{"id":"https://openalex.org/W4393405241","doi":"https://doi.org/10.1109/tetci.2024.3377671","title":"Physics-Informed Graph Capsule Generative Autoencoder for Probabilistic AC Optimal Power Flow","display_name":"Physics-Informed Graph Capsule Generative Autoencoder for Probabilistic AC Optimal Power Flow","publication_year":2024,"publication_date":"2024-04-02","ids":{"openalex":"https://openalex.org/W4393405241","doi":"https://doi.org/10.1109/tetci.2024.3377671"},"language":"en","primary_location":{"id":"doi:10.1109/tetci.2024.3377671","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tetci.2024.3377671","pdf_url":null,"source":{"id":"https://openalex.org/S4210210251","display_name":"IEEE Transactions on Emerging Topics in Computational Intelligence","issn_l":"2471-285X","issn":["2471-285X"],"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 Emerging Topics in Computational Intelligence","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/A5052831041","display_name":"Mohsen Saffari","orcid":"https://orcid.org/0000-0002-8336-8542"},"institutions":[{"id":"https://openalex.org/I87208437","display_name":"University of Tulsa","ror":"https://ror.org/04wn28048","country_code":"US","type":"education","lineage":["https://openalex.org/I87208437"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Mohsen Saffari","raw_affiliation_strings":["Department of Computer Science, University of Tulsa, Tulsa, OK, USA"],"raw_orcid":"https://orcid.org/0000-0002-8336-8542","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Tulsa, Tulsa, OK, USA","institution_ids":["https://openalex.org/I87208437"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037009406","display_name":"Mahdi Khodayar","orcid":"https://orcid.org/0000-0003-4683-7810"},"institutions":[{"id":"https://openalex.org/I87208437","display_name":"University of Tulsa","ror":"https://ror.org/04wn28048","country_code":"US","type":"education","lineage":["https://openalex.org/I87208437"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mahdi Khodayar","raw_affiliation_strings":["Department of Computer Science, University of Tulsa, Tulsa, OK, USA"],"raw_orcid":"https://orcid.org/0000-0003-4683-7810","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Tulsa, Tulsa, OK, USA","institution_ids":["https://openalex.org/I87208437"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019296796","display_name":"Mohammad E. Khodayar","orcid":"https://orcid.org/0000-0003-3856-5704"},"institutions":[{"id":"https://openalex.org/I178169726","display_name":"Southern Methodist University","ror":"https://ror.org/042tdr378","country_code":"US","type":"education","lineage":["https://openalex.org/I178169726"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mohammad E. Khodayar","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Southern Methodist University, Dallas, TX, USA"],"raw_orcid":"https://orcid.org/0000-0003-3856-5704","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Southern Methodist University, Dallas, TX, USA","institution_ids":["https://openalex.org/I178169726"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5052831041"],"corresponding_institution_ids":["https://openalex.org/I87208437"],"apc_list":null,"apc_paid":null,"fwci":3.108,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.91838478,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"8","issue":"5","first_page":"3382","last_page":"3395"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11052","display_name":"Energy Load and Power Forecasting","score":0.9944000244140625,"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/T11052","display_name":"Energy Load and Power Forecasting","score":0.9944000244140625,"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/T11941","display_name":"Power System Reliability and Maintenance","score":0.9868000149726868,"subfield":{"id":"https://openalex.org/subfields/2213","display_name":"Safety, Risk, Reliability and Quality"},"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/T11343","display_name":"Power Transformer Diagnostics and Insulation","score":0.9822999835014343,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/autoencoder","display_name":"Autoencoder","score":0.6929929256439209},{"id":"https://openalex.org/keywords/generative-grammar","display_name":"Generative grammar","score":0.6669578552246094},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.6397984623908997},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5645552277565002},{"id":"https://openalex.org/keywords/power-flow","display_name":"Power flow","score":0.4770966172218323},{"id":"https://openalex.org/keywords/capsule","display_name":"Capsule","score":0.4686657190322876},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.4120684564113617},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3944341838359833},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.3794195055961609},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.35666394233703613},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.31907498836517334},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.24327760934829712},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.23348525166511536},{"id":"https://openalex.org/keywords/electric-power-system","display_name":"Electric power system","score":0.13488110899925232},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.1320784091949463},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.0940915048122406},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08916854858398438}],"concepts":[{"id":"https://openalex.org/C101738243","wikidata":"https://www.wikidata.org/wiki/Q786435","display_name":"Autoencoder","level":3,"score":0.6929929256439209},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.6669578552246094},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6397984623908997},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5645552277565002},{"id":"https://openalex.org/C2986056383","wikidata":"https://www.wikidata.org/wiki/Q556030","display_name":"Power flow","level":4,"score":0.4770966172218323},{"id":"https://openalex.org/C2778778583","wikidata":"https://www.wikidata.org/wiki/Q147768","display_name":"Capsule","level":2,"score":0.4686657190322876},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4120684564113617},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3944341838359833},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.3794195055961609},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.35666394233703613},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.31907498836517334},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24327760934829712},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.23348525166511536},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.13488110899925232},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.1320784091949463},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.0940915048122406},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08916854858398438},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tetci.2024.3377671","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tetci.2024.3377671","pdf_url":null,"source":{"id":"https://openalex.org/S4210210251","display_name":"IEEE Transactions on Emerging Topics in Computational Intelligence","issn_l":"2471-285X","issn":["2471-285X"],"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 Emerging Topics in Computational Intelligence","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.800000011920929,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W2033769630","https://openalex.org/W2106424475","https://openalex.org/W2560227968","https://openalex.org/W2578211507","https://openalex.org/W2793916350","https://openalex.org/W2807887237","https://openalex.org/W2807966350","https://openalex.org/W2890449072","https://openalex.org/W2914005633","https://openalex.org/W2938947773","https://openalex.org/W2954494862","https://openalex.org/W2987233755","https://openalex.org/W2994480493","https://openalex.org/W2997109357","https://openalex.org/W3011806874","https://openalex.org/W3016983759","https://openalex.org/W3034797134","https://openalex.org/W3034990881","https://openalex.org/W3039305152","https://openalex.org/W3048042099","https://openalex.org/W3086709907","https://openalex.org/W3088315405","https://openalex.org/W3112157041","https://openalex.org/W3115185893","https://openalex.org/W3117855720","https://openalex.org/W3130601125","https://openalex.org/W3136797957","https://openalex.org/W3152547783","https://openalex.org/W3153200540","https://openalex.org/W3202966491","https://openalex.org/W3205582757","https://openalex.org/W3207906311","https://openalex.org/W3209586344","https://openalex.org/W4205669430","https://openalex.org/W4231109964","https://openalex.org/W4250235493","https://openalex.org/W4285081983","https://openalex.org/W4287729747","https://openalex.org/W4292313857","https://openalex.org/W4312375505","https://openalex.org/W4317521089","https://openalex.org/W4381327818","https://openalex.org/W6726873649","https://openalex.org/W6743446608","https://openalex.org/W6779850432","https://openalex.org/W7069948914"],"related_works":["https://openalex.org/W3013693939","https://openalex.org/W2159052453","https://openalex.org/W2566616303","https://openalex.org/W3131327266","https://openalex.org/W2734887215","https://openalex.org/W4297051394","https://openalex.org/W2752972570","https://openalex.org/W2145836866","https://openalex.org/W2803255133","https://openalex.org/W2909431601"],"abstract_inverted_index":{"Due":[0],"to":[1,17,113,129,158,188,191],"the":[2,8,18,31,40,45,75,82,98,119,131,139,142,161,166,182,186,192,200,208,216,224],"increasing":[3],"demand":[4],"for":[5,88],"electricity":[6],"and":[7,33,57,91,105,164,242],"inherent":[9],"uncertainty":[10],"in":[11,54,77,181,245],"power":[12,23,78,99,197],"generation,":[13],"finding":[14],"efficient":[15],"solutions":[16],"stochastic":[19],"alternating":[20],"current":[21],"optimal":[22],"flow":[24],"(AC-OPF)":[25],"problem":[26],"has":[27],"become":[28],"crucial.":[29],"However,":[30],"nonlinear":[32],"non-convex":[34],"nature":[35],"of":[36,47,84,141,173,185,210,247],"AC-OPF,":[37],"coupled":[38],"with":[39,149],"growing":[41],"stochasticity":[42],"resulting":[43],"from":[44,118],"integration":[46],"renewable":[48],"energy":[49],"sources,":[50],"presents":[51],"significant":[52],"challenges":[53],"achieving":[55],"fast":[56],"reliable":[58],"solutions.":[59],"To":[60],"address":[61],"these":[62],"challenges,":[63],"this":[64],"study":[65],"proposes":[66],"a":[67,102,107,146,150,171],"novel":[68],"graph-based":[69],"generative":[70],"methodology":[71],"that":[72,136],"effectively":[73,214],"captures":[74],"uncertainties":[76],"system":[79,100],"measurements,":[80],"enabling":[81],"learning":[83,218],"probability":[85],"distribution":[86],"functions":[87,178,204],"generation":[89],"dispatch":[90],"voltage":[92],"setpoints.":[93],"Our":[94],"approach":[95,126],"involves":[96],"modeling":[97],"as":[101],"weighted":[103],"graph":[104,110,121],"utilizing":[106],"deep":[108,217],"spectral":[109],"convolution":[111],"network":[112,148],"extract":[114],"powerful":[115],"spatial":[116],"patterns":[117],"input":[120],"measurements.":[122],"A":[123],"unique":[124],"variational":[125],"is":[127,156,179],"introduced":[128],"identify":[130],"most":[132],"relevant":[133,248],"latent":[134,162],"features":[135,163],"accurately":[137],"describe":[138],"setpoints":[140],"AC-OPF":[143,168,211],"problem.":[144,169],"Additionally,":[145],"capsule":[147],"new":[151],"greedy":[152],"dynamic":[153],"routing":[154],"algorithm":[155],"proposed":[157,201,236],"precisely":[159],"decode":[160],"estimate":[165],"probabilistic":[167,241],"Further,":[170],"set":[172],"carefully":[174],"designed":[175],"physics-informed":[176,202],"loss":[177,203],"incorporated":[180],"training":[183],"procedure":[184],"model":[187,219],"ensure":[189],"adherence":[190],"fundamental":[193],"physics":[194],"rules":[195],"governing":[196],"systems.":[198],"Notably,":[199],"not":[205],"only":[206],"enhance":[207],"accuracy":[209],"estimation":[212],"by":[213],"regularizing":[215],"but":[220],"also":[221],"significantly":[222],"reduce":[223],"time":[225],"complexity.":[226],"Extensive":[227],"experimental":[228],"evaluations":[229],"conducted":[230],"on":[231],"various":[232],"benchmarks":[233],"demonstrate":[234],"our":[235],"model's":[237],"superiority":[238],"over":[239],"both":[240],"deterministic":[243],"approaches":[244],"terms":[246],"criteria.":[249]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":13}],"updated_date":"2026-05-14T08:36:36.166977","created_date":"2025-10-10T00:00:00"}
