{"id":"https://openalex.org/W2466347430","doi":"https://doi.org/10.1137/16m1086637","title":"Exact Recovery of Chaotic Systems from Highly Corrupted Data","display_name":"Exact Recovery of Chaotic Systems from Highly Corrupted Data","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2466347430","doi":"https://doi.org/10.1137/16m1086637","mag":"2466347430"},"language":"en","primary_location":{"id":"doi:10.1137/16m1086637","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1086637","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Multiscale Modeling &amp; Simulation","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1607.01067","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109179791","display_name":"Giang Tran","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Giang Tran","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5040543665","display_name":"Rachel Ward","orcid":"https://orcid.org/0000-0001-7651-089X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rachel Ward","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6466,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.77566049,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"15","issue":"3","first_page":"1108","last_page":"1129"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9884999990463257,"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"}},"topics":[{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9884999990463257,"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"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9883000254631042,"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/T13487","display_name":"Statistical and numerical algorithms","score":0.9825000166893005,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.6499300003051758},{"id":"https://openalex.org/keywords/lorenz-system","display_name":"Lorenz system","score":0.6440589427947998},{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.615658700466156},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6082673072814941},{"id":"https://openalex.org/keywords/outlier","display_name":"Outlier","score":0.5064932107925415},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49079784750938416},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.47888773679733276},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4639899730682373},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.4638640284538269},{"id":"https://openalex.org/keywords/generality","display_name":"Generality","score":0.4615350663661957},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.4479146897792816},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35333865880966187},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2868264317512512},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.249067485332489},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2392720878124237},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.21177974343299866},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19395241141319275},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09075266122817993},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07875123620033264}],"concepts":[{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6499300003051758},{"id":"https://openalex.org/C151510863","wikidata":"https://www.wikidata.org/wiki/Q899844","display_name":"Lorenz system","level":3,"score":0.6440589427947998},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.615658700466156},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6082673072814941},{"id":"https://openalex.org/C79337645","wikidata":"https://www.wikidata.org/wiki/Q779824","display_name":"Outlier","level":2,"score":0.5064932107925415},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49079784750938416},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.47888773679733276},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4639899730682373},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.4638640284538269},{"id":"https://openalex.org/C2780767217","wikidata":"https://www.wikidata.org/wiki/Q5532421","display_name":"Generality","level":2,"score":0.4615350663661957},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.4479146897792816},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35333865880966187},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2868264317512512},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.249067485332489},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2392720878124237},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21177974343299866},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19395241141319275},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09075266122817993},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07875123620033264},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/16m1086637","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1086637","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Multiscale Modeling &amp; Simulation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1607.01067","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1607.01067","pdf_url":"https://arxiv.org/pdf/1607.01067","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2466347430","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1607.01067.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1607.01067","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1607.01067","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:1607.01067","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1607.01067","pdf_url":"https://arxiv.org/pdf/1607.01067","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1523888516","display_name":null,"funder_award_id":"FA9550-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G1700646021","display_name":null,"funder_award_id":"#FA9550-13-1-0125","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G5809100787","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8155642744","display_name":null,"funder_award_id":"1255631","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/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2466347430.pdf","grobid_xml":"https://content.openalex.org/works/W2466347430.grobid-xml"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W133148819","https://openalex.org/W1644425553","https://openalex.org/W1901616594","https://openalex.org/W1972649461","https://openalex.org/W1974983064","https://openalex.org/W1979769287","https://openalex.org/W1984391316","https://openalex.org/W1988202149","https://openalex.org/W1994859578","https://openalex.org/W1997126009","https://openalex.org/W1999165386","https://openalex.org/W1999534682","https://openalex.org/W2006784971","https://openalex.org/W2018683990","https://openalex.org/W2019398782","https://openalex.org/W2020390700","https://openalex.org/W2031365860","https://openalex.org/W2031668778","https://openalex.org/W2040135606","https://openalex.org/W2049709948","https://openalex.org/W2050651297","https://openalex.org/W2052228280","https://openalex.org/W2053095324","https://openalex.org/W2053186076","https://openalex.org/W2054110507","https://openalex.org/W2056626217","https://openalex.org/W2067746767","https://openalex.org/W2093346147","https://openalex.org/W2099738274","https://openalex.org/W2102264602","https://openalex.org/W2111480264","https://openalex.org/W2119334003","https://openalex.org/W2128018231","https://openalex.org/W2141394518","https://openalex.org/W2141454789","https://openalex.org/W2143834888","https://openalex.org/W2147779004","https://openalex.org/W2158038039","https://openalex.org/W2164452299","https://openalex.org/W2239232218","https://openalex.org/W2308444223","https://openalex.org/W2964216518","https://openalex.org/W4246840991","https://openalex.org/W4250955649"],"related_works":["https://openalex.org/W2239232218","https://openalex.org/W2964145209","https://openalex.org/W2510030309","https://openalex.org/W2135046866","https://openalex.org/W2093828424","https://openalex.org/W1979769287","https://openalex.org/W2582771730","https://openalex.org/W2525748878","https://openalex.org/W2067035505","https://openalex.org/W2573798107","https://openalex.org/W2137258853","https://openalex.org/W2050651297","https://openalex.org/W3100641539","https://openalex.org/W1549386224","https://openalex.org/W3071135787","https://openalex.org/W2601040923","https://openalex.org/W3101512171","https://openalex.org/W2770582672","https://openalex.org/W40335791","https://openalex.org/W2743814236"],"abstract_inverted_index":{"Learning":[0],"the":[1,33,43,60,118,142,151,163,172,178,196,202],"governing":[2,61,143,206],"equations":[3,62,144,207],"in":[4],"dynamical":[5,73],"systems":[6,74,189],"from":[7,100,208],"time-varying":[8],"measurements":[9,104],"is":[10,56,86,120,133,165],"of":[11,40,81,90,162,186,201],"great":[12],"interest":[13],"across":[14],"different":[15],"scientific":[16],"fields.":[17],"This":[18],"task":[19],"becomes":[20],"prohibitive":[21],"when":[22],"such":[23,49],"data":[24,125,164],"is,":[25],"moreover,":[26],"highly":[27,102,211],"corrupted,":[28],"for":[29,137,204],"example,":[30],"due":[31],"to":[32,52,58,96,135,153,176],"recording":[34],"mechanism":[35],"failing":[36],"over":[37],"unknown":[38],"intervals":[39],"time.":[41],"When":[42],"underlying":[44],"system":[45,119],"exhibits":[46],"chaotic":[47,138,188],"behavior,":[48],"as":[50,150],"sensitivity":[51],"initial":[53],"conditions,":[54],"it":[55],"crucial":[57],"recover":[59],"with":[63],"high":[64],"precision.":[65],"In":[66],"this":[67,124],"work,":[68],"we":[69,94,114,170,194],"consider":[70],"continuous":[71],"time":[72],"$\\dot{x}":[75],"=":[76],"f(x)$":[77],"where":[78],"each":[79],"component":[80],"$f:":[82],"\\mathbb{R}^{d}":[83],"\\rightarrow":[84],"\\mathbb{R}^d$":[85],"a":[87,127,159],"multivariate":[88],"polynomial":[89],"maximal":[91],"degree":[92],"$p$;":[93],"aim":[95],"identify":[97],"$f$":[98,145],"exactly":[99,148],"possibly":[101],"corrupted":[103,166,212],"$x(t_1),":[105],"x(t_2),":[106],"\\dots,":[107],"x(t_m)$.":[108],"As":[109],"our":[110],"main":[111],"theoretical":[112],"result,":[113],"show":[115],"that":[116,123],"if":[117,158],"sufficiently":[121],"ergodic":[122],"satisfies":[126],"strong":[128],"central":[129],"limit":[130],"theorem":[131],"(as":[132],"known":[134],"hold":[136],"Lorenz":[139],"systems),":[140],"then":[141],"can":[146],"be":[147],"recovered":[149],"solution":[152],"an":[154],"$\\ell_1$":[155],"minimization":[156,174],"problem---even":[157],"large":[160],"percentage":[161],"by":[167],"outliers.":[168],"Numerically,":[169],"apply":[171],"alternating":[173],"method":[175],"solve":[177],"corresponding":[179],"constrained":[180],"optimization":[181],"problem.":[182],"Through":[183],"several":[184],"examples":[185],"three-dimensional":[187],"and":[190,199,210],"higher-dimensional":[191],"hyperchaotic":[192],"systems,":[193],"illustrate":[195],"power,":[197],"generality,":[198],"efficiency":[200],"algorithm":[203],"recovering":[205],"noisy":[209],"measurement":[213],"data.":[214]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
