{"id":"https://openalex.org/W4406463034","doi":"https://doi.org/10.1007/s10994-024-06732-7","title":"Adaptive parameters identification for nonlinear dynamics using deep permutation invariant networks","display_name":"Adaptive parameters identification for nonlinear dynamics using deep permutation invariant networks","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4406463034","doi":"https://doi.org/10.1007/s10994-024-06732-7"},"language":"en","primary_location":{"id":"doi:10.1007/s10994-024-06732-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10994-024-06732-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10994-024-06732-7.pdf","source":{"id":"https://openalex.org/S62148650","display_name":"Machine Learning","issn_l":"0885-6125","issn":["0885-6125","1573-0565"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10994-024-06732-7.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5115905403","display_name":"Mouad Elaarabi","orcid":null},"institutions":[{"id":"https://openalex.org/I100445878","display_name":"\u00c9cole Centrale de Nantes","ror":"https://ror.org/03nh7d505","country_code":"FR","type":"education","lineage":["https://openalex.org/I100445878","https://openalex.org/I97188460"]},{"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/I4210096006","display_name":"IRT Jules Verne","ror":"https://ror.org/00qxv3c44","country_code":"FR","type":"facility","lineage":["https://openalex.org/I4210096006","https://openalex.org/I97188460"]},{"id":"https://openalex.org/I4210137520","display_name":"Institut de Recherche en G\u00e9nie Civil et M\u00e9canique","ror":"https://ror.org/03x30hb31","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100445878","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210095849","https://openalex.org/I4210137520","https://openalex.org/I97188460","https://openalex.org/I97188460"]},{"id":"https://openalex.org/I97188460","display_name":"Nantes Universit\u00e9","ror":"https://ror.org/03gnr7b55","country_code":"FR","type":"education","lineage":["https://openalex.org/I97188460"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Mouad Elaarabi","raw_affiliation_strings":["Ecole Centrale Nantes, CNRS, GeM, UMR 6183, Nantes Universit\u00e9, 44321, Nantes, France","IRT Jules Verne, Nantes Universit\u00e9, 44340, Bouguenais, France","Nantes Univ - ECN - NANTES UNIVERSIT\u00c9 - \u00c9cole Centrale de Nantes (1 rue de la No\u00eb - BP 92101 - 44321 Nantes cedex 3 - France)","Nantes Univ - IRT - Nantes Universit\u00e9 -Institut de Recherche Technologique Jules Verne (France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ecole Centrale Nantes, CNRS, GeM, UMR 6183, Nantes Universit\u00e9, 44321, Nantes, France","institution_ids":["https://openalex.org/I4210137520","https://openalex.org/I100445878","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"IRT Jules Verne, Nantes Universit\u00e9, 44340, Bouguenais, France","institution_ids":["https://openalex.org/I4210096006"]},{"raw_affiliation_string":"Nantes Univ - ECN - NANTES UNIVERSIT\u00c9 - \u00c9cole Centrale de Nantes (1 rue de la No\u00eb - BP 92101 - 44321 Nantes cedex 3 - France)","institution_ids":["https://openalex.org/I100445878","https://openalex.org/I97188460"]},{"raw_affiliation_string":"Nantes Univ - IRT - Nantes Universit\u00e9 -Institut de Recherche Technologique Jules Verne (France)","institution_ids":["https://openalex.org/I4210096006","https://openalex.org/I97188460"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008848609","display_name":"Domenico Borzacchiello","orcid":"https://orcid.org/0000-0001-5382-3172"},"institutions":[{"id":"https://openalex.org/I100445878","display_name":"\u00c9cole Centrale de Nantes","ror":"https://ror.org/03nh7d505","country_code":"FR","type":"education","lineage":["https://openalex.org/I100445878","https://openalex.org/I97188460"]},{"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/I4210137520","display_name":"Institut de Recherche en G\u00e9nie Civil et M\u00e9canique","ror":"https://ror.org/03x30hb31","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100445878","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210095849","https://openalex.org/I4210137520","https://openalex.org/I97188460","https://openalex.org/I97188460"]},{"id":"https://openalex.org/I97188460","display_name":"Nantes Universit\u00e9","ror":"https://ror.org/03gnr7b55","country_code":"FR","type":"education","lineage":["https://openalex.org/I97188460"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Domenico Borzacchiello","raw_affiliation_strings":["Ecole Centrale Nantes, CNRS, GeM, UMR 6183, Nantes Universit\u00e9, 44321, Nantes, France","Nantes Univ - ECN - NANTES UNIVERSIT\u00c9 - \u00c9cole Centrale de Nantes (1 rue de la No\u00eb - BP 92101 - 44321 Nantes cedex 3 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ecole Centrale Nantes, CNRS, GeM, UMR 6183, Nantes Universit\u00e9, 44321, Nantes, France","institution_ids":["https://openalex.org/I4210137520","https://openalex.org/I100445878","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Nantes Univ - ECN - NANTES UNIVERSIT\u00c9 - \u00c9cole Centrale de Nantes (1 rue de la No\u00eb - BP 92101 - 44321 Nantes cedex 3 - France)","institution_ids":["https://openalex.org/I100445878","https://openalex.org/I97188460"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076350872","display_name":"Philippe Le Bot","orcid":null},"institutions":[{"id":"https://openalex.org/I4210096006","display_name":"IRT Jules Verne","ror":"https://ror.org/00qxv3c44","country_code":"FR","type":"facility","lineage":["https://openalex.org/I4210096006","https://openalex.org/I97188460"]},{"id":"https://openalex.org/I97188460","display_name":"Nantes Universit\u00e9","ror":"https://ror.org/03gnr7b55","country_code":"FR","type":"education","lineage":["https://openalex.org/I97188460"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Philippe Le Bot","raw_affiliation_strings":["IRT Jules Verne, Nantes Universit\u00e9, 44340, Bouguenais, France","Nantes Univ - IRT - Nantes Universit\u00e9 -Institut de Recherche Technologique Jules Verne (France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IRT Jules Verne, Nantes Universit\u00e9, 44340, Bouguenais, France","institution_ids":["https://openalex.org/I4210096006"]},{"raw_affiliation_string":"Nantes Univ - IRT - Nantes Universit\u00e9 -Institut de Recherche Technologique Jules Verne (France)","institution_ids":["https://openalex.org/I4210096006","https://openalex.org/I97188460"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039922127","display_name":"Yves Le Guennec","orcid":"https://orcid.org/0000-0003-2652-8383"},"institutions":[{"id":"https://openalex.org/I4210096006","display_name":"IRT Jules Verne","ror":"https://ror.org/00qxv3c44","country_code":"FR","type":"facility","lineage":["https://openalex.org/I4210096006","https://openalex.org/I97188460"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Yves L. E. Guennec","raw_affiliation_strings":["IRT Jules Verne, Nantes Universit\u00e9, 44340, Bouguenais, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IRT Jules Verne, Nantes Universit\u00e9, 44340, Bouguenais, France","institution_ids":["https://openalex.org/I4210096006"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001112451","display_name":"S\u00e9bastien Comas-Cardona","orcid":"https://orcid.org/0000-0002-7184-7968"},"institutions":[{"id":"https://openalex.org/I100445878","display_name":"\u00c9cole Centrale de Nantes","ror":"https://ror.org/03nh7d505","country_code":"FR","type":"education","lineage":["https://openalex.org/I100445878","https://openalex.org/I97188460"]},{"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/I4210137520","display_name":"Institut de Recherche en G\u00e9nie Civil et M\u00e9canique","ror":"https://ror.org/03x30hb31","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100445878","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210095849","https://openalex.org/I4210137520","https://openalex.org/I97188460","https://openalex.org/I97188460"]},{"id":"https://openalex.org/I97188460","display_name":"Nantes Universit\u00e9","ror":"https://ror.org/03gnr7b55","country_code":"FR","type":"education","lineage":["https://openalex.org/I97188460"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Sebastien Comas-Cardona","raw_affiliation_strings":["Ecole Centrale Nantes, CNRS, GeM, UMR 6183, Nantes Universit\u00e9, 44321, Nantes, France","Nantes Univ - ECN - NANTES UNIVERSIT\u00c9 - \u00c9cole Centrale de Nantes (1 rue de la No\u00eb - BP 92101 - 44321 Nantes cedex 3 - France)","GeM - Institut de Recherche en G\u00e9nie Civil et M\u00e9canique (1, rue de la No\u00eb BP92101 44321 Nantes cedex 3 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ecole Centrale Nantes, CNRS, GeM, UMR 6183, Nantes Universit\u00e9, 44321, Nantes, France","institution_ids":["https://openalex.org/I4210137520","https://openalex.org/I100445878","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Nantes Univ - ECN - NANTES UNIVERSIT\u00c9 - \u00c9cole Centrale de Nantes (1 rue de la No\u00eb - BP 92101 - 44321 Nantes cedex 3 - France)","institution_ids":["https://openalex.org/I100445878","https://openalex.org/I97188460"]},{"raw_affiliation_string":"GeM - Institut de Recherche en G\u00e9nie Civil et M\u00e9canique (1, rue de la No\u00eb BP92101 44321 Nantes cedex 3 - France)","institution_ids":["https://openalex.org/I4210137520"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5115905403"],"corresponding_institution_ids":["https://openalex.org/I100445878","https://openalex.org/I1294671590","https://openalex.org/I4210096006","https://openalex.org/I4210137520","https://openalex.org/I97188460"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":2.4723,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.86965992,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":97},"biblio":{"volume":"114","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9988999962806702,"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":0.9988999962806702,"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/T12560","display_name":"Nuclear Engineering Thermal-Hydraulics","score":0.9869999885559082,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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":0.9842000007629395,"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/interpretability","display_name":"Interpretability","score":0.6806752681732178},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6668860912322998},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5828214883804321},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5382127165794373},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5256943702697754},{"id":"https://openalex.org/keywords/nonlinear-system-identification","display_name":"Nonlinear system identification","score":0.4793879985809326},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4710160493850708},{"id":"https://openalex.org/keywords/system-identification","display_name":"System identification","score":0.3837655782699585},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3559300899505615},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.23024940490722656}],"concepts":[{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.6806752681732178},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6668860912322998},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5828214883804321},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5382127165794373},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5256943702697754},{"id":"https://openalex.org/C22157029","wikidata":"https://www.wikidata.org/wiki/Q17080460","display_name":"Nonlinear system identification","level":4,"score":0.4793879985809326},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4710160493850708},{"id":"https://openalex.org/C119247159","wikidata":"https://www.wikidata.org/wiki/Q1366192","display_name":"System identification","level":3,"score":0.3837655782699585},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3559300899505615},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.23024940490722656},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"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":3,"locations":[{"id":"doi:10.1007/s10994-024-06732-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10994-024-06732-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10994-024-06732-7.pdf","source":{"id":"https://openalex.org/S62148650","display_name":"Machine Learning","issn_l":"0885-6125","issn":["0885-6125","1573-0565"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2501.11350","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2501.11350","pdf_url":"https://arxiv.org/pdf/2501.11350","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-04892926v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04892926","pdf_url":"https://hal.science/hal-04892926/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Machine Learning, 2025, 114 (1), pp.22. ⟨10.1007/s10994-024-06732-7⟩","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s10994-024-06732-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10994-024-06732-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10994-024-06732-7.pdf","source":{"id":"https://openalex.org/S62148650","display_name":"Machine Learning","issn_l":"0885-6125","issn":["0885-6125","1573-0565"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9","score":0.5}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4406463034.pdf","grobid_xml":"https://content.openalex.org/works/W4406463034.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W1723433682","https://openalex.org/W1978060721","https://openalex.org/W2135046866","https://openalex.org/W2177804662","https://openalex.org/W2239232218","https://openalex.org/W2525748878","https://openalex.org/W2734911284","https://openalex.org/W2768748954","https://openalex.org/W2791651676","https://openalex.org/W2889716319","https://openalex.org/W2894384847","https://openalex.org/W2899283552","https://openalex.org/W2903660960","https://openalex.org/W2945976633","https://openalex.org/W2963739154","https://openalex.org/W2964265215","https://openalex.org/W2990138404","https://openalex.org/W3003257820","https://openalex.org/W3028073062","https://openalex.org/W3042959663","https://openalex.org/W3100769368","https://openalex.org/W3105090572","https://openalex.org/W3182706339","https://openalex.org/W3207471124","https://openalex.org/W3209840040","https://openalex.org/W4210720128","https://openalex.org/W4213170186","https://openalex.org/W4281782255","https://openalex.org/W4311129667","https://openalex.org/W4366815875","https://openalex.org/W4385261839","https://openalex.org/W4387178584","https://openalex.org/W4390502602","https://openalex.org/W6739901393","https://openalex.org/W6744580074","https://openalex.org/W6810210838"],"related_works":["https://openalex.org/W2152282424","https://openalex.org/W2091914113","https://openalex.org/W564324191","https://openalex.org/W2319800497","https://openalex.org/W2021395081","https://openalex.org/W2004841036","https://openalex.org/W4386033416","https://openalex.org/W1595492935","https://openalex.org/W1987213476","https://openalex.org/W176335707"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"promising":[2],"outcomes":[3],"of":[4,87,124,128,253],"dynamical":[5,89,199,238],"system":[6,57,90,200,234,239],"identification":[7,136,201,250],"techniques,":[8],"such":[9],"as":[10],"SINDy":[11],"(Brunton":[12],"et":[13,71,159,176],"al.":[14,72,160,177],"in":[15,25,38,50,73,99,161],"Proc":[16],"Natl":[17],"Acad":[18],"Sci":[19],"113(15):3932\u20133937,":[20],"2016),":[21],"highlight":[22],"their":[23],"advantages":[24],"providing":[26],"qualitative":[27],"interpretability":[28],"and":[29,169,202,251],"extrapolation":[30],"compared":[31],"to":[32,61,83,191,216,248],"non-interpretable":[33],"deep":[34],"neural":[35],"networks":[36],"(Rudin":[37],"Nat":[39],"Mach":[40],"Intell":[41],"1(5):206\u2013215,":[42],"2019).":[43,187],"These":[44],"techniques":[45],"suffer":[46],"from":[47],"parameter":[48],"updating":[49],"real-time":[51,88,197],"use":[52,123],"cases,":[53],"especially":[54],"when":[55],"the":[56,68,85,122,153,170,209,225,232],"parameters":[58,91],"are":[59,151],"likely":[60],"change":[62],"during":[63],"or":[64],"between":[65],"processes.":[66],"Recently,":[67],"OASIS":[69,192],"(Bhadriraju":[70],"AIChE":[74],"J":[75],"66(11):16980,":[76],"2020)":[77],"framework":[78,193],"introduced":[79],"a":[80,244],"data-driven":[81],"technique":[82],"address":[84],"limitations":[86],"updating,":[92],"yielding":[93],"interesting":[94],"results.":[95],"Nevertheless,":[96],"we":[97,206,242],"show":[98],"this":[100],"work":[101],"that":[102,208],"superior":[103],"performance":[104],"can":[105],"be":[106],"achieved":[107],"using":[108],"more":[109],"advanced":[110],"model":[111,135,247],"architectures.":[112],"We":[113,222],"present":[114],"an":[115],"innovative":[116],"encoding":[117],"approach,":[118],"based":[119,230],"mainly":[120],"on":[121,181,194,231],"Set":[125,148,157,173,189,210,227,246],"Encoding":[126,149,228],"methods":[127,150,229],"sequence":[129],"data,":[130],"which":[131],"give":[132],"accurate":[133],"adaptive":[134],"for":[137,196,235,255],"complex":[138],"dynamic":[139],"systems,":[140],"with":[141],"variable":[142],"input":[143],"time":[144,203],"series":[145,204],"length.":[146],"Two":[147],"used:":[152],"first":[154],"is":[155,172,213],"Deep":[156,245],"(Zaheer":[158],"Adv":[162],"Neural":[163],"Inf":[164],"Process":[165],"Syst":[166],"30,":[167],"2017),":[168],"second":[171],"Transformer":[174,190,211],"(Lee":[175],"in:":[178],"International":[179],"conference":[180],"machine":[182],"learning,":[183],"PMLR,":[184],"pp":[185],"3744\u20133753":[186],"Comparing":[188],"Lotka\u2013Volterra":[195],"local":[198],"forecasting,":[205],"find":[207],"architecture":[212],"well":[214],"adapted":[215],"learning":[217],"relationships":[218],"within":[219],"data":[220],"sets.":[221],"then":[223],"compare":[224],"two":[226],"Lorenz":[233],"online":[236],"global":[237],"identification.":[240],"Finally,":[241],"trained":[243],"perform":[249],"characterization":[252],"abnormalities":[254],"1D":[256],"heat-transfer":[257],"problem.":[258]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2}],"updated_date":"2026-07-06T08:01:05.025921","created_date":"2025-10-10T00:00:00"}