{"id":"https://openalex.org/W7155043046","doi":"https://doi.org/10.48550/arxiv.2604.18507","title":"Learning the Riccati solution operator for time-varying LQR via Deep Operator Networks","display_name":"Learning the Riccati solution operator for time-varying LQR via Deep Operator Networks","publication_year":2026,"publication_date":"2026-04-20","ids":{"openalex":"https://openalex.org/W7155043046","doi":"https://doi.org/10.48550/arxiv.2604.18507"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.18507","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.18507","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":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.18507","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5134172752","display_name":"Jun Chen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Jun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029871921","display_name":"Umberto Biccari","orcid":"https://orcid.org/0000-0003-0096-5630"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Biccari, Umberto","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100608812","display_name":"Junmin Wang","orcid":"https://orcid.org/0000-0001-7133-7311"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Junmin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9351999759674072,"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":0.9351999759674072,"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/T11416","display_name":"Numerical methods for differential equations","score":0.01759999990463257,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.003700000001117587,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/linear-quadratic-regulator","display_name":"Linear-quadratic regulator","score":0.7301999926567078},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5891000032424927},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.48559999465942383},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.4805000126361847},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.4794999957084656},{"id":"https://openalex.org/keywords/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.4648999869823456},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.462799996137619},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.42340001463890076},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4133000075817108}],"concepts":[{"id":"https://openalex.org/C98779006","wikidata":"https://www.wikidata.org/wiki/Q2520550","display_name":"Linear-quadratic regulator","level":3,"score":0.7301999926567078},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5891000032424927},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.48559999465942383},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.4805000126361847},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.4794999957084656},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4733000099658966},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.4648999869823456},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4645000100135803},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.462799996137619},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.42340001463890076},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4180000126361847},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4133000075817108},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.37599998712539673},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.36059999465942383},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.35260000824928284},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.34310001134872437},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3418999910354614},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.33000001311302185},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.33000001311302185},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3197999894618988},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.3019999861717224},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.2957000136375427},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.2930000126361847},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.28859999775886536},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2687000036239624},{"id":"https://openalex.org/C774472","wikidata":"https://www.wikidata.org/wiki/Q6760393","display_name":"Margin (machine learning)","level":2,"score":0.2671000063419342},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.26589998602867126},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2621999979019165},{"id":"https://openalex.org/C204495892","wikidata":"https://www.wikidata.org/wiki/Q1798304","display_name":"Linear-quadratic-Gaussian control","level":3,"score":0.2574999928474426},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.25110000371932983}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.18507","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.18507","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":"doi:10.48550/arxiv.2604.18507","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.18507","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":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2,23,30,70,85,90,140,167,201],"computational":[3,78,154,210],"framework":[4,141],"for":[5,35,97,161,224],"replacing":[6],"the":[7,46,55,77,127,144,153,177,191],"repeated":[8,81],"numerical":[9,82],"solution":[10,48],"of":[11,28,45,65,73,126,146,204],"differential":[12,33],"Riccati":[13,56],"equations":[14],"in":[15,149],"finite-horizon":[16],"Linear":[17],"Quadratic":[18],"Regulator":[19],"(LQR)":[20],"problems":[21,164,188],"by":[22],"learned":[24],"operator":[25,49,108,135],"surrogate.":[26],"Instead":[27],"solving":[29],"nonlinear":[31],"matrix-valued":[32],"equation":[34],"each":[36],"new":[37],"system":[38,52,129,178,205],"instance,":[39],"we":[40,93,103,121,156],"construct":[41],"offline":[42],"an":[43,219],"approximation":[44,109],"associated":[47],"mapping":[50],"time-dependent":[51,163],"parameters":[53],"to":[54,84,112,142,171,176,213],"trajectory.":[57],"The":[58,216],"resulting":[59],"model":[60],"enables":[61],"fast":[62],"online":[63],"evaluation":[64],"approximate":[66],"optimal":[67,150,228],"feedbacks":[68],"across":[69,200],"wide":[71,202],"class":[72],"systems,":[74],"thereby":[75],"shifting":[76],"burden":[79],"from":[80],"integration":[83],"one-time":[86],"learning":[87,169],"stage.":[88],"From":[89],"theoretical":[91],"perspective,":[92],"establish":[94],"control-theoretic":[95],"guarantees":[96],"this":[98],"operator-based":[99],"approximation.":[100,136],"In":[101],"particular,":[102],"derive":[104],"bounds":[105],"quantifying":[106],"how":[107],"errors":[110],"propagate":[111],"feedback":[113],"performance,":[114],"trajectory":[115],"accuracy,":[116],"and":[117,120,165,185,197,221,226],"cost":[118],"suboptimality,":[119],"prove":[122],"that":[123,190],"exponential":[124],"stability":[125],"closed-loop":[128],"is":[130],"preserved":[131],"under":[132],"sufficiently":[133],"accurate":[134],"These":[137],"results":[138],"provide":[139],"assess":[143],"reliability":[145],"data-driven":[147],"approximations":[148],"control.":[151],"On":[152],"side,":[155],"design":[157],"tailored":[158],"DeepONet":[159],"architectures":[160],"matrix-valued,":[162],"introduce":[166],"progressive":[168],"strategy":[170],"address":[172],"scalability":[173],"with":[174],"respect":[175],"dimension.":[179],"Numerical":[180],"experiments":[181],"on":[182],"both":[183],"time-invariant":[184],"time-varying":[186],"LQR":[187],"demonstrate":[189],"proposed":[192],"approach":[193],"achieves":[194],"high":[195],"accuracy":[196],"strong":[198],"generalization":[199],"range":[203],"configurations,":[206],"while":[207],"delivering":[208],"substantial":[209],"speedups":[211],"compared":[212],"classical":[214],"solvers.":[215],"method":[217],"offers":[218],"effective":[220],"scalable":[222],"alternative":[223],"parametric":[225],"real-time":[227],"control":[229],"applications.":[230]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-04-22T00:00:00"}