{"id":"https://openalex.org/W4409426165","doi":"https://doi.org/10.1109/tase.2025.3560450","title":"ICODE: Modeling Dynamical Systems With Extrinsic Input Information","display_name":"ICODE: Modeling Dynamical Systems With Extrinsic Input Information","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4409426165","doi":"https://doi.org/10.1109/tase.2025.3560450"},"language":"en","primary_location":{"id":"doi:10.1109/tase.2025.3560450","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tase.2025.3560450","pdf_url":null,"source":{"id":"https://openalex.org/S34881539","display_name":"IEEE Transactions on Automation Science and Engineering","issn_l":"1545-5955","issn":["1545-5955","1558-3783"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automation Science and Engineering","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":null,"display_name":"Zhaoyi Li","orcid":"https://orcid.org/0009-0000-8279-4577"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhaoyi Li","raw_affiliation_strings":["School of Automation and the Key Laboratory of MCCSE of the Ministry of Education, Southeast University, Nanjing, China"],"raw_orcid":"https://orcid.org/0009-0000-8279-4577","affiliations":[{"raw_affiliation_string":"School of Automation and the Key Laboratory of MCCSE of the Ministry of Education, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055037527","display_name":"Wenjie Mei","orcid":"https://orcid.org/0000-0001-6964-9797"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenjie Mei","raw_affiliation_strings":["School of Automation and the Key Laboratory of MCCSE of the Ministry of Education, Southeast University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0001-6964-9797","affiliations":[{"raw_affiliation_string":"School of Automation and the Key Laboratory of MCCSE of the Ministry of Education, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036442273","display_name":"Ke Yu","orcid":"https://orcid.org/0009-0000-9449-9006"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ke Yu","raw_affiliation_strings":["School of Automation and the Key Laboratory of MCCSE of the Ministry of Education, Southeast University, Nanjing, China"],"raw_orcid":"https://orcid.org/0009-0000-9449-9006","affiliations":[{"raw_affiliation_string":"School of Automation and the Key Laboratory of MCCSE of the Ministry of Education, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045548180","display_name":"Yang Bai","orcid":"https://orcid.org/0000-0003-1080-1939"},"institutions":[{"id":"https://openalex.org/I113306721","display_name":"Hiroshima University","ror":"https://ror.org/03t78wx29","country_code":"JP","type":"education","lineage":["https://openalex.org/I113306721"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yang Bai","raw_affiliation_strings":["Graduate School of Advanced Science and Engineering, Hiroshima University, Higashihiroshima, Japan"],"raw_orcid":"https://orcid.org/0000-0003-1080-1939","affiliations":[{"raw_affiliation_string":"Graduate School of Advanced Science and Engineering, Hiroshima University, Higashihiroshima, Japan","institution_ids":["https://openalex.org/I113306721"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100618284","display_name":"Shihua Li","orcid":"https://orcid.org/0000-0001-9044-7137"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shihua Li","raw_affiliation_strings":["School of Automation and the Key Laboratory of MCCSE of the Ministry of Education, Southeast University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0001-9044-7137","affiliations":[{"raw_affiliation_string":"School of Automation and the Key Laboratory of MCCSE of the Ministry of Education, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2761,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.83362423,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"22","issue":null,"first_page":"14358","last_page":"14370"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.7074000239372253,"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"}},"topics":[{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.7074000239372253,"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/computer-science","display_name":"Computer science","score":0.46563804149627686},{"id":"https://openalex.org/keywords/control-engineering","display_name":"Control engineering","score":0.33534151315689087},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.3232930898666382}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46563804149627686},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.33534151315689087},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.3232930898666382}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tase.2025.3560450","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tase.2025.3560450","pdf_url":null,"source":{"id":"https://openalex.org/S34881539","display_name":"IEEE Transactions on Automation Science and Engineering","issn_l":"1545-5955","issn":["1545-5955","1558-3783"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automation Science and Engineering","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3161381184","display_name":null,"funder_award_id":"BK20241283","funder_id":"https://openalex.org/F4320334982","funder_display_name":"Basic Research Program of Jiangsu Province"},{"id":"https://openalex.org/G4646319520","display_name":null,"funder_award_id":"62403125","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5331813728","display_name":null,"funder_award_id":"2242024k30037","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G5523117722","display_name":null,"funder_award_id":"2242024k30037; 2242024k30038","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G577080679","display_name":null,"funder_award_id":"BK20241283","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G8718091638","display_name":null,"funder_award_id":"2242024k30038","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322769","display_name":"Natural Science Foundation of Jiangsu Province","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334982","display_name":"Basic Research Program of Jiangsu Province","ror":null},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1973452000","https://openalex.org/W2018431869","https://openalex.org/W2027920176","https://openalex.org/W2044719823","https://openalex.org/W2119750039","https://openalex.org/W2134889984","https://openalex.org/W2886834111","https://openalex.org/W2899283552","https://openalex.org/W3094058178","https://openalex.org/W3105175154","https://openalex.org/W3138821690","https://openalex.org/W3140906137","https://openalex.org/W3175557532","https://openalex.org/W3194456427","https://openalex.org/W4246315078","https://openalex.org/W4285159933","https://openalex.org/W4285806933","https://openalex.org/W4308454280","https://openalex.org/W4386453781","https://openalex.org/W4392979569","https://openalex.org/W4395450059","https://openalex.org/W4409426165","https://openalex.org/W6752307458","https://openalex.org/W6760979436","https://openalex.org/W6763340073","https://openalex.org/W6770437322","https://openalex.org/W6774847170","https://openalex.org/W6775127026","https://openalex.org/W6778353478","https://openalex.org/W6800464454","https://openalex.org/W6803640674","https://openalex.org/W6809818660","https://openalex.org/W6847221705","https://openalex.org/W6854061267","https://openalex.org/W6874196754"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052"],"abstract_inverted_index":{"Learning":[0],"models":[1,170],"of":[2,60,90,100,124,167],"dynamical":[3],"systems":[4,174],"with":[5,175,180],"external":[6,177],"inputs,":[7],"which":[8,27,50],"may":[9],"be,":[10],"for":[11,18,30,171],"example,":[12],"nonsmooth":[13],"or":[14],"piecewise,":[15],"is":[16,28,193],"crucial":[17],"studying":[19],"complex":[20],"phenomena":[21],"and":[22,36,133,158,189],"predicting":[23],"future":[24],"state":[25],"evolution,":[26],"essential":[29],"applications":[31,183],"such":[32,186],"as":[33,68,187],"safety":[34],"guarantees":[35],"decision-making.":[37],"In":[38],"this":[39],"work,":[40],"we":[41],"introduce":[42],"<italic":[43],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[44],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">Input":[45],"Concomitant":[46],"Neural":[47],"ODEs":[48],"(ICODEs)</i>,":[49],"incorporate":[51],"precise":[52],"real-time":[53],"input":[54,178],"information":[55],"into":[56],"the":[57,61,66,79,91,147],"learning":[58],"process":[59],"models,":[62],"rather":[63],"than":[64],"treating":[65],"inputs":[67],"hidden":[69],"parameters":[70],"to":[71,77,85,95],"be":[72],"learned.":[73],"The":[74,137],"sufficient":[75],"conditions":[76,102],"ensure":[78],"model\u2019s":[80],"contraction":[81],"property":[82],"are":[83],"provided":[84],"guarantee":[86],"that":[87,141],"system":[88],"trajectories":[89],"trained":[92],"model":[93],"converge":[94],"a":[96,125,164],"fixed":[97],"point,":[98],"regardless":[99],"initial":[101],"across":[103],"different":[104],"training":[105],"processes.":[106],"We":[107],"validate":[108],"our":[109,142],"method":[110],"through":[111],"experiments":[112],"on":[113],"several":[114],"representative":[115],"real":[116],"dynamics:":[117],"Single-link":[118],"robot,":[119],"DC-to-DC":[120],"converter,":[121],"motion":[122],"dynamics":[123],"rigid":[126],"body,":[127],"Rabinovich-Fabrikant":[128],"equation,":[129],"Glycolytic-glycogenolytic":[130],"pathway":[131],"model,":[132],"heat":[134],"conduction":[135],"equation.":[136],"experimental":[138],"results":[139],"demonstrate":[140],"proposed":[143],"ICODEs":[144],"efficiently":[145],"learn":[146],"ground":[148],"truth":[149],"systems,":[150],"achieving":[151],"superior":[152],"prediction":[153],"performance":[154],"under":[155],"both":[156],"typical":[157],"atypical":[159],"inputs.":[160],"This":[161],"work":[162],"offers":[163],"valuable":[165],"class":[166],"neural":[168],"ODE":[169],"understanding":[172],"physical":[173],"explicit":[176],"information,":[179],"potentially":[181],"promising":[182],"in":[184],"fields":[185],"physics":[188],"robotics.":[190],"Our":[191],"code":[192],"available":[194],"online":[195],"at":[196],"https://github.com/EEE-ai59/ICODE.git.":[197]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-07-21T08:15:58.654021","created_date":"2025-10-10T00:00:00"}