{"id":"https://openalex.org/W4416235988","doi":"https://doi.org/10.48550/arxiv.2511.08992","title":"Learning to Control PDEs with Differentiable Predictive Control and Time-Integrated Neural Operators","display_name":"Learning to Control PDEs with Differentiable Predictive Control and Time-Integrated Neural Operators","publication_year":2025,"publication_date":"2025-11-12","ids":{"openalex":"https://openalex.org/W4416235988","doi":"https://doi.org/10.48550/arxiv.2511.08992"},"language":null,"primary_location":{"id":"pmh:oai:arXiv.org:2511.08992","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2511.08992","pdf_url":"https://arxiv.org/pdf/2511.08992","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2511.08992","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109791255","display_name":"Dibakar Roy Sarkar","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sarkar, Dibakar Roy","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019969465","display_name":"J\u00e1n Drgo\u0148a","orcid":"https://orcid.org/0000-0003-1223-208X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Drgo\u0148a, J\u00e1n","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5015683810","display_name":"Somdatta Goswami","orcid":"https://orcid.org/0000-0002-8255-9080"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Goswami, Somdatta","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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":0.8690999746322632,"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":0.8690999746322632,"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/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.026100000366568565,"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"}},{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.019099999219179153,"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/leverage","display_name":"Leverage (statistics)","score":0.7258999943733215},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.6335999965667725},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5722000002861023},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5242999792098999},{"id":"https://openalex.org/keywords/model-predictive-control","display_name":"Model predictive control","score":0.5142999887466431},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4968999922275543},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.4643000066280365},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4453999996185303},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4214000105857849}],"concepts":[{"id":"https://openalex.org/C153083717","wikidata":"https://www.wikidata.org/wiki/Q6535263","display_name":"Leverage (statistics)","level":2,"score":0.7258999943733215},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.650600016117096},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.6335999965667725},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5722000002861023},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5242999792098999},{"id":"https://openalex.org/C172205157","wikidata":"https://www.wikidata.org/wiki/Q1782962","display_name":"Model predictive control","level":3,"score":0.5142999887466431},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4968999922275543},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4643000066280365},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4636000096797943},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45260000228881836},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4453999996185303},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4214000105857849},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.4165000021457672},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.4092000126838684},{"id":"https://openalex.org/C55660270","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization","level":2,"score":0.3443000018596649},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.34380000829696655},{"id":"https://openalex.org/C64357122","wikidata":"https://www.wikidata.org/wiki/Q1149766","display_name":"Causality (physics)","level":2,"score":0.33640000224113464},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.32910001277923584},{"id":"https://openalex.org/C22367795","wikidata":"https://www.wikidata.org/wiki/Q7625208","display_name":"Structured prediction","level":2,"score":0.32820001244544983},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3093000054359436},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.29980000853538513},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.28209999203681946},{"id":"https://openalex.org/C153240184","wikidata":"https://www.wikidata.org/wiki/Q3243772","display_name":"Control variable","level":2,"score":0.2815999984741211},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.2784000039100647},{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.27709999680519104},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2606000006198883},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.2538999915122986}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2511.08992","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2511.08992","pdf_url":"https://arxiv.org/pdf/2511.08992","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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.2511.08992","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2511.08992","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":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2511.08992","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2511.08992","pdf_url":"https://arxiv.org/pdf/2511.08992","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320310145","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4416235988.pdf","grobid_xml":"https://content.openalex.org/works/W4416235988.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,92],"present":[1],"a":[2],"data-driven":[3],"control":[4,36,68,149,162],"framework":[5,32],"for":[6,33,86,159],"partial":[7],"differential":[8],"equations":[9],"(PDEs).":[10],"Our":[11],"approach":[12,75],"integrates":[13],"Time-Integrated":[14],"Deep":[15],"Operator":[16],"Networks":[17],"(TI-DeepONets)":[18],"as":[19],"differentiable":[20],"PDE":[21,100],"surrogate":[22],"models":[23],"within":[24],"the":[25,51,63,66,71,84,95,103,105,109,154],"Differentiable":[26],"Predictive":[27],"Control":[28],"(DPC)-a":[29],"self-supervised":[30],"learning":[31,158],"constrained":[34],"neural":[35,81],"policies.":[37],"The":[38,112],"TI-DeepONet":[39],"architecture":[40],"learns":[41],"temporal":[42],"derivatives":[43],"and":[44,108,120,131],"couples":[45],"them":[46],"with":[47],"numerical":[48],"integrators,":[49],"while":[50,124],"DPC":[52],"algorithm":[53],"uses":[54],"automatic":[55],"differentiation":[56],"to":[57,145],"compute":[58],"policy":[59],"gradients":[60],"by":[61],"backpropagating":[62],"expectations":[64],"of":[65,80,128,138,156,163],"optimal":[67],"loss":[69],"through":[70],"learned":[72,113],"TI-DeepONet.":[73],"This":[74],"enables":[76],"efficient":[77],"offline":[78],"optimization":[79,88],"policies":[82,114],"without":[83],"need":[85],"online":[87],"or":[89],"supervisory":[90],"controllers.":[91],"empirically":[93],"demonstrate":[94,135],"proposed":[96],"method":[97],"across":[98,126],"diverse":[99],"systems,":[101],"including":[102],"heat,":[104],"nonlinear":[106,146],"Burgers',":[107],"reaction-diffusion":[110],"equations.":[111],"achieve":[115],"target":[116],"tracking,":[117],"constraint":[118],"satisfaction,":[119],"curvature":[121],"minimization":[122],"objectives,":[123],"generalizing":[125],"distributions":[127],"initial":[129],"conditions":[130],"parameters.":[132],"Moreover,":[133],"we":[134],"four":[136],"orders":[137],"magnitude":[139],"acceleration":[140],"at":[141],"inference":[142],"time":[143],"compared":[144],"model":[147],"predictive":[148],"benchmarks.":[150],"These":[151],"results":[152],"highlight":[153],"promise":[155],"operator":[157],"scalable":[160],"model-based":[161],"PDEs.":[164]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-11-14T00:00:00"}
