{"id":"https://openalex.org/W7118193116","doi":"https://doi.org/10.1016/j.jfranklin.2025.108396","title":"Design and analysis of a predefined-time zeroing neural network model for solving the Stein tensor equation","display_name":"Design and analysis of a predefined-time zeroing neural network model for solving the Stein tensor equation","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7118193116","doi":"https://doi.org/10.1016/j.jfranklin.2025.108396"},"language":"en","primary_location":{"id":"doi:10.1016/j.jfranklin.2025.108396","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.jfranklin.2025.108396","pdf_url":null,"source":{"id":"https://openalex.org/S183498172","display_name":"Journal of the Franklin Institute","issn_l":"0016-0032","issn":["0016-0032","1879-2693"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the Franklin Institute","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/A5062829411","display_name":"Shu-Xin Miao","orcid":"https://orcid.org/0000-0002-0905-7770"},"institutions":[{"id":"https://openalex.org/I68986083","display_name":"Northwest Normal University","ror":"https://ror.org/00gx3j908","country_code":"CN","type":"education","lineage":["https://openalex.org/I68986083"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shu-Xin Miao","raw_affiliation_strings":["organization=College of Mathematics and Statistics, Northwest Normal University, addressline=Lanzhou, postcode=730070, country=P.R. China","organization=College of Mathematics and Statistics, Northwest Normal University, addressline=Lanzhou, postcode=730070, country=PR China"],"raw_orcid":"https://orcid.org/0000-0002-0905-7770","affiliations":[{"raw_affiliation_string":"organization=College of Mathematics and Statistics, Northwest Normal University, addressline=Lanzhou, postcode=730070, country=P.R. China","institution_ids":["https://openalex.org/I68986083"]},{"raw_affiliation_string":"organization=College of Mathematics and Statistics, Northwest Normal University, addressline=Lanzhou, postcode=730070, country=PR China","institution_ids":["https://openalex.org/I68986083"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067442518","display_name":"Tomohiro Sogabe","orcid":"https://orcid.org/0000-0001-6803-0407"},"institutions":[{"id":"https://openalex.org/I60134161","display_name":"Nagoya University","ror":"https://ror.org/04chrp450","country_code":"JP","type":"education","lineage":["https://openalex.org/I60134161"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Tomohiro Sogabe","raw_affiliation_strings":["organization=Department of Applied Physics, Graduate School of Engineering, Nagoya University, addressline=Furo-cho Chikusa-ku, postcode=464-8603, city=Nagoya Aichi, country=Japan","organization=Department of Applied Physics, Graduate School of Engineering, Nagoya University, addressline=Furo-cho Chikusa-ku, postcode=464\u20138603, city=Nagoya Aichi, country=Japan"],"raw_orcid":"https://orcid.org/0000-0001-6803-0407","affiliations":[{"raw_affiliation_string":"organization=Department of Applied Physics, Graduate School of Engineering, Nagoya University, addressline=Furo-cho Chikusa-ku, postcode=464-8603, city=Nagoya Aichi, country=Japan","institution_ids":["https://openalex.org/I60134161"]},{"raw_affiliation_string":"organization=Department of Applied Physics, Graduate School of Engineering, Nagoya University, addressline=Furo-cho Chikusa-ku, postcode=464\u20138603, city=Nagoya Aichi, country=Japan","institution_ids":["https://openalex.org/I60134161"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5121929910","display_name":"Shao-Liang Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I60134161","display_name":"Nagoya University","ror":"https://ror.org/04chrp450","country_code":"JP","type":"education","lineage":["https://openalex.org/I60134161"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Shao-Liang Zhang","raw_affiliation_strings":["organization=Department of Applied Physics, Graduate School of Engineering, Nagoya University, addressline=Furo-cho Chikusa-ku, postcode=464-8603, city=Nagoya Aichi, country=Japan","organization=Department of Applied Physics, Graduate School of Engineering, Nagoya University, addressline=Furo-cho Chikusa-ku, postcode=464\u20138603, city=Nagoya Aichi, country=Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"organization=Department of Applied Physics, Graduate School of Engineering, Nagoya University, addressline=Furo-cho Chikusa-ku, postcode=464-8603, city=Nagoya Aichi, country=Japan","institution_ids":["https://openalex.org/I60134161"]},{"raw_affiliation_string":"organization=Department of Applied Physics, Graduate School of Engineering, Nagoya University, addressline=Furo-cho Chikusa-ku, postcode=464\u20138603, city=Nagoya Aichi, country=Japan","institution_ids":["https://openalex.org/I60134161"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5062829411"],"corresponding_institution_ids":["https://openalex.org/I68986083"],"apc_list":{"value":2700,"currency":"USD","value_usd":2700},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06085526,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"363","issue":"2","first_page":"108396","last_page":"108396"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.6080999970436096,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.6080999970436096,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.19140000641345978,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.032600000500679016,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/convergence","display_name":"Convergence (economics)","score":0.6384000182151794},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.589900016784668},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.5720000267028809},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.5702999830245972},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.5375999808311462},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.48089998960494995},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.42570000886917114},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4113999903202057}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6384000182151794},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.589900016784668},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5842999815940857},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.5720000267028809},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.5702999830245972},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5375999808311462},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4821999967098236},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.48089998960494995},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42989999055862427},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.42570000886917114},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4113999903202057},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.3531999886035919},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33480000495910645},{"id":"https://openalex.org/C812465","wikidata":"https://www.wikidata.org/wiki/Q5058375","display_name":"Cellular neural network","level":3,"score":0.31839999556541443},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.30239999294281006},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2971000075340271},{"id":"https://openalex.org/C2779843651","wikidata":"https://www.wikidata.org/wiki/Q7390335","display_name":"SIGNAL (programming language)","level":2,"score":0.2946000099182129},{"id":"https://openalex.org/C2779585090","wikidata":"https://www.wikidata.org/wiki/Q3457762","display_name":"Resilience (materials science)","level":2,"score":0.2696000039577484},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.2680000066757202},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.2639000117778778},{"id":"https://openalex.org/C2986737658","wikidata":"https://www.wikidata.org/wiki/Q30103009","display_name":"Tensor decomposition","level":3,"score":0.2558000087738037},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.25450000166893005},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.2524000108242035}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.jfranklin.2025.108396","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.jfranklin.2025.108396","pdf_url":null,"source":{"id":"https://openalex.org/S183498172","display_name":"Journal of the Franklin Institute","issn_l":"0016-0032","issn":["0016-0032","1879-2693"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the Franklin Institute","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1763682823","display_name":null,"funder_award_id":"JP25H00449","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G3431994521","display_name":null,"funder_award_id":"12461074","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5280961409","display_name":null,"funder_award_id":"202308620246","funder_id":"https://openalex.org/F4320322725","funder_display_name":"China Scholarship Council"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321940","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08"},{"id":"https://openalex.org/F4320322449","display_name":"Tongji University","ror":"https://ror.org/03rc6as71"},{"id":"https://openalex.org/F4320322725","display_name":"China Scholarship Council","ror":"https://ror.org/04atp4p48"},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W1964400575","https://openalex.org/W1973446088","https://openalex.org/W1985463596","https://openalex.org/W2015113370","https://openalex.org/W2123268478","https://openalex.org/W2130317597","https://openalex.org/W2133702739","https://openalex.org/W2738417046","https://openalex.org/W2793728421","https://openalex.org/W2911281195","https://openalex.org/W2911992324","https://openalex.org/W2938800094","https://openalex.org/W2949379566","https://openalex.org/W2988010182","https://openalex.org/W2995997745","https://openalex.org/W3002708972","https://openalex.org/W3018832276","https://openalex.org/W3149086699","https://openalex.org/W3196353935","https://openalex.org/W3199885834","https://openalex.org/W3211420099","https://openalex.org/W3212356522","https://openalex.org/W4206211217","https://openalex.org/W4232315234","https://openalex.org/W4313644237","https://openalex.org/W4382934619","https://openalex.org/W4389762816","https://openalex.org/W4391609619","https://openalex.org/W4394862641","https://openalex.org/W4396712995","https://openalex.org/W4408399684"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-01-10T23:39:48.068659","created_date":"2026-01-05T00:00:00"}