{"id":"https://openalex.org/W7127282968","doi":"https://doi.org/10.1137/24m1679690","title":"Universal Approximation of Dynamical Systems by Semiautonomous Neural ODEs and Applications","display_name":"Universal Approximation of Dynamical Systems by Semiautonomous Neural ODEs and Applications","publication_year":2026,"publication_date":"2026-02-03","ids":{"openalex":"https://openalex.org/W7127282968","doi":"https://doi.org/10.1137/24m1679690"},"language":"en","primary_location":{"id":"doi:10.1137/24m1679690","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1679690","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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":"SIAM Journal on Numerical Analysis","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/A5102008736","display_name":"Ziqian Li","orcid":"https://orcid.org/0000-0002-0306-6844"},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]},{"id":"https://openalex.org/I194450716","display_name":"Jilin University","ror":"https://ror.org/00js3aw79","country_code":"CN","type":"education","lineage":["https://openalex.org/I194450716"]}],"countries":["CN","DE"],"is_corresponding":true,"raw_author_name":"Ziqian Li","raw_affiliation_strings":["Department of Mathematics, Friedrich\u2013Alexander-Universit\u00e4t Erlangen\u2013N\u00fcrnberg, 91058 Erlangen, Germany","School of Mathematics, Jilin University, Changchun 130012, People\u2019s Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Friedrich\u2013Alexander-Universit\u00e4t Erlangen\u2013N\u00fcrnberg, 91058 Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]},{"raw_affiliation_string":"School of Mathematics, Jilin University, Changchun 130012, People\u2019s Republic of China","institution_ids":["https://openalex.org/I194450716"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100389879","display_name":"Kang Liu","orcid":"https://orcid.org/0000-0001-7231-8315"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210112333","display_name":"Institut de Math\u00e9matiques de Bourgogne","ror":"https://ror.org/021f0sa24","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4210112333","https://openalex.org/I4405253280"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Kang Liu","raw_affiliation_strings":["Institut de Math\u00e9matiques de Bourgogne, Universit\u00e9 Bourgogne Europe, CNRS, 21000 Dijon, France"],"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques de Bourgogne, Universit\u00e9 Bourgogne Europe, CNRS, 21000 Dijon, France","institution_ids":["https://openalex.org/I4210112333","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005336774","display_name":"Lorenzo Liverani","orcid":"https://orcid.org/0000-0003-2538-8868"},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Lorenzo Liverani","raw_affiliation_strings":["Department of Mathematics, Friedrich\u2013Alexander-Universit\u00e4t Erlangen\u2013N\u00fcrnberg, 91058 Erlangen, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Friedrich\u2013Alexander-Universit\u00e4t Erlangen\u2013N\u00fcrnberg, 91058 Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5106674625","display_name":"Enrique Zuazua","orcid":null},"institutions":[{"id":"https://openalex.org/I136040515","display_name":"Universidad de Deusto","ror":"https://ror.org/00ne6sr39","country_code":"ES","type":"education","lineage":["https://openalex.org/I136040515"]},{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]},{"id":"https://openalex.org/I63634437","display_name":"Universidad Aut\u00f3noma de Madrid","ror":"https://ror.org/01cby8j38","country_code":"ES","type":"education","lineage":["https://openalex.org/I63634437"]}],"countries":["DE","ES"],"is_corresponding":false,"raw_author_name":"Enrique Zuazua","raw_affiliation_strings":["Chair of Computational Mathematics, Fundaci\u00f3n Deusto. Av. de las Universidades, 24, 48007 Bilbao, Basque Country, Spain","Departamento de Matem\u00e1ticas, Universidad Aut\u00f3noma de Madrid, 28049 Madrid, Spain","Department of Mathematics, Friedrich\u2013Alexander-Universit\u00e4t Erlangen\u2013N\u00fcrnberg, 91058 Erlangen, Germany"],"affiliations":[{"raw_affiliation_string":"Chair of Computational Mathematics, Fundaci\u00f3n Deusto. Av. de las Universidades, 24, 48007 Bilbao, Basque Country, Spain","institution_ids":["https://openalex.org/I136040515"]},{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad Aut\u00f3noma de Madrid, 28049 Madrid, Spain","institution_ids":["https://openalex.org/I63634437"]},{"raw_affiliation_string":"Department of Mathematics, Friedrich\u2013Alexander-Universit\u00e4t Erlangen\u2013N\u00fcrnberg, 91058 Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5102008736"],"corresponding_institution_ids":["https://openalex.org/I181369854","https://openalex.org/I194450716"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.33696766,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"64","issue":"1","first_page":"193","last_page":"223"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.4154999852180481,"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":0.4154999852180481,"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/T10320","display_name":"Neural Networks and Applications","score":0.1914999932050705,"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/T11416","display_name":"Numerical methods for differential equations","score":0.04690000042319298,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6620000004768372},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.647599995136261},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.4219000041484833},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.36079999804496765},{"id":"https://openalex.org/keywords/linear-dynamical-system","display_name":"Linear dynamical system","score":0.3598000109195709},{"id":"https://openalex.org/keywords/nonlinear-dynamical-systems","display_name":"Nonlinear dynamical systems","score":0.3517000079154968},{"id":"https://openalex.org/keywords/projected-dynamical-system","display_name":"Projected dynamical system","score":0.34060001373291016}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7233999967575073},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6620000004768372},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.647599995136261},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5141000151634216},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.4219000041484833},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.36079999804496765},{"id":"https://openalex.org/C114275822","wikidata":"https://www.wikidata.org/wiki/Q621512","display_name":"Linear dynamical system","level":3,"score":0.3598000109195709},{"id":"https://openalex.org/C2983030100","wikidata":"https://www.wikidata.org/wiki/Q638328","display_name":"Nonlinear dynamical systems","level":3,"score":0.3517000079154968},{"id":"https://openalex.org/C93812963","wikidata":"https://www.wikidata.org/wiki/Q7249433","display_name":"Projected dynamical system","level":5,"score":0.34060001373291016},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.336899995803833},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.311599999666214},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.3001999855041504},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.29510000348091125},{"id":"https://openalex.org/C2986878899","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical approximation","level":3,"score":0.2827000021934509},{"id":"https://openalex.org/C193817511","wikidata":"https://www.wikidata.org/wiki/Q7291964","display_name":"Random dynamical system","level":4,"score":0.2799000144004822},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.2614000141620636},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.2599000036716461},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.25060001015663147}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/24m1679690","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1679690","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1547431580","https://openalex.org/W1988115241","https://openalex.org/W2015327391","https://openalex.org/W2049332145","https://openalex.org/W2102955267","https://openalex.org/W2103496339","https://openalex.org/W2158581396","https://openalex.org/W2166116275","https://openalex.org/W2194775991","https://openalex.org/W2600297185","https://openalex.org/W2803636134","https://openalex.org/W2899283552","https://openalex.org/W2963003308","https://openalex.org/W2978409183","https://openalex.org/W3006049408","https://openalex.org/W3125537303","https://openalex.org/W3155438876","https://openalex.org/W3165099133","https://openalex.org/W3193494219","https://openalex.org/W3194828218","https://openalex.org/W3207108121","https://openalex.org/W4205634890","https://openalex.org/W4239539940","https://openalex.org/W4248262852","https://openalex.org/W4281870568","https://openalex.org/W4285291683","https://openalex.org/W4308906282","https://openalex.org/W4313397686","https://openalex.org/W4385658405","https://openalex.org/W4388311457","https://openalex.org/W4388460381","https://openalex.org/W4388928889","https://openalex.org/W4389610088","https://openalex.org/W4392607756","https://openalex.org/W4401689654","https://openalex.org/W4408074280","https://openalex.org/W4409524051","https://openalex.org/W4410354534"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2026-02-04T00:00:00"}