{"id":"https://openalex.org/W4406179956","doi":"https://doi.org/10.3390/computation13010013","title":"Solving Nonlinear Energy Supply and Demand System Using Physics-Informed Neural Networks","display_name":"Solving Nonlinear Energy Supply and Demand System Using Physics-Informed Neural Networks","publication_year":2025,"publication_date":"2025-01-08","ids":{"openalex":"https://openalex.org/W4406179956","doi":"https://doi.org/10.3390/computation13010013"},"language":"en","primary_location":{"id":"doi:10.3390/computation13010013","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation13010013","pdf_url":"https://www.mdpi.com/2079-3197/13/1/13/pdf?version=1736345629","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2079-3197/13/1/13/pdf?version=1736345629","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5115812733","display_name":"Van Truong Vo","orcid":"https://orcid.org/0009-0008-2701-4775"},"institutions":[{"id":"https://openalex.org/I4210122217","display_name":"Irkutsk National Research Technical University","ror":"https://ror.org/01zzkcm34","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210122217"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Van Truong Vo","raw_affiliation_strings":["Scientific Research Department, Irkutsk National Research Technical University, 664074 Irkutsk, Russia"],"raw_orcid":"https://orcid.org/0009-0008-2701-4775","affiliations":[{"raw_affiliation_string":"Scientific Research Department, Irkutsk National Research Technical University, 664074 Irkutsk, Russia","institution_ids":["https://openalex.org/I4210122217"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056748367","display_name":"Samad Noeiaghdam","orcid":null},"institutions":[{"id":"https://openalex.org/I4210091706","display_name":"Henan Academy of Sciences","ror":"https://ror.org/00hy87220","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210091706"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Samad Noeiaghdam","raw_affiliation_strings":["Institute of Mathematics, Henan Academy of Sciences, Zhengzhou 450046, China"],"raw_orcid":"https://orcid.org/0000-0002-2307-0891","affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Henan Academy of Sciences, Zhengzhou 450046, China","institution_ids":["https://openalex.org/I4210091706"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084429273","display_name":"Denis Sidorov","orcid":"https://orcid.org/0000-0002-3131-1325"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]},{"id":"https://openalex.org/I4210114158","display_name":"Melentiev Energy Systems Institute","ror":"https://ror.org/02726j593","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210114158","https://openalex.org/I4210164537"]},{"id":"https://openalex.org/I4210122217","display_name":"Irkutsk National Research Technical University","ror":"https://ror.org/01zzkcm34","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210122217"]}],"countries":["CN","RU"],"is_corresponding":true,"raw_author_name":"Denis Sidorov","raw_affiliation_strings":["Applied Mathematics Department, Melentiev Energy Systems Institute, Siberian Branch of Russian Academy of Sciences, 664003 Irkutsk, Russia","School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China","Scientific Research Department, Irkutsk National Research Technical University, 664074 Irkutsk, Russia"],"raw_orcid":"https://orcid.org/0000-0002-3131-1325","affiliations":[{"raw_affiliation_string":"Applied Mathematics Department, Melentiev Energy Systems Institute, Siberian Branch of Russian Academy of Sciences, 664003 Irkutsk, Russia","institution_ids":["https://openalex.org/I4210114158"]},{"raw_affiliation_string":"School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China","institution_ids":["https://openalex.org/I204983213"]},{"raw_affiliation_string":"Scientific Research Department, Irkutsk National Research Technical University, 664074 Irkutsk, Russia","institution_ids":["https://openalex.org/I4210122217"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059347972","display_name":"Aliona Dreglea","orcid":"https://orcid.org/0000-0002-5032-0665"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]},{"id":"https://openalex.org/I4210122217","display_name":"Irkutsk National Research Technical University","ror":"https://ror.org/01zzkcm34","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210122217"]}],"countries":["CN","RU"],"is_corresponding":false,"raw_author_name":"Aliona Dreglea","raw_affiliation_strings":["School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China","Scientific Research Department, Irkutsk National Research Technical University, 664074 Irkutsk, Russia"],"raw_orcid":"https://orcid.org/0000-0002-5032-0665","affiliations":[{"raw_affiliation_string":"School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China","institution_ids":["https://openalex.org/I204983213"]},{"raw_affiliation_string":"Scientific Research Department, Irkutsk National Research Technical University, 664074 Irkutsk, Russia","institution_ids":["https://openalex.org/I4210122217"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100636415","display_name":"Liguo Wang","orcid":"https://orcid.org/0000-0002-4842-1029"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liguo Wang","raw_affiliation_strings":["School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China","institution_ids":["https://openalex.org/I204983213"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5084429273","https://openalex.org/A5115812733"],"corresponding_institution_ids":["https://openalex.org/I204983213","https://openalex.org/I4210114158","https://openalex.org/I4210122217"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":3.9187,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.92783204,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"13","issue":"1","first_page":"13","last_page":"13"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10603","display_name":"Smart Grid Energy Management","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10603","display_name":"Smart Grid Energy Management","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T11052","display_name":"Energy Load and Power Forecasting","score":0.9943000078201294,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10320","display_name":"Neural Networks and Applications","score":0.9825999736785889,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7100309729576111},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6589623093605042},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.4787535071372986},{"id":"https://openalex.org/keywords/energy-demand","display_name":"Energy demand","score":0.4572533965110779},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.42144858837127686},{"id":"https://openalex.org/keywords/energy-supply","display_name":"Energy supply","score":0.41106632351875305},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3922067880630493},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3744240403175354},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.34667736291885376},{"id":"https://openalex.org/keywords/theoretical-physics","display_name":"Theoretical physics","score":0.33235546946525574},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.18968051671981812},{"id":"https://openalex.org/keywords/natural-resource-economics","display_name":"Natural resource economics","score":0.1685386300086975},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1370793581008911}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7100309729576111},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6589623093605042},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.4787535071372986},{"id":"https://openalex.org/C2983177510","wikidata":"https://www.wikidata.org/wiki/Q1853339","display_name":"Energy demand","level":2,"score":0.4572533965110779},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.42144858837127686},{"id":"https://openalex.org/C2776190866","wikidata":"https://www.wikidata.org/wiki/Q1341477","display_name":"Energy supply","level":3,"score":0.41106632351875305},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3922067880630493},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3744240403175354},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.34667736291885376},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.33235546946525574},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.18968051671981812},{"id":"https://openalex.org/C175605778","wikidata":"https://www.wikidata.org/wiki/Q3299701","display_name":"Natural resource economics","level":1,"score":0.1685386300086975},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1370793581008911}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/computation13010013","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation13010013","pdf_url":"https://www.mdpi.com/2079-3197/13/1/13/pdf?version=1736345629","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computation","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:cd25d8f703284b24a84bf25aabb39130","is_oa":true,"landing_page_url":"https://doaj.org/article/cd25d8f703284b24a84bf25aabb39130","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":"Computation, Vol 13, Iss 1, p 13 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/computation13010013","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation13010013","pdf_url":"https://www.mdpi.com/2079-3197/13/1/13/pdf?version=1736345629","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.8999999761581421}],"awards":[{"id":"https://openalex.org/G6390015653","display_name":null,"funder_award_id":"241819246","funder_id":"https://openalex.org/F4320327494","funder_display_name":"Ministry of Science and Higher Education of the Russian Federation"},{"id":"https://openalex.org/G6806780606","display_name":null,"funder_award_id":"FZZS-2024-0003","funder_id":"https://openalex.org/F4320327494","funder_display_name":"Ministry of Science and Higher Education of the Russian Federation"}],"funders":[{"id":"https://openalex.org/F4320327494","display_name":"Ministry of Science and Higher Education of the Russian Federation","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4406179956.pdf","grobid_xml":"https://content.openalex.org/works/W4406179956.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1969768564","https://openalex.org/W2027197837","https://openalex.org/W2045949513","https://openalex.org/W2050560113","https://openalex.org/W2103496339","https://openalex.org/W2144144709","https://openalex.org/W2158985775","https://openalex.org/W2899283552","https://openalex.org/W2980777739","https://openalex.org/W3014009018","https://openalex.org/W3046775702","https://openalex.org/W3080730553","https://openalex.org/W3151861680","https://openalex.org/W3185095713","https://openalex.org/W4210871879","https://openalex.org/W4225995462","https://openalex.org/W4285807730","https://openalex.org/W4295261174","https://openalex.org/W4387607827","https://openalex.org/W4388869396","https://openalex.org/W4390513382","https://openalex.org/W4398193404","https://openalex.org/W4400766328","https://openalex.org/W4405330897"],"related_works":["https://openalex.org/W1993360808","https://openalex.org/W2014108059","https://openalex.org/W2605747790","https://openalex.org/W2500104883","https://openalex.org/W414067917","https://openalex.org/W2075000130","https://openalex.org/W3133017790","https://openalex.org/W2147476353","https://openalex.org/W2371783788","https://openalex.org/W2760552270"],"abstract_inverted_index":{"Nonlinear":[0],"differential":[1,79,180],"equations":[2,80,181],"and":[3,30,93,98,121,143,223,246,278,286,292,298],"systems":[4,11,25],"play":[5],"a":[6,37,54,64,102,141,183,253,284],"crucial":[7],"role":[8],"in":[9,74,159,264],"modeling":[10],"where":[12,60],"time-dependent":[13],"factors":[14,258],"exhibit":[15],"nonlinear":[16,21,47,76,177,202],"characteristics.":[17],"Due":[18],"to":[19,44,68,100,195,227],"their":[20],"nature,":[22],"solving":[23,160],"such":[24,272],"often":[26],"presents":[27],"significant":[28,221,254],"difficulties":[29],"challenges.":[31],"In":[32,186],"this":[33,114,218,235,260],"study,":[34],"we":[35,119],"propose":[36],"method":[38,128,135,236],"utilizing":[39,136],"Physics-Informed":[40],"Neural":[41],"Networks":[42],"(PINNs)":[43],"solve":[45,175],"the":[46,71,75,82,94,110,125,134,150,167,176,197,201,209,214,228,244,250,262,266,274],"energy":[48],"supply\u2013demand":[49],"(ESD)":[50],"system.":[51],"We":[52],"design":[53],"neural":[55,87,111,137,168,189,267],"network":[56,88,112,169,268],"with":[57],"four":[58],"outputs,":[59],"each":[61],"output":[62],"approximates":[63],"function":[65],"that":[66,166],"corresponds":[67],"one":[69],"of":[70,78,129,154,179,249,276],"unknown":[72],"functions":[73,199],"system":[77,178,204],"describing":[81],"four-dimensional":[83],"ESD":[84,203],"problem.":[85],"The":[86,106,256],"model":[89,231,251],"is":[90,139,165,237,270,283],"then":[91],"trained,":[92,173],"parameters":[95],"are":[96,116,191],"identified":[97],"optimized":[99],"achieve":[101],"more":[103],"accurate":[104],"solution.":[105],"solutions":[107],"obtained":[108],"from":[109],"for":[113,200,230],"problem":[115],"equivalent":[117],"when":[118],"compare":[120],"evaluate":[122],"them":[123],"against":[124],"Runge\u2013Kutta":[126],"numerical":[127],"order":[130],"5(4)":[131],"(RK45).":[132],"However,":[133,217],"networks":[138,190],"considered":[140],"modern":[142],"promising":[144],"approach,":[145],"as":[146,234,273],"it":[147],"effectively":[148],"exploits":[149],"superior":[151],"computational":[152,224],"power":[153,225],"advanced":[155],"computer":[156],"systems,":[157],"especially":[158],"complex":[161,210,288],"problems.":[162],"Another":[163],"advantage":[164],"model,":[170],"after":[171],"being":[172],"can":[174,206],"across":[182],"continuous":[184],"domain.":[185],"other":[187],"words,":[188],"not":[192],"only":[193],"trained":[194],"approximate":[196],"solution":[198],"but":[205],"also":[207],"represent":[208],"dynamic":[211],"relationships":[212],"between":[213],"system\u2019s":[215],"components.":[216],"approach":[219],"requires":[220],"time":[222],"due":[226],"need":[229],"training.":[232],"Furthermore,":[233],"evaluated":[238],"based":[239],"on":[240],"experimental":[241],"results,":[242],"ensuring":[243],"stability":[245],"convergence":[247],"speed":[248],"poses":[252],"challenge.":[255],"key":[257],"influencing":[259],"include":[261],"manner":[263],"which":[265,294],"architecture":[269],"designed,":[271],"selection":[275],"hyperparameters":[277],"appropriate":[279],"optimization":[280],"functions.":[281],"This":[282],"critical":[285],"highly":[287],"task,":[289],"requiring":[290],"experimentation":[291],"fine-tuning,":[293],"demand":[295],"substantial":[296],"expertise":[297],"time.":[299]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5}],"updated_date":"2026-03-08T06:56:09.383167","created_date":"2025-10-10T00:00:00"}
