{"id":"https://openalex.org/W4406543533","doi":"https://doi.org/10.3389/fdata.2024.1506443","title":"Toward a physics-guided machine learning approach for predicting chaotic systems dynamics","display_name":"Toward a physics-guided machine learning approach for predicting chaotic systems dynamics","publication_year":2025,"publication_date":"2025-01-17","ids":{"openalex":"https://openalex.org/W4406543533","doi":"https://doi.org/10.3389/fdata.2024.1506443","pmid":"https://pubmed.ncbi.nlm.nih.gov/39897066"},"language":"en","primary_location":{"id":"doi:10.3389/fdata.2024.1506443","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fdata.2024.1506443","pdf_url":null,"source":{"id":"https://openalex.org/S4210201220","display_name":"Frontiers in Big Data","issn_l":"2624-909X","issn":["2624-909X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Big Data","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3389/fdata.2024.1506443","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100415353","display_name":"Feng Liu","orcid":"https://orcid.org/0000-0003-4720-0571"},"institutions":[{"id":"https://openalex.org/I141568987","display_name":"Hong Kong Baptist University","ror":"https://ror.org/0145fw131","country_code":"HK","type":"education","lineage":["https://openalex.org/I141568987"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Liu Feng","raw_affiliation_strings":["Department of Computer Science, Hong Kong Baptist University, Hong Kong, China"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Hong Kong Baptist University, Hong Kong, China","institution_ids":["https://openalex.org/I141568987"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5120061442","display_name":"Yang Liu","orcid":"https://orcid.org/0000-0003-4468-3926"},"institutions":[{"id":"https://openalex.org/I141568987","display_name":"Hong Kong Baptist University","ror":"https://ror.org/0145fw131","country_code":"HK","type":"education","lineage":["https://openalex.org/I141568987"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Yang Liu","raw_affiliation_strings":["Department of Computer Science, Hong Kong Baptist University, Hong Kong, China"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Hong Kong Baptist University, Hong Kong, China","institution_ids":["https://openalex.org/I141568987"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048137853","display_name":"Benyun Shi","orcid":"https://orcid.org/0000-0003-2734-3794"},"institutions":[{"id":"https://openalex.org/I134687103","display_name":"Nanjing Tech University","ror":"https://ror.org/03sd35x91","country_code":"CN","type":"education","lineage":["https://openalex.org/I134687103"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Benyun Shi","raw_affiliation_strings":["College of Computer and Information Engineering, Nanjing Tech University, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"College of Computer and Information Engineering, Nanjing Tech University, Nanjing, China","institution_ids":["https://openalex.org/I134687103"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5114376575","display_name":"Jiming Liu","orcid":"https://orcid.org/0000-0003-1798-5021"},"institutions":[{"id":"https://openalex.org/I141568987","display_name":"Hong Kong Baptist University","ror":"https://ror.org/0145fw131","country_code":"HK","type":"education","lineage":["https://openalex.org/I141568987"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"Jiming Liu","raw_affiliation_strings":["Department of Computer Science, Hong Kong Baptist University, Hong Kong, China"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Hong Kong Baptist University, Hong Kong, China","institution_ids":["https://openalex.org/I141568987"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5114376575"],"corresponding_institution_ids":["https://openalex.org/I141568987"],"apc_list":{"value":1150,"currency":"USD","value_usd":1150},"apc_paid":{"value":1150,"currency":"USD","value_usd":1150},"fwci":4.6338,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.93405922,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"7","issue":null,"first_page":"1506443","last_page":"1506443"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13650","display_name":"Computational Physics and Python Applications","score":0.9765999913215637,"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/T13650","display_name":"Computational Physics and Python Applications","score":0.9765999913215637,"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"}},{"id":"https://openalex.org/T12205","display_name":"Time Series Analysis and Forecasting","score":0.9686999917030334,"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"}},{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9578999876976013,"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/chaotic","display_name":"Chaotic","score":0.6989859938621521},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.625281035900116},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5974833369255066},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.5431496500968933},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.500861406326294},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4941423237323761},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.49138179421424866},{"id":"https://openalex.org/keywords/complex-system","display_name":"Complex system","score":0.4511626362800598},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4498969614505768},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.4286201298236847},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4232103228569031},{"id":"https://openalex.org/keywords/system-dynamics","display_name":"System dynamics","score":0.42033514380455017},{"id":"https://openalex.org/keywords/scope","display_name":"Scope (computer science)","score":0.4126286208629608},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2006121277809143}],"concepts":[{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6989859938621521},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.625281035900116},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5974833369255066},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.5431496500968933},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.500861406326294},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4941423237323761},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.49138179421424866},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.4511626362800598},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4498969614505768},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.4286201298236847},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4232103228569031},{"id":"https://openalex.org/C77405623","wikidata":"https://www.wikidata.org/wiki/Q598451","display_name":"System dynamics","level":2,"score":0.42033514380455017},{"id":"https://openalex.org/C2778012447","wikidata":"https://www.wikidata.org/wiki/Q1034415","display_name":"Scope (computer science)","level":2,"score":0.4126286208629608},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2006121277809143},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3389/fdata.2024.1506443","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fdata.2024.1506443","pdf_url":null,"source":{"id":"https://openalex.org/S4210201220","display_name":"Frontiers in Big Data","issn_l":"2624-909X","issn":["2624-909X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Big Data","raw_type":"journal-article"},{"id":"pmid:39897066","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/39897066","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":"Frontiers in big data","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:11782262","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/11782262","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Front Big Data","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:6289ff16e6aa491d8980855f45c72931","is_oa":true,"landing_page_url":"https://doaj.org/article/6289ff16e6aa491d8980855f45c72931","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Frontiers in Big Data, Vol 7 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3389/fdata.2024.1506443","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fdata.2024.1506443","pdf_url":null,"source":{"id":"https://openalex.org/S4210201220","display_name":"Frontiers in Big Data","issn_l":"2624-909X","issn":["2624-909X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Big Data","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.7099999785423279,"id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G1121271761","display_name":null,"funder_award_id":"Program","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4233178061","display_name":null,"funder_award_id":"12202220","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5939423041","display_name":null,"funder_award_id":"Technology","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6629397870","display_name":null,"funder_award_id":"62261160387","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7033253288","display_name":null,"funder_award_id":"Grants","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8369339599","display_name":null,"funder_award_id":"122022","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8513333314","display_name":null,"funder_award_id":"2021ZD01","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320320955","display_name":"Hong Kong Baptist University","ror":"https://ror.org/0145fw131"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321605","display_name":"Government of Jiangsu Province","ror":"https://ror.org/004svx814"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":69,"referenced_works":["https://openalex.org/W562378484","https://openalex.org/W1967008192","https://openalex.org/W1970442252","https://openalex.org/W1977219044","https://openalex.org/W1978956130","https://openalex.org/W2007477210","https://openalex.org/W2056651346","https://openalex.org/W2064675550","https://openalex.org/W2069436097","https://openalex.org/W2069937458","https://openalex.org/W2094864723","https://openalex.org/W2102871258","https://openalex.org/W2112246162","https://openalex.org/W2141394518","https://openalex.org/W2158985775","https://openalex.org/W2162651880","https://openalex.org/W2171238132","https://openalex.org/W2171987742","https://openalex.org/W2549742044","https://openalex.org/W2576489192","https://openalex.org/W2749028154","https://openalex.org/W2765128778","https://openalex.org/W2782714865","https://openalex.org/W2899283552","https://openalex.org/W2920288855","https://openalex.org/W2994028939","https://openalex.org/W2998511158","https://openalex.org/W3012621877","https://openalex.org/W3033003925","https://openalex.org/W3040211378","https://openalex.org/W3097095082","https://openalex.org/W3101278268","https://openalex.org/W3101766586","https://openalex.org/W3105585588","https://openalex.org/W3114000978","https://openalex.org/W3133007915","https://openalex.org/W3136433498","https://openalex.org/W3154019914","https://openalex.org/W3170977978","https://openalex.org/W3193942810","https://openalex.org/W3201489801","https://openalex.org/W3212966444","https://openalex.org/W3213541597","https://openalex.org/W4234402252","https://openalex.org/W4234831671","https://openalex.org/W4247794243","https://openalex.org/W4288735490","https://openalex.org/W4293565759","https://openalex.org/W4312056444","https://openalex.org/W4317611882","https://openalex.org/W4321594350","https://openalex.org/W4366779076","https://openalex.org/W4378469105","https://openalex.org/W4382203079","https://openalex.org/W4385877467","https://openalex.org/W4386069224","https://openalex.org/W4389347592","https://openalex.org/W4390511677","https://openalex.org/W4391862394","https://openalex.org/W4392381163","https://openalex.org/W4398216490","https://openalex.org/W4399940222","https://openalex.org/W4402389487","https://openalex.org/W4402790794","https://openalex.org/W6739901393","https://openalex.org/W6756040250","https://openalex.org/W6770852944","https://openalex.org/W6788003310","https://openalex.org/W6801755687"],"related_works":["https://openalex.org/W3208095355","https://openalex.org/W2177370417","https://openalex.org/W2052507016","https://openalex.org/W2180461068","https://openalex.org/W2051816080","https://openalex.org/W2004708907","https://openalex.org/W4310813911","https://openalex.org/W2377429601","https://openalex.org/W2386043911","https://openalex.org/W2021384951"],"abstract_inverted_index":{"Predicting":[0],"the":[1,13,30,39,44,78,83,97,158,176,185,217,221,227,239,243,274,284],"dynamics":[2,289],"of":[3,15,33,141,160,180,193,220,241,276,279,286],"chaotic":[4,65,114,181,257,287],"systems":[5,115,182],"is":[6,107],"crucial":[7],"across":[8],"various":[9],"practical":[10],"domains,":[11],"including":[12],"control":[14],"infectious":[16],"diseases":[17],"and":[18,41,134,205,225,230,245],"responses":[19],"to":[20,54,63,102,120,129,171,183,223],"extreme":[21],"weather":[22],"events.":[23],"Such":[24],"predictions":[25,93,106],"provide":[26],"quantitative":[27],"insights":[28],"into":[29],"future":[31,187],"behaviors":[32],"these":[34,69],"complex":[35],"systems,":[36,253],"thereby":[37],"guiding":[38],"decision-making":[40],"planning":[42],"within":[43],"respective":[45],"fields.":[46],"Recently,":[47],"data-driven":[48,198,244],"approaches,":[49],"renowned":[50],"for":[51],"their":[52,100,118],"capacity":[53],"learn":[55],"from":[56,208],"empirical":[57],"data,":[58,98],"have":[59],"been":[60],"widely":[61],"used":[62],"predict":[64,184],"system":[66,222,288],"dynamics.":[67,188],"However,":[68],"methods":[70],"rely":[71],"solely":[72],"on":[73,250],"historical":[74,209],"observations":[75],"while":[76],"ignoring":[77],"underlying":[79],"mechanisms":[80],"that":[81,201,215,236,260],"govern":[82],"systems'":[84,186],"behaviors.":[85],"Consequently,":[86],"they":[87],"may":[88],"perform":[89],"well":[90],"in":[91,112,117,132,282],"short-term":[92],"by":[94],"effectively":[95,237],"fitting":[96],"but":[99],"ability":[101],"make":[103],"accurate":[104,161],"long-term":[105],"limited.":[108],"A":[109],"critical":[110],"challenge":[111],"modeling":[113],"lies":[116],"sensitivity":[119],"initial":[121],"conditions;":[122],"even":[123],"a":[124,138,149,197,211,231],"slight":[125],"variation":[126],"can":[127],"lead":[128],"significant":[130],"divergence":[131],"actual":[133],"predicted":[135],"trajectories":[136],"over":[137],"finite":[139],"number":[140],"time":[142],"steps.":[143],"In":[144],"this":[145],"paper,":[146],"we":[147],"propose":[148],"novel":[150],"Physics-Guided":[151],"Learning":[152],"(PGL)":[153],"method,":[154],"aiming":[155],"at":[156],"extending":[157],"scope":[159],"forecasting":[162],"as":[163,165],"much":[164],"possible.":[166],"The":[167,271],"proposed":[168],"method":[169,191],"aims":[170],"synergize":[172],"observational":[173],"data":[174],"with":[175],"governing":[177,218],"physical":[178],"laws":[179],"Specifically,":[189],"our":[190,277],"consists":[192],"three":[194],"key":[195],"elements:":[196],"component":[199,213,234],"(DDC)":[200],"captures":[202],"dynamic":[203],"patterns":[204],"mapping":[206],"functions":[207],"data;":[210],"physics-guided":[212,246],"(PGC)":[214],"leverages":[216],"principles":[219],"inform":[224],"constrain":[226],"learning":[228,233],"process;":[229],"nonlinear":[232],"(NLC)":[235],"synthesizes":[238],"outputs":[240],"both":[242],"components.":[247],"Empirical":[248],"validation":[249],"six":[251],"dynamical":[252],"each":[254],"exhibiting":[255],"unique":[256],"behaviors,":[258],"demonstrates":[259],"PGL":[261],"achieves":[262],"lower":[263],"prediction":[264],"errors":[265],"than":[266],"existing":[267],"benchmark":[268],"predictive":[269],"models.":[270],"results":[272],"highlight":[273],"efficacy":[275],"design":[278],"data-physics":[280],"integration":[281],"improving":[283],"precision":[285],"forecasts.":[290]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2026-04-13T07:58:08.660418","created_date":"2025-10-10T00:00:00"}