{"id":"https://openalex.org/W7220407137","doi":"https://doi.org/10.48550/arxiv.2610.02564","title":"Learning Closure of Dynamical Systems with Kernel Ridge Regression","display_name":"Learning Closure of Dynamical Systems with Kernel Ridge Regression","publication_year":2026,"publication_date":"2026-10-01","ids":{"openalex":"https://openalex.org/W7220407137","doi":"https://doi.org/10.48550/arxiv.2610.02564"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.02564","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02564","pdf_url":"https://arxiv.org/pdf/2610.02564","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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.02564","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093104539","display_name":"Evan Habbershaw","orcid":"https://orcid.org/0009-0009-0137-5852","observed_orcids":["https://orcid.org/0009-0009-0137-5852"]},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Habbershaw, Evan","raw_affiliation_strings":["Department of Mathematics , The Pennsylvania State University ;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , The Pennsylvania State University ;","institution_ids":["https://openalex.org/I130769515"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112564733","display_name":"John Harlim","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Harlim, John","raw_affiliation_strings":["Department of Mathematics and Institute for Computational and Data Sciences , The Pennsylvania State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Institute for Computational and Data Sciences , The Pennsylvania State University","institution_ids":["https://openalex.org/I130769515"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081680496","display_name":"Senwei Liang","orcid":"https://orcid.org/0000-0002-3558-6828","observed_orcids":["https://orcid.org/0000-0002-3558-6828","https://orcid.org/0009-0009-8603-9160"]},"institutions":[{"id":"https://openalex.org/I12315562","display_name":"Texas Tech University","ror":"https://ror.org/0405mnx93","country_code":"US","type":"education","lineage":["https://openalex.org/I12315562"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Liang, Senwei","raw_affiliation_strings":["Department of Mathematics and Statistics , Texas Tech University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics , Texas Tech University","institution_ids":["https://openalex.org/I12315562"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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":0.9990000128746033,"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":0.9990000128746033,"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/T11236","display_name":"Control Systems and Identification","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.00019999999494757503,"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/closure-modeling","display_name":"closure modeling","score":0.9240000247955322},{"id":"https://openalex.org/keywords/kernel-ridge-regression","display_name":"kernel ridge regression","score":0.7879999876022339},{"id":"https://openalex.org/keywords/dynamical-systems","display_name":"dynamical systems","score":0.781000018119812},{"id":"https://openalex.org/keywords/moment-closure","display_name":"moment closure","score":0.734000027179718},{"id":"https://openalex.org/keywords/kinetic-equations","display_name":"kinetic equations","score":0.9679999947547913},{"id":"https://openalex.org/keywords/unresolved-scales","display_name":"unresolved scales","score":0.7289999723434448},{"id":"https://openalex.org/keywords/lorenz-63-system","display_name":"Lorenz-63 system","score":0.8690000176429749},{"id":"https://openalex.org/keywords/kuramoto-sivashinsky-equation","display_name":"Kuramoto-Sivashinsky equation","score":1.0},{"id":"https://openalex.org/keywords/long-horizon-prediction","display_name":"long-horizon prediction","score":0.796999990940094}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7044000029563904},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.6191999912261963},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.6003000140190125},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.54339998960495},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.47130000591278076},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.4480000138282776},{"id":"https://openalex.org/C2778513689","wikidata":"https://www.wikidata.org/wiki/Q6897109","display_name":"Moment closure","level":3,"score":0.4374000132083893},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4253000020980835},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.4214000105857849},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.41510000824928284},{"id":"https://openalex.org/C58626813","wikidata":"https://www.wikidata.org/wiki/Q5135529","display_name":"Closure problem","level":3,"score":0.337799996137619},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.3285999894142151},{"id":"https://openalex.org/C32277403","wikidata":"https://www.wikidata.org/wiki/Q740445","display_name":"Ridge","level":2,"score":0.3231000006198883},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.31049999594688416},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3027999997138977},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2867000102996826},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.27970001101493835},{"id":"https://openalex.org/C77405623","wikidata":"https://www.wikidata.org/wiki/Q598451","display_name":"System dynamics","level":2,"score":0.27649998664855957},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.2750000059604645},{"id":"https://openalex.org/C179003449","wikidata":"https://www.wikidata.org/wiki/Q1757458","display_name":"Particle system","level":2,"score":0.27320000529289246},{"id":"https://openalex.org/C179024874","wikidata":"https://www.wikidata.org/wiki/Q5395728","display_name":"Errors-in-variables models","level":2,"score":0.25049999356269836}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.02564","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02564","pdf_url":"https://arxiv.org/pdf/2610.02564","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.2610.02564","doi":"https://doi.org/10.48550/arxiv.2610.02564","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.02564","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.02564","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02564","pdf_url":"https://arxiv.org/pdf/2610.02564","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/G267040807","display_name":"Leveraging Geometric Structure in Learning Dynamical Systems","funder_award_id":"2505605","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/F4320309537","display_name":"Texas Tech University","ror":"https://ror.org/0405mnx93"},{"id":"https://openalex.org/F4320310419","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220407137.pdf","grobid_xml":"https://content.openalex.org/works/W7220407137.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W2964121744","https://openalex.org/W7167094393","https://openalex.org/W7202178562"],"related_works":["https://openalex.org/W7117079149","https://openalex.org/W6983673316","https://openalex.org/W4386215559","https://openalex.org/W2795317885","https://openalex.org/W7163712764","https://openalex.org/W3117945935","https://openalex.org/W6977184648","https://openalex.org/W7128805760","https://openalex.org/W4403254920","https://openalex.org/W7202312184"],"abstract_inverted_index":{"We":[0,129],"develop":[1],"a":[2,109,122],"closure":[3,24,40,98,107],"modeling":[4,114,164],"framework":[5,19],"for":[6,108,148,155],"identifying":[7],"missing":[8],"components":[9],"of":[10,23,64,124],"dynamical":[11],"systems":[12],"using":[13],"Kernel":[14],"Ridge":[15],"Regression":[16],"(KRR).":[17],"The":[18],"addresses":[20],"two":[21],"classes":[22],"problems:":[25],"difference-equation":[26],"closures":[27,36],"arising":[28,37],"in":[29,41,53],"ODE":[30,55],"and":[31,34,67,84,92,118,168],"PDE":[32],"settings,":[33],"algebraic":[35],"from":[38,60],"moment":[39,106],"kinetic":[42,111,117],"equations.":[43],"For":[44,100],"the":[45,75,81,85,101,125,143],"first":[46],"class,":[47,103],"we":[48,104],"derive":[49],"an":[50,54,96],"error":[51],"bound":[52],"setting":[56],"that":[57],"quantifies":[58],"contributions":[59],"time":[61],"integration,":[62],"approximation":[63],"unresolved":[65],"scales,":[66],"interpolation":[68],"required":[69],"to":[70,74],"couple":[71],"unresolved-scale":[72],"effects":[73],"resolved":[76,126],"solver.":[77],"Numerical":[78],"experiments":[79],"on":[80,135],"Lorenz-63":[82],"system":[83],"Kuramoto-Sivashinsky":[86],"equation":[87,112],"demonstrate":[88],"accurate":[89],"long-horizon":[90],"predictions":[91],"substantial":[93],"improvements":[94],"over":[95],"LSTM-based":[97],"model.":[99],"second":[102],"consider":[105],"one-dimensional":[110],"by":[113],"discrepancies":[115],"between":[116],"macroscopic":[119,127],"fluxes":[120],"as":[121],"function":[123],"variables.":[128],"compare":[130],"global":[131,144],"KRR":[132],"models":[133,161],"based":[134],"PCA":[136],"coordinates":[137],"with":[138,162],"spatially":[139],"local":[140,160],"models.":[141],"While":[142],"model":[145],"performs":[146],"well":[147],"unimodal":[149],"initial":[150,157],"conditions,":[151],"its":[152],"accuracy":[153],"deteriorates":[154],"bimodal":[156],"conditions.":[158],"Spatially":[159],"appropriate":[163],"inputs":[165],"improve":[166],"robustness":[167],"achieve":[169],"higher":[170],"predictive":[171],"accuracy.":[172]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-06T00:00:00"}