{"id":"https://openalex.org/W7171772302","doi":"https://doi.org/10.48550/arxiv.2607.26414","title":"Origins and mitigation of double descent in reduced order modeling","display_name":"Origins and mitigation of double descent in reduced order modeling","publication_year":2026,"publication_date":"2026-07-29","ids":{"openalex":"https://openalex.org/W7171772302","doi":"https://doi.org/10.48550/arxiv.2607.26414"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2607.26414","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.26414","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.2607.26414","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027042013","display_name":"Andrei A. Klishin","orcid":"https://orcid.org/0000-0002-5740-8520"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Klishin, Andrei A.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5144061486","display_name":"J. Nathan Kutz","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kutz, J. Nathan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5060988111","display_name":"Krithika Manohar","orcid":"https://orcid.org/0000-0002-1582-6767"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Manohar, Krithika","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":0.8510000109672546,"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":0.8510000109672546,"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":0.09700000286102295,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.011800000444054604,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5131999850273132},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.47870001196861267},{"id":"https://openalex.org/keywords/coordinate-descent","display_name":"Coordinate descent","score":0.4277999997138977},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.4147000014781952},{"id":"https://openalex.org/keywords/instability","display_name":"Instability","score":0.38190001249313354},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.3644999861717224},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.3528999984264374},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.32850000262260437}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.583899974822998},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5131999850273132},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.47870001196861267},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4627000093460083},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45509999990463257},{"id":"https://openalex.org/C157553263","wikidata":"https://www.wikidata.org/wiki/Q5168004","display_name":"Coordinate descent","level":2,"score":0.4277999997138977},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.4147000014781952},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.38190001249313354},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.3644999861717224},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.36000001430511475},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3544999957084656},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.3528999984264374},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33239999413490295},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.32850000262260437},{"id":"https://openalex.org/C70958404","wikidata":"https://www.wikidata.org/wiki/Q7512728","display_name":"Signal reconstruction","level":4,"score":0.3255999982357025},{"id":"https://openalex.org/C24552861","wikidata":"https://www.wikidata.org/wiki/Q2670177","display_name":"Data assimilation","level":2,"score":0.3172999918460846},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3140999972820282},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3073999881744385},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.2994999885559082},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.2888999879360199},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.2624000012874603},{"id":"https://openalex.org/C67186912","wikidata":"https://www.wikidata.org/wiki/Q367664","display_name":"Data modeling","level":2,"score":0.2596000134944916},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.2590000033378601},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.25839999318122864}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2607.26414","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.26414","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.2607.26414","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.26414","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":[{"display_name":"Life below water","id":"https://metadata.un.org/sdg/14","score":0.4786481261253357}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Latent":[0],"low-dimensional":[1],"structure":[2],"in":[3,50,56,89],"datasets":[4],"of":[5,44,85,101,128,136,141],"natural":[6],"and":[7,20,34,110,113,133],"engineered":[8],"systems":[9],"enables":[10],"their":[11,111],"sparse":[12],"sensing,":[13],"or":[14],"full-state":[15],"reconstruction":[16,30,38,105,127],"from":[17],"historical":[18],"data":[19],"very":[21],"few":[22],"carefully":[23],"chosen":[24],"localized":[25],"measurements.":[26],"Depending":[27],"on":[28],"the":[29,37,94,119],"algorithm,":[31],"sensor":[32],"locations,":[33],"measurement":[35],"noise,":[36],"risk":[39,96],"curves":[40,97],"demonstrate":[41,122],"a":[42,47,66,82,86,99,137,142],"diversity":[43],"patterns":[45,132],"including":[46],"dramatic":[48],"peak":[49],"error":[51],"known":[52],"as":[53],"double":[54,77],"descent":[55,78],"Machine":[57],"Learning":[58],"literature.":[59],"Here":[60],"we":[61,72,92],"explore":[62],"those":[63],"scenarios":[64],"under":[65],"unified":[67],"Data-Noise":[68],"Averaging":[69],"theory.":[70],"Qualitatively,":[71],"formulate":[73],"sufficient":[74],"criteria":[75],"for":[76,124],"to":[79,107,117],"emerge":[80],"through":[81],"catastrophic":[83],"amplification":[84],"pathological":[87],"signal":[88],"reconstruction.":[90],"Quantitatively,":[91],"predict":[93],"detailed":[95],"at":[98],"fraction":[100],"computational":[102],"cost,":[103],"trace":[104],"instability":[106],"individual":[108],"sensors":[109],"combinations,":[112],"provide":[114],"regularization":[115],"mechanisms":[116],"mitigate":[118],"instability.":[120],"We":[121],"results":[123],"both":[125],"static":[126],"Sea":[129],"Surface":[130],"Temperature":[131],"time":[134],"integration":[135],"reduced":[138],"order":[139],"model":[140],"PDE.":[143]},"counts_by_year":[],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2026-07-31T00:00:00"}