{"id":"https://openalex.org/W4410242348","doi":"https://doi.org/10.1038/s43588-025-00804-x","title":"Bi-level identification of governing equations for nonlinear physical systems","display_name":"Bi-level identification of governing equations for nonlinear physical systems","publication_year":2025,"publication_date":"2025-05-09","ids":{"openalex":"https://openalex.org/W4410242348","doi":"https://doi.org/10.1038/s43588-025-00804-x","pmid":"https://pubmed.ncbi.nlm.nih.gov/40346196"},"language":"en","primary_location":{"id":"doi:10.1038/s43588-025-00804-x","is_oa":false,"landing_page_url":"https://doi.org/10.1038/s43588-025-00804-x","pdf_url":null,"source":{"id":"https://openalex.org/S4210228084","display_name":"Nature Computational Science","issn_l":"2662-8457","issn":["2662-8457"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nature Computational Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5100455064","display_name":"Zeyu Li","orcid":"https://orcid.org/0000-0002-2961-5565"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zeyu Li","raw_affiliation_strings":["School of Astronautics, Beihang University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Astronautics, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045660743","display_name":"Huining Yuan","orcid":"https://orcid.org/0000-0003-1275-972X"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huining Yuan","raw_affiliation_strings":["School of Astronautics, Beihang University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Astronautics, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089819466","display_name":"Wang Han","orcid":"https://orcid.org/0000-0003-4901-4668"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang Han","raw_affiliation_strings":["School of Astronautics, Beihang University, Beijing, China. drwanghan@buaa.edu.cn"],"affiliations":[{"raw_affiliation_string":"School of Astronautics, Beihang University, Beijing, China. drwanghan@buaa.edu.cn","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039449317","display_name":"Yimin Hou","orcid":"https://orcid.org/0000-0002-1106-8233"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yimin Hou","raw_affiliation_strings":["School of Astronautics, Beihang University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Astronautics, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043970469","display_name":"Hongjue Li","orcid":"https://orcid.org/0000-0002-0504-2555"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongjue Li","raw_affiliation_strings":["School of Astronautics, Beihang University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Astronautics, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016353967","display_name":"Haidong Ding","orcid":null},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haidong Ding","raw_affiliation_strings":["School of Astronautics, Beihang University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Astronautics, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016853247","display_name":"Zhiguo Jiang","orcid":"https://orcid.org/0000-0001-8786-2540"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhiguo Jiang","raw_affiliation_strings":["School of Astronautics, Beihang University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Astronautics, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030997691","display_name":"Lijun Yang","orcid":"https://orcid.org/0000-0002-4625-4028"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lijun Yang","raw_affiliation_strings":["School of Astronautics, Beihang University, Beijing, China. yanglijun@buaa.edu.cn"],"affiliations":[{"raw_affiliation_string":"School of Astronautics, Beihang University, Beijing, China. yanglijun@buaa.edu.cn","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":8,"corresponding_author_ids":["https://openalex.org/A5100455064"],"corresponding_institution_ids":["https://openalex.org/I82880672"],"apc_list":{"value":9750,"currency":"EUR","value_usd":11690},"apc_paid":null,"fwci":1.4198,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.81256981,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"5","issue":"6","first_page":"456","last_page":"466"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9976000189781189,"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":0.9835000038146973,"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/identification","display_name":"Identification (biology)","score":0.7515166997909546},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7060328722000122},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44211825728416443},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4053701162338257},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4022020101547241},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.22438091039657593}],"concepts":[{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.7515166997909546},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7060328722000122},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44211825728416443},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4053701162338257},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4022020101547241},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.22438091039657593},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","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":2,"locations":[{"id":"doi:10.1038/s43588-025-00804-x","is_oa":false,"landing_page_url":"https://doi.org/10.1038/s43588-025-00804-x","pdf_url":null,"source":{"id":"https://openalex.org/S4210228084","display_name":"Nature Computational Science","issn_l":"2662-8457","issn":["2662-8457"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nature Computational Science","raw_type":"journal-article"},{"id":"pmid:40346196","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/40346196","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nature computational science","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":61,"referenced_works":["https://openalex.org/W1979769287","https://openalex.org/W2014725748","https://openalex.org/W2016735301","https://openalex.org/W2017718765","https://openalex.org/W2024081693","https://openalex.org/W2042775870","https://openalex.org/W2046131409","https://openalex.org/W2053635242","https://openalex.org/W2064675550","https://openalex.org/W2112548197","https://openalex.org/W2123124652","https://openalex.org/W2153671025","https://openalex.org/W2170631832","https://openalex.org/W2239232218","https://openalex.org/W2525748878","https://openalex.org/W2594102100","https://openalex.org/W2739492614","https://openalex.org/W2745110207","https://openalex.org/W2766437506","https://openalex.org/W2774755163","https://openalex.org/W2783380616","https://openalex.org/W2889523591","https://openalex.org/W2899283552","https://openalex.org/W2903660960","https://openalex.org/W2925075625","https://openalex.org/W2963739154","https://openalex.org/W2968873109","https://openalex.org/W2981906852","https://openalex.org/W3000852976","https://openalex.org/W3002919193","https://openalex.org/W3003922491","https://openalex.org/W3006800618","https://openalex.org/W3016401366","https://openalex.org/W3025593802","https://openalex.org/W3028073062","https://openalex.org/W3047141442","https://openalex.org/W3086458503","https://openalex.org/W3104338246","https://openalex.org/W3109497592","https://openalex.org/W3128704025","https://openalex.org/W3129940801","https://openalex.org/W3134241784","https://openalex.org/W3152256596","https://openalex.org/W3161200675","https://openalex.org/W3164124231","https://openalex.org/W3207471124","https://openalex.org/W3211856448","https://openalex.org/W3215447930","https://openalex.org/W4229786028","https://openalex.org/W4234698323","https://openalex.org/W4243066586","https://openalex.org/W4283751222","https://openalex.org/W4290653188","https://openalex.org/W4377862893","https://openalex.org/W4384561839","https://openalex.org/W4392567326","https://openalex.org/W6678625315","https://openalex.org/W6684205842","https://openalex.org/W6770420047","https://openalex.org/W6963923761","https://openalex.org/W6967730307"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-01-13T01:12:25.745995","created_date":"2025-10-10T00:00:00"}
