSR-FA9550","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G374640923","display_name":null,"funder_award_id":"FA9550-17-1-0280","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G5809100787","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G6486366848","display_name":null,"funder_award_id":"1821211","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6655819997","display_name":null,"funder_award_id":"1546392","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6894402473","display_name":null,"funder_award_id":"Fellowship","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G771402758","display_name":null,"funder_award_id":"NSF-1821211","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"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3177956798.pdf","grobid_xml":"https://content.openalex.org/works/W3177956798.grobid-xml"},"referenced_works_count":62,"referenced_works":["https://openalex.org/W37686529","https://openalex.org/W597932189","https://openalex.org/W1483804921","https://openalex.org/W1484867920","https://openalex.org/W1494628843","https://openalex.org/W1531455566","https://openalex.org/W1583323312","https://openalex.org/W1600293573","https://openalex.org/W1604048358","https://openalex.org/W1975318518","https://openalex.org/W2001040001","https://openalex.org/W2008740515","https://openalex.org/W2009903154","https://openalex.org/W2012405657","https://openalex.org/W2026679679","https://openalex.org/W2047278710","https://openalex.org/W2076451073","https://openalex.org/W2082733456","https://openalex.org/W2090344516","https://openalex.org/W2099589402","https://openalex.org/W2101465094","https://openalex.org/W2107396783","https://openalex.org/W2110112426","https://openalex.org/W2113096089","https://openalex.org/W2125875378","https://openalex.org/W2129293958","https://openalex.org/W2135617799","https://openalex.org/W2157942701","https://openalex.org/W2170316986","https://openalex.org/W2498028294","https://openalex.org/W2546505240","https://openalex.org/W2594862268","https://openalex.org/W2729138981","https://openalex.org/W2885549115","https://openalex.org/W2894841727","https://openalex.org/W2905558281","https://openalex.org/W2927093237","https://openalex.org/W2963093896","https://openalex.org/W2963376365","https://openalex.org/W2963941258","https://openalex.org/W2964057431","https://openalex.org/W2964061010","https://openalex.org/W2975616582","https://openalex.org/W2979653043","https://openalex.org/W2984962910","https://openalex.org/W2990366675","https://openalex.org/W3025749473","https://openalex.org/W3095238954","https://openalex.org/W3098358723","https://openalex.org/W3101007008","https://openalex.org/W3105959977","https://openalex.org/W3111739917","https://openalex.org/W3117030357","https://openalex.org/W3128929428","https://openalex.org/W3180501569","https://openalex.org/W3206411490","https://openalex.org/W4229928878","https://openalex.org/W4230104359","https://openalex.org/W4245558064","https://openalex.org/W4247095481","https://openalex.org/W4249973417","https://openalex.org/W7043940998"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W2359063982","https://openalex.org/W2360658320","https://openalex.org/W1907128005","https://openalex.org/W2514909387","https://openalex.org/W2120339885","https://openalex.org/W4246247437","https://openalex.org/W2032229253"],"abstract_inverted_index":{"Abstract":[0],"We":[1,23,50,75,136],"consider":[2],"stochastic":[3,208],"systems":[4,206],"of":[5,27,34,37,88,95,114,124,127,145,152,157,177,198],"interacting":[6],"particles":[7],"or":[8,43],"agents,":[9],"with":[10,201],"dynamics":[11,210],"determined":[12],"by":[13],"an":[14,183],"interaction":[15,30],"kernel,":[16],"which":[17,131],"only":[18],"depends":[19],"on":[20,61,204],"pairwise":[21],"distances.":[22],"study":[24],"the":[25,35,38,85,93,111,125,128,139,143,158,168,172,178,189,196],"problem":[26,90],"inferring":[28],"this":[29,57,89,120],"kernel":[31],"from":[32,191],"observations":[33],"positions":[36],"particles,":[39],"in":[40,100,142,155],"either":[41],"continuous":[42],"discrete":[44],"time,":[45],"along":[46],"multiple":[47],"independent":[48,123],"trajectories.":[49],"introduce":[51],"a":[52,62,78,105,212],"nonparametric":[53,116],"inference":[54],"approach":[55],"to":[56,68,73,83,110,187],"inverse":[58],"problem,":[59],"based":[60],"regularized":[63],"maximum":[64],"likelihood":[65],"estimator":[66,190],"constrained":[67],"suitable":[69],"hypothesis":[70],"spaces":[71],"adaptive":[72],"data.":[74],"show":[76],"that":[77,99,149],"coercivity":[79],"condition":[80,86],"enables":[81],"us":[82],"control":[84],"number":[87],"and":[91,98,171,193,211],"prove":[92],"consistency":[94],"our":[96,199],"estimator,":[97],"fact":[101],"it":[102,150],"converges":[103],"at":[104],"near-optimal":[106],"learning":[107],"rate,":[108],"equal":[109],"min\u2013max":[112],"rate":[113,121],"one-dimensional":[115],"regression.":[117],"In":[118],"particular,":[119],"is":[122,132,151],"dimension":[126],"state":[129],"space,":[130],"typically":[133],"very":[134],"high.":[135],"also":[137],"analyze":[138],"discretization":[140],"errors":[141],"case":[144],"discrete-time":[146],"observations,":[147],"showing":[148],"order":[153],"1/2":[154],"terms":[156],"time":[159],"spacings":[160],"between":[161],"observations.":[162],"This":[163],"term,":[164],"when":[165],"large,":[166],"dominates":[167],"sampling":[169],"error":[170],"approximation":[173],"error,":[174],"preventing":[175],"convergence":[176],"estimator.":[179],"Finally,":[180],"we":[181,194],"exhibit":[182],"efficient":[184],"parallel":[185],"algorithm":[186,200],"construct":[188],"data,":[192],"demonstrate":[195],"effectiveness":[197],"numerical":[202],"tests":[203],"prototype":[205],"including":[207],"opinion":[209],"Lennard-Jones":[213],"model.":[214]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}