{"id":"https://openalex.org/W4200258636","doi":"https://doi.org/10.1142/s0218127421502291","title":"Generalized Cell Mapping Method with Deep Learning for Global Analysis and Response Prediction of Dynamical Systems","display_name":"Generalized Cell Mapping Method with Deep Learning for Global Analysis and Response Prediction of Dynamical Systems","publication_year":2021,"publication_date":"2021-12-07","ids":{"openalex":"https://openalex.org/W4200258636","doi":"https://doi.org/10.1142/s0218127421502291"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127421502291","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127421502291","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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/A5061543625","display_name":"Xiaole Yue","orcid":"https://orcid.org/0000-0003-2983-5821"},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiao-Le Yue","raw_affiliation_strings":["School of Mathematics and Statistics, Northwestern Polytechnical University, Xi\u2019an, Shanxi 710072, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Northwestern Polytechnical University, Xi\u2019an, Shanxi 710072, P. R. China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068248405","display_name":"Suping Cui","orcid":null},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Su-Ping Cui","raw_affiliation_strings":["School of Mathematics and Statistics, Northwestern Polytechnical University, Xi\u2019an, Shanxi 710072, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Northwestern Polytechnical University, Xi\u2019an, Shanxi 710072, P. R. China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048138372","display_name":"Hao Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hao Zhang","raw_affiliation_strings":["School of Mathematics and Statistics, Northwestern Polytechnical University, Xi\u2019an, Shanxi 710072, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Northwestern Polytechnical University, Xi\u2019an, Shanxi 710072, P. R. China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017350937","display_name":"Jian\u2010Qiao Sun","orcid":"https://orcid.org/0000-0002-5441-7982"},"institutions":[{"id":"https://openalex.org/I156087764","display_name":"University of California, Merced","ror":"https://ror.org/00d9ah105","country_code":"US","type":"education","lineage":["https://openalex.org/I156087764"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jian-Qiao Sun","raw_affiliation_strings":["Department of Mechanical Engineering, School of Engineering, University of California, Merced, CA 95343, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, School of Engineering, University of California, Merced, CA 95343, USA","institution_ids":["https://openalex.org/I156087764"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062310230","display_name":"Yong Xu","orcid":"https://orcid.org/0000-0002-8407-4650"},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yong Xu","raw_affiliation_strings":["School of Mathematics and Statistics, Northwestern Polytechnical University, Xi\u2019an, Shanxi 710072, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Northwestern Polytechnical University, Xi\u2019an, Shanxi 710072, P. R. China","institution_ids":["https://openalex.org/I17145004"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5061543625"],"corresponding_institution_ids":["https://openalex.org/I17145004"],"apc_list":null,"apc_paid":null,"fwci":1.0522,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.77276013,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"31","issue":"15","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":0.9990000128746033,"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":0.9990000128746033,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9908999800682068,"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"}},{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9865000247955322,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6624161005020142},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6126720309257507},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.5915365815162659},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.5842491388320923},{"id":"https://openalex.org/keywords/hyperparameter","display_name":"Hyperparameter","score":0.5651890635490417},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5315392017364502},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.49662262201309204},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.4585734009742737},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.4389890432357788},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4281110465526581},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3835202157497406},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.366701602935791},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.36147770285606384},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.22259566187858582}],"concepts":[{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6624161005020142},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6126720309257507},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.5915365815162659},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.5842491388320923},{"id":"https://openalex.org/C8642999","wikidata":"https://www.wikidata.org/wiki/Q4171168","display_name":"Hyperparameter","level":2,"score":0.5651890635490417},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5315392017364502},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.49662262201309204},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.4585734009742737},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.4389890432357788},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4281110465526581},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3835202157497406},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.366701602935791},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.36147770285606384},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.22259566187858582},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127421502291","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127421502291","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7363664854","display_name":null,"funder_award_id":"11672230","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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W55565704","https://openalex.org/W1770420856","https://openalex.org/W1933216107","https://openalex.org/W1993669342","https://openalex.org/W2001658863","https://openalex.org/W2001659478","https://openalex.org/W2025475113","https://openalex.org/W2025488308","https://openalex.org/W2051266746","https://openalex.org/W2064053127","https://openalex.org/W2082207998","https://openalex.org/W2093828424","https://openalex.org/W2101021792","https://openalex.org/W2158985775","https://openalex.org/W2171972705","https://openalex.org/W2239232218","https://openalex.org/W2534240011","https://openalex.org/W2749028154","https://openalex.org/W2765128778","https://openalex.org/W2770250658","https://openalex.org/W2777417212","https://openalex.org/W2782714865","https://openalex.org/W2801813398","https://openalex.org/W2899283552","https://openalex.org/W2912912713","https://openalex.org/W2913323966","https://openalex.org/W2921773029","https://openalex.org/W2921873091","https://openalex.org/W2945114464","https://openalex.org/W2945672665","https://openalex.org/W2947320005","https://openalex.org/W2951629468","https://openalex.org/W2962844669","https://openalex.org/W2964268202","https://openalex.org/W2966299158","https://openalex.org/W2969311375","https://openalex.org/W2998647093","https://openalex.org/W3002873949","https://openalex.org/W3084454974","https://openalex.org/W3098172061","https://openalex.org/W3100626142","https://openalex.org/W3105585588","https://openalex.org/W4235488236"],"related_works":["https://openalex.org/W2379488025","https://openalex.org/W2318462079","https://openalex.org/W2585728124","https://openalex.org/W2169362996","https://openalex.org/W2340294931","https://openalex.org/W2565482338","https://openalex.org/W2082884906","https://openalex.org/W2377705019","https://openalex.org/W2001163940","https://openalex.org/W2384473241"],"abstract_inverted_index":{"A":[0],"novel":[1],"method":[2,27,99,175],"that":[3,172],"combines":[4],"generalized":[5],"cell":[6],"mapping":[7,76],"and":[8,18,38,53,60,68,94,148,159,183],"deep":[9],"learning":[10],"is":[11,78,157,167,176],"developed":[12],"to":[13,100,135],"analyze":[14,101],"the":[15,20,34,43,50,74,82,89,96,102,114,118,121,137,143,149,164,173],"global":[16,103,181],"properties":[17,41],"predict":[19],"responses":[21,106],"of":[22,33,42,120,123,142,145,151,163],"dynamical":[23,40,84],"systems.":[24],"The":[25,140],"proposed":[26,138,174],"only":[28],"requires":[29],"some":[30],"prior":[31],"knowledge":[32],"system":[35,44,85],"governing":[36],"equations":[37],"obtains":[39],"from":[45],"observed":[46],"data.":[47],"By":[48,80],"combining":[49],"theoretical":[51],"demonstration":[52],"empirical":[54],"inference":[55],"results,":[56],"appropriate":[57],"network":[58,71,166],"structure":[59],"training":[61,152],"hyperparameters":[62],"are":[63,133],"computed.":[64],"Then":[65],"a":[66],"robust":[67],"efficient":[69],"neural":[70,165],"approximation":[72],"with":[73,113,128],"estimated":[75],"parameters":[77],"obtained.":[79],"using":[81],"approximate":[83],"model,":[86],"we":[87],"construct":[88],"one-step":[90],"transition":[91],"probability":[92],"matrix":[93],"introduce":[95],"digraph":[97],"analysis":[98,182],"properties.":[104],"System":[105],"at":[107],"any":[108],"time":[109],"can":[110],"be":[111],"obtained":[112],"trained":[115],"model":[116],"on":[117,154],"basis":[119],"property":[122],"Markov":[124],"chain.":[125],"Several":[126],"examples":[127],"periodic":[129],"or":[130],"chaotic":[131],"attractors":[132],"presented":[134],"validate":[136],"method.":[139],"influence":[141],"number":[144],"hidden":[146],"layers":[147],"size":[150],"data":[153],"calculated":[155],"results":[156,170],"discussed,":[158],"an":[160],"admissible":[161],"architecture":[162],"found.":[168],"Numerical":[169],"indicate":[171],"quite":[177],"effective":[178],"for":[179],"both":[180],"response":[184],"prediction.":[185]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2}],"updated_date":"2026-03-27T14:29:43.386196","created_date":"2025-10-10T00:00:00"}