{"id":"https://openalex.org/W4392251542","doi":"https://doi.org/10.1109/tcyb.2024.3364186","title":"EgPDE-Net: Building Continuous Neural Networks for Time Series Prediction With Exogenous Variables","display_name":"EgPDE-Net: Building Continuous Neural Networks for Time Series Prediction With Exogenous Variables","publication_year":2024,"publication_date":"2024-02-28","ids":{"openalex":"https://openalex.org/W4392251542","doi":"https://doi.org/10.1109/tcyb.2024.3364186","pmid":"https://pubmed.ncbi.nlm.nih.gov/38416628"},"language":"en","primary_location":{"id":"doi:10.1109/tcyb.2024.3364186","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2024.3364186","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"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 Cybernetics","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/A5009625156","display_name":"Penglei Gao","orcid":"https://orcid.org/0000-0003-1935-5752"},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Penglei Gao","raw_affiliation_strings":["Department of Computer Science, University of Liverpool, Liverpool, U.K"],"raw_orcid":"https://orcid.org/0000-0003-1935-5752","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Liverpool, Liverpool, U.K","institution_ids":["https://openalex.org/I146655781"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055411456","display_name":"Xi Yang","orcid":"https://orcid.org/0000-0002-8600-2570"},"institutions":[{"id":"https://openalex.org/I69356397","display_name":"Xi\u2019an Jiaotong-Liverpool University","ror":"https://ror.org/03zmrmn05","country_code":"CN","type":"education","lineage":["https://openalex.org/I69356397"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xi Yang","raw_affiliation_strings":["Department of Intelligent Science, Xi’an Jiaotong–Liverpool University, Suzhou, China"],"raw_orcid":"https://orcid.org/0000-0002-8600-2570","affiliations":[{"raw_affiliation_string":"Department of Intelligent Science, Xi’an Jiaotong–Liverpool University, Suzhou, China","institution_ids":["https://openalex.org/I69356397"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100422091","display_name":"Rui Zhang","orcid":"https://orcid.org/0000-0002-8104-5432"},"institutions":[{"id":"https://openalex.org/I69356397","display_name":"Xi\u2019an Jiaotong-Liverpool University","ror":"https://ror.org/03zmrmn05","country_code":"CN","type":"education","lineage":["https://openalex.org/I69356397"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Rui Zhang","raw_affiliation_strings":["Department of Foundational Mathematics, Xi’an Jiaotong–Liverpool University, Suzhou, China"],"raw_orcid":"https://orcid.org/0000-0002-8104-5432","affiliations":[{"raw_affiliation_string":"Department of Foundational Mathematics, Xi’an Jiaotong–Liverpool University, Suzhou, China","institution_ids":["https://openalex.org/I69356397"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020083340","display_name":"Ping Guo","orcid":"https://orcid.org/0000-0002-7122-1084"},"institutions":[{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ping Guo","raw_affiliation_strings":["Department of School of Systems Science, Beijing Normal University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-7122-1084","affiliations":[{"raw_affiliation_string":"Department of School of Systems Science, Beijing Normal University, Beijing, China","institution_ids":["https://openalex.org/I25254941"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079825375","display_name":"John Y. Goulermas","orcid":"https://orcid.org/0000-0003-0381-124X"},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"John Y. Goulermas","raw_affiliation_strings":["Department of Computer Science, University of Liverpool, Liverpool, U.K"],"raw_orcid":"https://orcid.org/0000-0003-0381-124X","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Liverpool, Liverpool, U.K","institution_ids":["https://openalex.org/I146655781"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026022035","display_name":"Kaizhu Huang","orcid":"https://orcid.org/0000-0002-3034-9639"},"institutions":[{"id":"https://openalex.org/I4210159968","display_name":"Duke Kunshan University","ror":"https://ror.org/04sr5ys16","country_code":"CN","type":"education","lineage":["https://openalex.org/I170897317","https://openalex.org/I37461747","https://openalex.org/I4210159968"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kaizhu Huang","raw_affiliation_strings":["Data Science Research Center, Duke Kunshan University, Kunshan, China"],"raw_orcid":"https://orcid.org/0000-0002-3034-9639","affiliations":[{"raw_affiliation_string":"Data Science Research Center, Duke Kunshan University, Kunshan, China","institution_ids":["https://openalex.org/I4210159968"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.5233,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.89053603,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"54","issue":"9","first_page":"5381","last_page":"5393"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.998199999332428,"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":0.998199999332428,"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/T11326","display_name":"Stock Market Forecasting Methods","score":0.9894000291824341,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12205","display_name":"Time Series Analysis and Forecasting","score":0.9853000044822693,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/parameterized-complexity","display_name":"Parameterized complexity","score":0.7616621255874634},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.7129335403442383},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.6937752962112427},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6128523945808411},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.557299017906189},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5426372289657593},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.535662055015564},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5303578972816467},{"id":"https://openalex.org/keywords/time-series","display_name":"Time series","score":0.5298430919647217},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.525192141532898},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.49965882301330566},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.48276081681251526},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4612281620502472},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4292571544647217},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33022522926330566},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.28681355714797974},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.23626112937927246},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.19069090485572815},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07177677750587463}],"concepts":[{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.7616621255874634},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.7129335403442383},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.6937752962112427},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6128523945808411},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.557299017906189},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5426372289657593},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.535662055015564},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5303578972816467},{"id":"https://openalex.org/C151406439","wikidata":"https://www.wikidata.org/wiki/Q186588","display_name":"Time series","level":2,"score":0.5298430919647217},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.525192141532898},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.49965882301330566},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.48276081681251526},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4612281620502472},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4292571544647217},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33022522926330566},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.28681355714797974},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.23626112937927246},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.19069090485572815},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07177677750587463},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tcyb.2024.3364186","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2024.3364186","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"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 Cybernetics","raw_type":"journal-article"},{"id":"pmid:38416628","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/38416628","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":"IEEE transactions on cybernetics","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1698772872","display_name":null,"funder_award_id":"92370119","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4391515551","display_name":null,"funder_award_id":"22KJB520039","funder_id":"https://openalex.org/F4320335440","funder_display_name":"Natural Science Research of Jiangsu Higher Education Institutions of China"},{"id":"https://openalex.org/G5412516101","display_name":null,"funder_award_id":"62206225","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5866557873","display_name":null,"funder_award_id":"62376113","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335440","display_name":"Natural Science Research of Jiangsu Higher Education Institutions of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W336979425","https://openalex.org/W2019459021","https://openalex.org/W2076170369","https://openalex.org/W2604847698","https://openalex.org/W2625995436","https://openalex.org/W2749028154","https://openalex.org/W2761742597","https://openalex.org/W2791994602","https://openalex.org/W2903660960","https://openalex.org/W2954388788","https://openalex.org/W2958796454","https://openalex.org/W2966276668","https://openalex.org/W2969855422","https://openalex.org/W2984594917","https://openalex.org/W2986385482","https://openalex.org/W2998367712","https://openalex.org/W3007906701","https://openalex.org/W3016899151","https://openalex.org/W3046470859","https://openalex.org/W3082260983","https://openalex.org/W3099661895","https://openalex.org/W3121870452","https://openalex.org/W3134794314","https://openalex.org/W3135778552","https://openalex.org/W3137948146","https://openalex.org/W3170140111","https://openalex.org/W3177318507","https://openalex.org/W4205650351","https://openalex.org/W4224282912","https://openalex.org/W4226057022","https://openalex.org/W4242688646","https://openalex.org/W4283817628","https://openalex.org/W4289258409","https://openalex.org/W4290948537","https://openalex.org/W4309951073","https://openalex.org/W4380611142","https://openalex.org/W4385245566","https://openalex.org/W6631190155","https://openalex.org/W6726186668","https://openalex.org/W6736456187","https://openalex.org/W6745131042","https://openalex.org/W6746017139","https://openalex.org/W6751165238","https://openalex.org/W6752307458","https://openalex.org/W6755056417","https://openalex.org/W6762929618","https://openalex.org/W6765671628","https://openalex.org/W6767279920","https://openalex.org/W6770064641","https://openalex.org/W6770177100","https://openalex.org/W6777558877","https://openalex.org/W6778353478","https://openalex.org/W6779731125","https://openalex.org/W6782585448","https://openalex.org/W6792015825"],"related_works":["https://openalex.org/W3082668976","https://openalex.org/W2517973022","https://openalex.org/W1543121148","https://openalex.org/W1580703421","https://openalex.org/W2618518959","https://openalex.org/W2231364979","https://openalex.org/W4295745414","https://openalex.org/W4382202915","https://openalex.org/W2489516236","https://openalex.org/W4297273858"],"abstract_inverted_index":{"While":[0],"exogenous":[1,105],"variables":[2,106],"have":[3],"a":[4,48,63,121],"major":[5],"impact":[6],"on":[7,110,172,182,186],"performance":[8],"improvement":[9],"in":[10,24,51,75],"time":[11,17,34,77,156],"series":[12,35,78,153],"analysis,":[13],"interseries":[14],"correlation":[15],"and":[16,56,86,107,143,184],"dependence":[18],"among":[19,103],"them":[20],"are":[21,82],"rarely":[22],"considered":[23],"the":[25,101,104,111,115,135,151,176],"present":[26],"continuous":[27],"methods.":[28],"The":[29,91],"dynamical":[30],"systems":[31],"of":[32,54,100,150],"multivariate":[33,76],"could":[36,165],"be":[37,118],"modeled":[38],"with":[39,128],"complex":[40],"unknown":[41,72],"partial":[42],"differential":[43,124],"equations":[44,81],"(PDEs)":[45],"which":[46,133],"play":[47],"prominent":[49],"role":[50],"many":[52],"disciplines":[53],"science":[55],"engineering.":[57],"In":[58],"this":[59],"article,":[60],"we":[61],"propose":[62],"continuous-time":[64],"model":[65,116,164],"for":[66,188],"arbitrary-step":[67,189],"prediction":[68],"to":[69,139,145],"learn":[70],"an":[71],"PDE":[73,95,136],"system":[74],"whose":[79],"governing":[80],"parameterized":[83],"by":[84,179],"self-attention":[85],"gated":[87],"recurrent":[88],"neural":[89],"networks.":[90],"proposed":[92,163],"model,":[93],"exogenous-guided":[94],"network":[96],"(EgPDE-Net),":[97],"takes":[98],"account":[99],"relationships":[102],"their":[108],"effects":[109],"target":[112,152],"series.":[113],"Importantly,":[114],"can":[117],"reduced":[119],"into":[120],"regularized":[122],"ordinary":[123],"equation":[125],"(ODE)":[126],"problem":[127,137],"specially":[129],"designed":[130],"regularization":[131],"guidance,":[132],"makes":[134],"tractable":[138],"obtain":[140],"numerical":[141],"solutions":[142],"feasible":[144],"predict":[146],"multiple":[147],"future":[148],"values":[149],"at":[154],"arbitrary":[155],"points.":[157],"Extensive":[158],"experiments":[159],"demonstrate":[160],"that":[161],"our":[162],"achieve":[166],"competitive":[167],"accuracy":[168],"over":[169],"strong":[170],"baselines:":[171],"average,":[173],"it":[174],"outperforms":[175],"best":[177],"baseline":[178],"reducing":[180],"9.85%":[181],"RMSE":[183],"13.98%":[185],"MAE":[187],"prediction.":[190]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":9}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}