{"id":"https://openalex.org/W3087723685","doi":"https://doi.org/10.1088/2632-2153/ac567a","title":"Automatic differentiation to simultaneously identify nonlinear dynamics and extract noise probability distributions from data","display_name":"Automatic differentiation to simultaneously identify nonlinear dynamics and extract noise probability distributions from data","publication_year":2022,"publication_date":"2022-02-17","ids":{"openalex":"https://openalex.org/W3087723685","doi":"https://doi.org/10.1088/2632-2153/ac567a","mag":"3087723685"},"language":"en","primary_location":{"id":"doi:10.1088/2632-2153/ac567a","is_oa":true,"landing_page_url":"https://doi.org/10.1088/2632-2153/ac567a","pdf_url":null,"source":{"id":"https://openalex.org/S4210200687","display_name":"Machine Learning Science and Technology","issn_l":"2632-2153","issn":["2632-2153"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning: Science and Technology","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1088/2632-2153/ac567a","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017403086","display_name":"Kadierdan Kaheman","orcid":"https://orcid.org/0000-0003-2279-2793"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Kadierdan Kaheman","raw_affiliation_strings":["Department of Mechanical Engineering, University of Washington, Seattle, WA 98195, United States of America"],"raw_orcid":"https://orcid.org/0000-0003-2279-2793","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of Washington, Seattle, WA 98195, United States of America","institution_ids":["https://openalex.org/I201448701"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062653961","display_name":"Steven L. Brunton","orcid":null},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Steven L Brunton","raw_affiliation_strings":["Department of Mechanical Engineering, University of Washington, Seattle, WA 98195, United States of America"],"raw_orcid":"https://orcid.org/0000-0002-6565-5118","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of Washington, Seattle, WA 98195, United States of America","institution_ids":["https://openalex.org/I201448701"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083450863","display_name":"J. Nathan Kutz","orcid":"https://orcid.org/0000-0002-6004-2275"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J Nathan Kutz","raw_affiliation_strings":["Department of Applied Mathematics, University of Washington, Seattle, WA 98195, United States of America"],"raw_orcid":"https://orcid.org/0000-0002-6004-2275","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Washington, Seattle, WA 98195, United States of America","institution_ids":["https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5017403086"],"corresponding_institution_ids":["https://openalex.org/I201448701"],"apc_list":{"value":1600,"currency":"GBP","value_usd":1962},"apc_paid":{"value":1600,"currency":"GBP","value_usd":1962},"fwci":8.5121,"has_fulltext":false,"cited_by_count":78,"citation_normalized_percentile":{"value":0.98587847,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"3","issue":"1","first_page":"015031","last_page":"015031"},"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":0.978600025177002,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.974399983882904,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5702932476997375},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.5521470904350281},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5208866596221924},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.49250850081443787},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.4915963113307953},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4678177535533905},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.4567800760269165},{"id":"https://openalex.org/keywords/gaussian-noise","display_name":"Gaussian noise","score":0.43538427352905273},{"id":"https://openalex.org/keywords/time-series","display_name":"Time series","score":0.43256333470344543},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35982558131217957},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.33963102102279663},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.30867600440979004},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.17705589532852173}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5702932476997375},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.5521470904350281},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5208866596221924},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.49250850081443787},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.4915963113307953},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4678177535533905},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.4567800760269165},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.43538427352905273},{"id":"https://openalex.org/C151406439","wikidata":"https://www.wikidata.org/wiki/Q186588","display_name":"Time series","level":2,"score":0.43256333470344543},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35982558131217957},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.33963102102279663},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.30867600440979004},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.17705589532852173},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1088/2632-2153/ac567a","is_oa":true,"landing_page_url":"https://doi.org/10.1088/2632-2153/ac567a","pdf_url":null,"source":{"id":"https://openalex.org/S4210200687","display_name":"Machine Learning Science and Technology","issn_l":"2632-2153","issn":["2632-2153"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning: Science and Technology","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1088/2632-2153/ac567a","is_oa":true,"landing_page_url":"https://doi.org/10.1088/2632-2153/ac567a","pdf_url":null,"source":{"id":"https://openalex.org/S4210200687","display_name":"Machine Learning Science and Technology","issn_l":"2632-2153","issn":["2632-2153"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning: Science and Technology","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6526921895","display_name":null,"funder_award_id":"FA9550-17-1-0329","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":134,"referenced_works":["https://openalex.org/W570566252","https://openalex.org/W616193750","https://openalex.org/W1490488263","https://openalex.org/W1522301498","https://openalex.org/W1591018827","https://openalex.org/W1979769287","https://openalex.org/W2014356541","https://openalex.org/W2048951385","https://openalex.org/W2069338608","https://openalex.org/W2070681743","https://openalex.org/W2080991705","https://openalex.org/W2093828424","https://openalex.org/W2099272284","https://openalex.org/W2126999002","https://openalex.org/W2135046866","https://openalex.org/W2239232218","https://openalex.org/W2262368014","https://openalex.org/W2402144811","https://openalex.org/W2525748878","https://openalex.org/W2556930732","https://openalex.org/W2565830380","https://openalex.org/W2573798107","https://openalex.org/W2573864470","https://openalex.org/W2578607490","https://openalex.org/W2582771730","https://openalex.org/W2588198210","https://openalex.org/W2615252773","https://openalex.org/W2619381903","https://openalex.org/W2626693943","https://openalex.org/W2740145400","https://openalex.org/W2745110207","https://openalex.org/W2745846861","https://openalex.org/W2765372792","https://openalex.org/W2765861397","https://openalex.org/W2768748954","https://openalex.org/W2774755163","https://openalex.org/W2782714865","https://openalex.org/W2783288880","https://openalex.org/W2788403524","https://openalex.org/W2801128564","https://openalex.org/W2803477776","https://openalex.org/W2887383111","https://openalex.org/W2887661471","https://openalex.org/W2888178833","https://openalex.org/W2889716319","https://openalex.org/W2890411254","https://openalex.org/W2892208363","https://openalex.org/W2892393161","https://openalex.org/W2899283552","https://openalex.org/W2899580663","https://openalex.org/W2905262640","https://openalex.org/W2915622878","https://openalex.org/W2926251402","https://openalex.org/W2937653888","https://openalex.org/W2950593994","https://openalex.org/W2951191580","https://openalex.org/W2953384591","https://openalex.org/W2957969499","https://openalex.org/W2957989108","https://openalex.org/W2962727772","https://openalex.org/W2962957385","https://openalex.org/W2963113802","https://openalex.org/W2963210541","https://openalex.org/W2963739154","https://openalex.org/W2963755523","https://openalex.org/W2963787255","https://openalex.org/W2964078472","https://openalex.org/W2964079102","https://openalex.org/W2964145209","https://openalex.org/W2964265215","https://openalex.org/W2968695582","https://openalex.org/W2974301768","https://openalex.org/W2979458970","https://openalex.org/W2981906852","https://openalex.org/W2990568657","https://openalex.org/W2995408993","https://openalex.org/W2998790058","https://openalex.org/W2999026783","https://openalex.org/W3000852976","https://openalex.org/W3003922491","https://openalex.org/W3004450693","https://openalex.org/W3007399285","https://openalex.org/W3008321886","https://openalex.org/W3013803313","https://openalex.org/W3014009018","https://openalex.org/W3014869516","https://openalex.org/W3015146375","https://openalex.org/W3016325997","https://openalex.org/W3022136544","https://openalex.org/W3023027900","https://openalex.org/W3028073062","https://openalex.org/W3038118776","https://openalex.org/W3040454512","https://openalex.org/W3086458503","https://openalex.org/W3092527036","https://openalex.org/W3097405506","https://openalex.org/W3097427246","https://openalex.org/W3098734061","https://openalex.org/W3099205493","https://openalex.org/W3099423575","https://openalex.org/W3099674394","https://openalex.org/W3100641539","https://openalex.org/W3100769368","https://openalex.org/W3101607551","https://openalex.org/W3102299373","https://openalex.org/W3102548437","https://openalex.org/W3102913089","https://openalex.org/W3103516574","https://openalex.org/W3103987666","https://openalex.org/W3104338246","https://openalex.org/W3105370818","https://openalex.org/W3105691042","https://openalex.org/W3105919389","https://openalex.org/W3135480294","https://openalex.org/W3197500030","https://openalex.org/W3209274290","https://openalex.org/W4242688646","https://openalex.org/W4246840991","https://openalex.org/W4288104405","https://openalex.org/W4289363680","https://openalex.org/W6631190155","https://openalex.org/W6713134421","https://openalex.org/W6752307458","https://openalex.org/W6756449232","https://openalex.org/W6761542930","https://openalex.org/W6765231711","https://openalex.org/W6765482747","https://openalex.org/W6765578223","https://openalex.org/W6768298283","https://openalex.org/W6774354782","https://openalex.org/W6775154854","https://openalex.org/W6776952489","https://openalex.org/W6780033582","https://openalex.org/W6803767066"],"related_works":["https://openalex.org/W2770593030","https://openalex.org/W3154990682","https://openalex.org/W1919101720","https://openalex.org/W2560201613","https://openalex.org/W2171975302","https://openalex.org/W2022352247","https://openalex.org/W2119012848","https://openalex.org/W2622688551","https://openalex.org/W1550175370","https://openalex.org/W1990205660"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"sparse":[2],"identification":[3,29],"of":[4,15,38,50,172],"nonlinear":[5],"dynamics":[6],"(SINDy)":[7],"is":[8,118],"a":[9,48,135,170],"regression":[10],"framework":[11],"for":[12,73,96,175],"the":[13,34,39,51,77,83,90,98,142,158,166,176],"discovery":[14,41],"parsimonious":[16,92],"dynamic":[17],"models":[18,156],"and":[19,36,58,81,87,139,183],"governing":[20],"equations":[21],"from":[22,111,154],"time-series":[23,99,137],"data.":[24,100],"As":[25],"with":[26],"all":[27],"system":[28,94],"methods,":[30,127],"noisy":[31],"measurements":[32],"compromise":[33],"accuracy":[35],"robustness":[37],"model":[40],"procedure.":[42],"In":[43],"this":[44,148],"work":[45],"we":[46,164],"develop":[47],"variant":[49],"SINDy":[52],"algorithm":[53],"that":[54,117],"integrates":[55],"automatic":[56],"differentiation":[57],"recent":[59],"time-stepping":[60],"constrained":[61],"motivated":[62],"by":[63],"Rudy":[64],"et":[65],"al":[66],"(2019":[67],"J.":[68],"Computat.":[69],"Phys.":[70],"396":[71],"483\u2013506)":[72],"simultaneously":[74],"(1)":[75],"denoising":[76],"data,":[78],"(2)":[79],"learning":[80],"parametrizing":[82,141],"noise":[84,107,124,133,143],"probability":[85,144,173],"distribution,":[86],"(3)":[88],"identifying":[89],"underlying":[91],"dynamical":[93],"responsible":[95],"generating":[97],"Thus":[101],"within":[102],"an":[103,115],"integrated":[104],"optimization":[105],"framework,":[106],"can":[108,168],"be":[109],"separated":[110],"signal,":[112],"resulting":[113],"in":[114],"architecture":[116],"approximately":[119],"twice":[120],"as":[121,125,129,131],"robust":[122],"to":[123,157],"state-of-the-art":[126],"handling":[128],"much":[130],"40%":[132],"on":[134,150],"given":[136],"signal":[138],"explicitly":[140],"distribution.":[145],"We":[146],"demonstrate":[147],"approach":[149],"several":[151],"numerical":[152],"examples,":[153],"Lotka-Volterra":[155],"spatio-temporal":[159],"Lorenz":[160],"96":[161],"model.":[162],"Further,":[163],"show":[165],"method":[167],"learn":[169],"diversity":[171],"distributions":[174],"measurement":[177],"noise,":[178],"including":[179],"Gaussian,":[180],"uniform,":[181],"Gamma,":[182],"Rayleigh":[184],"distributions.":[185]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":21},{"year":2024,"cited_by_count":21},{"year":2023,"cited_by_count":19},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}