{"id":"https://openalex.org/W3093161520","doi":"https://doi.org/10.1137/18m1194730","title":"Extracting Structured Dynamical Systems Using Sparse Optimization With Very Few Samples","display_name":"Extracting Structured Dynamical Systems Using Sparse Optimization With Very Few Samples","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3093161520","doi":"https://doi.org/10.1137/18m1194730","mag":"3093161520"},"language":"en","primary_location":{"id":"doi:10.1137/18m1194730","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1194730","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":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086926394","display_name":"Hayden Schaeffer","orcid":"https://orcid.org/0000-0003-1379-1238"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hayden Schaeffer","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","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":"middle","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":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5102011577","display_name":"Linan Zhang","orcid":"https://orcid.org/0000-0001-6217-8806"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Linan Zhang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.606,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.93416388,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"18","issue":"4","first_page":"1435","last_page":"1461"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9994000196456909,"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":0.9994000196456909,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9879000186920166,"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"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9866999983787537,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.569414496421814},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.533876895904541},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5225276947021484},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5056107044219971},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.42669156193733215},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40174394845962524},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37812715768814087}],"concepts":[{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.569414496421814},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.533876895904541},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5225276947021484},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5056107044219971},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42669156193733215},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40174394845962524},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37812715768814087},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"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:10.1137/18m1194730","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1194730","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1238848045","display_name":null,"funder_award_id":"FA9550-17-1-0125","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G2801639669","display_name":null,"funder_award_id":"1752116","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3825437517","display_name":null,"funder_award_id":"RGPIN-2018-0613","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G6841656774","display_name":null,"funder_award_id":"N00014-17-S-F006","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"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/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"},{"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":36,"referenced_works":["https://openalex.org/W649382544","https://openalex.org/W1969957603","https://openalex.org/W1979769287","https://openalex.org/W1988202149","https://openalex.org/W2019226467","https://openalex.org/W2019569173","https://openalex.org/W2067746767","https://openalex.org/W2093346147","https://openalex.org/W2093828424","https://openalex.org/W2135046866","https://openalex.org/W2136235822","https://openalex.org/W2137198385","https://openalex.org/W2141454789","https://openalex.org/W2154332973","https://openalex.org/W2239232218","https://openalex.org/W2357566992","https://openalex.org/W2525748878","https://openalex.org/W2556930732","https://openalex.org/W2565830380","https://openalex.org/W2588198210","https://openalex.org/W2605147767","https://openalex.org/W2740145400","https://openalex.org/W2745110207","https://openalex.org/W2774755163","https://openalex.org/W2791651676","https://openalex.org/W2962957385","https://openalex.org/W2963862882","https://openalex.org/W2964078472","https://openalex.org/W2964145209","https://openalex.org/W2964216518","https://openalex.org/W2964258664","https://openalex.org/W2964265215","https://openalex.org/W3071135787","https://openalex.org/W3083245826","https://openalex.org/W3104338246","https://openalex.org/W3105090572"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W2989452537","https://openalex.org/W2052122378","https://openalex.org/W2544423928","https://openalex.org/W2062023542"],"abstract_inverted_index":{"Learning":[0],"governing":[1],"equations":[2],"allows":[3],"for":[4,20,55,79],"deeper":[5],"understanding":[6],"of":[7,12,38,47,68,75,109,126],"the":[8,36,65,69,73,76,80,91,95,100,120,124],"structure":[9],"and":[10,27,72,99,111,123],"dynamics":[11],"data.":[13],"We":[14],"present":[15],"a":[16,39,44,52],"random":[17,58],"sampling":[18],"method":[19],"learning":[21,33],"structured":[22],"dynamical":[23],"systems":[24],"from":[25],"undersampled":[26],"possibly":[28],"noisy":[29],"state-space":[30],"measurements.":[31],"The":[32],"problem":[34],"takes":[35],"form":[37],"sparse":[40,70],"least-squares":[41],"fitting":[42],"over":[43],"large":[45],"set":[46],"candidate":[48,77,127],"functions.":[49,128],"Based":[50],"on":[51,64,87],"Bernstein-like":[53],"inequality":[54],"partly":[56],"dependent":[57],"variables,":[59],"we":[60],"provide":[61],"theoretical":[62,107],"guarantees":[63,108],"recovery":[66],"rate":[67],"coefficients":[71],"identification":[74],"functions":[78],"corresponding":[81],"problem.":[82],"Computational":[83],"results":[84],"are":[85],"demonstrated":[86],"datasets":[88],"generated":[89],"by":[90],"Lorenz":[92],"96":[93],"equation,":[94,98],"viscous":[96],"Burgers'":[97],"two-component":[101],"reaction-diffusion":[102],"equations.":[103],"Our":[104],"formulation":[105],"includes":[106],"success":[110],"is":[112],"shown":[113],"to":[114,119],"be":[115],"efficient":[116],"with":[117],"respect":[118],"ambient":[121],"dimension":[122],"number":[125]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
