{"id":"https://openalex.org/W7167094393","doi":"https://doi.org/10.48550/arxiv.2607.00257","title":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","display_name":"Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression","publication_year":2026,"publication_date":"2026-06-30","ids":{"openalex":"https://openalex.org/W7167094393","doi":"https://doi.org/10.48550/arxiv.2607.00257"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2607.00257","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.00257","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,"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.2607.00257","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021940908","display_name":"Max Kreider","orcid":"https://orcid.org/0000-0003-1889-8261"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kreider, Max","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112564733","display_name":"John Harlim","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Harlim, John","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5139895052","display_name":"Daning Huang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huang, Daning","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":0.3889999985694885,"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":0.3889999985694885,"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/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.21889999508857727,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.10920000076293945,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/robustness","display_name":"Robustness (evolution)","score":0.6425999999046326},{"id":"https://openalex.org/keywords/noisy-data","display_name":"Noisy data","score":0.583899974822998},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5760999917984009},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.503600001335144},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.503000020980835},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.49000000953674316},{"id":"https://openalex.org/keywords/regression","display_name":"Regression","score":0.4717000126838684},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.4156000018119812},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.37940001487731934}],"concepts":[{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6425999999046326},{"id":"https://openalex.org/C2781170535","wikidata":"https://www.wikidata.org/wiki/Q30587856","display_name":"Noisy data","level":2,"score":0.583899974822998},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5760999917984009},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5042999982833862},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.503600001335144},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.503000020980835},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.49000000953674316},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48739999532699585},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.4717000126838684},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4212999939918518},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41679999232292175},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.4156000018119812},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3873000144958496},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.37940001487731934},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.375900000333786},{"id":"https://openalex.org/C200695384","wikidata":"https://www.wikidata.org/wiki/Q1739319","display_name":"Kernel regression","level":3,"score":0.34929999709129333},{"id":"https://openalex.org/C32277403","wikidata":"https://www.wikidata.org/wiki/Q740445","display_name":"Ridge","level":2,"score":0.3328000009059906},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3172000050544739},{"id":"https://openalex.org/C157286648","wikidata":"https://www.wikidata.org/wiki/Q846780","display_name":"Kalman filter","level":2,"score":0.3050000071525574},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.3034000098705292},{"id":"https://openalex.org/C29265498","wikidata":"https://www.wikidata.org/wiki/Q7047719","display_name":"Noise measurement","level":3,"score":0.2687999904155731},{"id":"https://openalex.org/C114275822","wikidata":"https://www.wikidata.org/wiki/Q621512","display_name":"Linear dynamical system","level":3,"score":0.2581999897956848},{"id":"https://openalex.org/C163294075","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Noise reduction","level":2,"score":0.257999986410141},{"id":"https://openalex.org/C117765406","wikidata":"https://www.wikidata.org/wiki/Q5362437","display_name":"Generalization error","level":3,"score":0.25529998540878296},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.2522999942302704},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.2522999942302704},{"id":"https://openalex.org/C2987469083","wikidata":"https://www.wikidata.org/wiki/Q166314","display_name":"Chaotic systems","level":3,"score":0.2522999942302704},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.251800000667572},{"id":"https://openalex.org/C184389593","wikidata":"https://www.wikidata.org/wiki/Q603159","display_name":"Curve fitting","level":2,"score":0.2515000104904175}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2607.00257","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.00257","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,"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.2607.00257","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.00257","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,"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":[{"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure","score":0.5024155378341675}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Accurate":[0],"prediction":[1],"of":[2,70,131],"complex":[3],"dynamical":[4,106],"systems":[5,136],"from":[6],"noisy":[7,34,48,120],"measurements":[8],"remains":[9],"a":[10,41,60,80,89,93],"significant":[11],"challenge":[12],"in":[13,137],"scientific":[14],"computing.":[15],"Kernel":[16,100],"ridge":[17],"regression":[18],"learning":[19,52,95,105],"strategies":[20,53],"are":[21],"often":[22],"effective":[23,115],"when":[24],"applied":[25],"to":[26,46,97,113,139],"clean":[27,118],"data,":[28,49,121],"but":[29],"have":[30,54],"limited":[31],"success":[32],"with":[33,59,92],"data.":[35,148],"Recent":[36],"work":[37],"has":[38],"observed":[39],"that":[40],"weak":[42,76,90],"formulation":[43,77,91],"can":[44],"act":[45],"filter":[47],"and":[50,78,119,122],"different":[51],"achieved":[55],"increased":[56],"noise":[57],"robustness":[58],"weak-form":[61],"framework.":[62],"In":[63],"this":[64],"manuscript,":[65],"we":[66,87],"give":[67],"an":[68],"overview":[69],"the":[71,75,129],"filtering":[72],"mechanism":[73],"behind":[74],"provide":[79],"bias-variance":[81],"error":[82],"decomposition.":[83],"Using":[84],"these":[85],"insights,":[86],"combine":[88],"kernel":[94],"strategy":[96],"propose":[98],"Weak-form":[99],"Ridge":[101],"Regression":[102],"(WKRR)":[103],"for":[104,116],"systems.":[107],"The":[108],"proposed":[109],"framework":[110],"is":[111],"simple":[112],"implement,":[114],"both":[117],"outperforms":[123],"several":[124],"baseline":[125],"methods.":[126],"We":[127],"demonstrate":[128],"performance":[130],"WKRR":[132],"on":[133],"chaotic":[134],"benchmark":[135],"up":[138],"64":[140],"dimensions,":[141],"as":[142,144],"well":[143],"15,000-dimensional":[145],"real-world":[146],"fluid":[147]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-07-03T00:00:00"}