{"id":"https://openalex.org/W4414456995","doi":"https://doi.org/10.48550/arxiv.2507.04868","title":"A Novel Approach for Estimating Largest Lyapunov Exponents in One-Dimensional Chaotic Time Series Using Machine Learning","display_name":"A Novel Approach for Estimating Largest Lyapunov Exponents in One-Dimensional Chaotic Time Series Using Machine Learning","publication_year":2025,"publication_date":"2025-07-07","ids":{"openalex":"https://openalex.org/W4414456995","doi":"https://doi.org/10.48550/arxiv.2507.04868"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2507.04868","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.04868","pdf_url":"https://arxiv.org/pdf/2507.04868","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":"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/2507.04868","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010613967","display_name":"Andrei Velichko","orcid":"https://orcid.org/0000-0002-9341-1831"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Velichko, A.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015748731","display_name":"Maksim Belyaev","orcid":"https://orcid.org/0000-0002-1771-6502"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Belyaev, M.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5009975277","display_name":"\u041f. \u041f. \u0411\u043e\u0440\u0438\u0441\u043a\u043e\u0432","orcid":"https://orcid.org/0000-0002-2904-9612"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Boriskov, P.","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/T10244","display_name":"Chaos control and synchronization","score":0.980400025844574,"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/T10244","display_name":"Chaos control and synchronization","score":0.980400025844574,"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/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9516000151634216,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9483000040054321,"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/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.7311000227928162},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6504999995231628},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.6230999827384949},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.5442000031471252},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.4916999936103821},{"id":"https://openalex.org/keywords/time-series","display_name":"Time series","score":0.4618000090122223},{"id":"https://openalex.org/keywords/white-noise","display_name":"White noise","score":0.4551999866962433},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.4041000008583069},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.3700000047683716}],"concepts":[{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.7311000227928162},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6504999995231628},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6230999827384949},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5536999702453613},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5442000031471252},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.498199999332428},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.4916999936103821},{"id":"https://openalex.org/C151406439","wikidata":"https://www.wikidata.org/wiki/Q186588","display_name":"Time series","level":2,"score":0.4618000090122223},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.4551999866962433},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4090000092983246},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4041000008583069},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3781000077724457},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.3700000047683716},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.3653999865055084},{"id":"https://openalex.org/C2987469083","wikidata":"https://www.wikidata.org/wiki/Q166314","display_name":"Chaotic systems","level":3,"score":0.35040000081062317},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35030001401901245},{"id":"https://openalex.org/C2781170535","wikidata":"https://www.wikidata.org/wiki/Q30587856","display_name":"Noisy data","level":2,"score":0.33239999413490295},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3301999866962433},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.32600000500679016},{"id":"https://openalex.org/C24552861","wikidata":"https://www.wikidata.org/wiki/Q2670177","display_name":"Data assimilation","level":2,"score":0.3237000107765198},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.31679999828338623},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.31209999322891235},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.2964000105857849},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.2897999882698059},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.28780001401901245},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.28130000829696655},{"id":"https://openalex.org/C2780148112","wikidata":"https://www.wikidata.org/wiki/Q1432581","display_name":"Proxy (statistics)","level":2,"score":0.26980000734329224},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.2655999958515167},{"id":"https://openalex.org/C167085575","wikidata":"https://www.wikidata.org/wiki/Q6803654","display_name":"Mean squared prediction error","level":2,"score":0.26089999079704285},{"id":"https://openalex.org/C21080849","wikidata":"https://www.wikidata.org/wiki/Q13611879","display_name":"Data point","level":2,"score":0.25519999861717224}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2507.04868","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.04868","pdf_url":"https://arxiv.org/pdf/2507.04868","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2507.04868","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2507.04868","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":"pmh:oai:arXiv.org:2507.04868","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.04868","pdf_url":"https://arxiv.org/pdf/2507.04868","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Understanding":[0],"and":[1,75,130,147,162,167,197],"quantifying":[2],"chaos":[3],"from":[4,20,42,118],"data":[5,200],"remains":[6],"challenging.":[7],"We":[8,64],"present":[9],"a":[10,59,152,171,177],"data-driven":[11],"method":[12,157],"for":[13,61,142,202],"estimating":[14],"the":[15,37,43,47,54,66,96,106,134,168],"largest":[16],"Lyapunov":[17],"exponent":[18],"(LLE)":[19],"one-dimensional":[21],"chaotic":[22],"time":[23],"series":[24,85],"using":[25],"machine":[26],"learning.":[27],"A":[28],"predictor":[29],"is":[30,39,122,158],"trained":[31],"to":[32,180,195],"produce":[33],"out-of-sample,":[34],"multi-horizon":[35],"forecasts;":[36],"LLE":[38,82,181],"then":[40],"inferred":[41],"exponential":[44],"growth":[45],"of":[46,170],"geometrically":[48],"averaged":[49],"forecast":[50],"error":[51],"(GMAE)":[52],"across":[53],"horizon,":[55],"which":[56],"serves":[57],"as":[58,86,88],"proxy":[60],"trajectory":[62],"divergence.":[63],"validate":[65],"approach":[67],"on":[68],"four":[69],"canonical":[70],"1D":[71],"maps-logistic,":[72],"sine,":[73],"cubic,":[74],"Chebyshev-achieving":[76],"R2pos":[77],"&gt;":[78,144],"0.99":[79],"against":[80],"reference":[81],"curves":[83],"with":[84,193],"short":[87],"M":[89],"=":[90],"450.":[91],"Among":[92],"baselines,":[93],"KNN":[94],"yields":[95],"closest":[97],"fits":[98],"(KNN-R":[99],"comparable;":[100],"RF":[101],"larger":[102],"deviations).":[103],"By":[104],"design":[105],"estimator":[107],"targets":[108],"positive":[109,173],"exponents:":[110],"in":[111,183],"periodic/stable":[112],"regimes":[113],"it":[114],"returns":[115],"values":[116],"indistinguishable":[117],"zero.":[119],"Noise":[120],"robustness":[121],"assessed":[123],"by":[124],"adding":[125],"zero-mean":[126],"white":[127],"measurement":[128],"noise":[129],"summarizing":[131],"performance":[132],"versus":[133],"average":[135],"SNR":[136],"over":[137],"parameter":[138],"sweeps:":[139],"accuracy":[140],"saturates":[141],"SNRm":[143],"30":[145],"dB":[146],"collapses":[148],"below":[149],"27":[150],"dB,":[151],"conservative":[153],"sensor-level":[154],"benchmark.":[155],"The":[156],"simple,":[159],"computationally":[160],"efficient,":[161],"model-agnostic,":[163],"requiring":[164],"only":[165,187],"stationarity":[166],"presence":[169],"dominant":[172],"exponent.":[174],"It":[175],"offers":[176],"practical":[178],"route":[179],"estimation":[182],"experimental":[184],"settings":[185],"where":[186],"scalar":[188],"time-series":[189],"measurements":[190],"are":[191],"available,":[192],"extensions":[194],"higher-dimensional":[196],"irregularly":[198],"sampled":[199],"left":[201],"future":[203],"work.":[204]},"counts_by_year":[],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}
