{"id":"https://openalex.org/W4391963294","doi":"https://doi.org/10.54097/b1d21816","title":"Machine Learning Through Physics\u2013Informed Neural Networks: Progress and Challenges","display_name":"Machine Learning Through Physics\u2013Informed Neural Networks: Progress and Challenges","publication_year":2024,"publication_date":"2024-01-20","ids":{"openalex":"https://openalex.org/W4391963294","doi":"https://doi.org/10.54097/b1d21816"},"language":"en","primary_location":{"id":"doi:10.54097/b1d21816","doi":"https://doi.org/10.54097/b1d21816","is_oa":true,"landing_page_url":"https://doi.org/10.54097/b1d21816","pdf_url":"https://drpress.org/ojs/index.php/ajst/article/download/16292/15810","source":{"id":"https://openalex.org/S4220651530","display_name":"Academic Journal of Science and Technology","issn_l":"2771-3032","issn":["2771-3032"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Academic Journal of Science and Technology","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://drpress.org/ojs/index.php/ajst/article/download/16292/15810","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093962356","display_name":"Klapa Antonion","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I80606768","display_name":"Universidad de Extremadura","ror":"https://ror.org/0174shg90","country_code":"ES","type":"education","lineage":["https://openalex.org/I80606768"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Klapa Antonion","raw_affiliation_strings":["Department of Technology of Computers and Communications, University of Extremadura, 10071 Caceres, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Technology of Computers and Communications, University of Extremadura, 10071 Caceres, Spain","institution_ids":["https://openalex.org/I80606768"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100411532","display_name":"Xiao Wang","orcid":"https://orcid.org/0000-0003-4435-7098","observed_orcids":["https://orcid.org/0000-0003-4435-7098"]},"institutions":[{"id":"https://openalex.org/I80606768","display_name":"Universidad de Extremadura","ror":"https://ror.org/0174shg90","country_code":"ES","type":"education","lineage":["https://openalex.org/I80606768"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Xiao Wang","raw_affiliation_strings":["Department of Technology of Computers and Communications, University of Extremadura, 10071 Caceres, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Technology of Computers and Communications, University of Extremadura, 10071 Caceres, Spain","institution_ids":["https://openalex.org/I80606768"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012536010","display_name":"Maziar Raissi","orcid":"https://orcid.org/0000-0002-8467-4568","observed_orcids":["https://orcid.org/0000-0002-8467-4568"]},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"The University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Maziar Raissi","raw_affiliation_strings":["Department of Applied Mathematics, The University of Sydney, Sydney, NSW 2006, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, The University of Sydney, Sydney, NSW 2006, Australia","institution_ids":["https://openalex.org/I129604602"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5093962357","display_name":"Laurn Joshie","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"The University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Laurn Joshie","raw_affiliation_strings":["Department of Applied Mathematics, The University of Sydney, Sydney, NSW 2006, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, The University of Sydney, Sydney, NSW 2006, Australia","institution_ids":["https://openalex.org/I129604602"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100411532"],"corresponding_institution_ids":["https://openalex.org/I80606768"],"apc_list":null,"apc_paid":null,"fwci":5.8325,"has_fulltext":true,"cited_by_count":40,"citation_normalized_percentile":{"value":0.97600386,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"9","issue":"1","first_page":"46","last_page":"49"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":1.0,"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":1.0,"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/T10320","display_name":"Neural Networks and Applications","score":0.0,"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/T11416","display_name":"Numerical methods for differential equations","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/physics-informed-neural-networks","display_name":"physics-informed neural networks","score":1.0},{"id":"https://openalex.org/keywords/partial-differential-equations","display_name":"partial differential equations","score":0.9279999732971191},{"id":"https://openalex.org/keywords/fractional-differential-equations","display_name":"fractional differential equations","score":0.7739999890327454},{"id":"https://openalex.org/keywords/integro-differential-equations","display_name":"integro-differential equations","score":0.9100000262260437},{"id":"https://openalex.org/keywords/stochastic-partial-differential-equations","display_name":"stochastic partial differential equations","score":0.890999972820282},{"id":"https://openalex.org/keywords/physics-constrained-neural-networks","display_name":"physics-constrained neural networks","score":0.9129999876022339},{"id":"https://openalex.org/keywords/activation-function-design","display_name":"activation function design","score":0.6179999709129333},{"id":"https://openalex.org/keywords/gradient-based-optimization","display_name":"gradient-based optimization","score":0.9229999780654907},{"id":"https://openalex.org/keywords/loss-function-design","display_name":"loss function design","score":0.9580000042915344}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5717642307281494},{"id":"https://openalex.org/C188147891","wikidata":"https://www.wikidata.org/wiki/Q147638","display_name":"Cognitive science","level":1,"score":0.4218951165676117},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3755718469619751},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.367728054523468},{"id":"https://openalex.org/C55587333","wikidata":"https://www.wikidata.org/wiki/Q1133029","display_name":"Engineering ethics","level":1,"score":0.3475920557975769},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.26282334327697754},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.1797773540019989}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.54097/b1d21816","doi":"https://doi.org/10.54097/b1d21816","is_oa":true,"landing_page_url":"https://doi.org/10.54097/b1d21816","pdf_url":"https://drpress.org/ojs/index.php/ajst/article/download/16292/15810","source":{"id":"https://openalex.org/S4220651530","display_name":"Academic Journal of Science and Technology","issn_l":"2771-3032","issn":["2771-3032"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Academic Journal of Science and Technology","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.54097/b1d21816","doi":"https://doi.org/10.54097/b1d21816","is_oa":true,"landing_page_url":"https://doi.org/10.54097/b1d21816","pdf_url":"https://drpress.org/ojs/index.php/ajst/article/download/16292/15810","source":{"id":"https://openalex.org/S4220651530","display_name":"Academic Journal of Science and Technology","issn_l":"2771-3032","issn":["2771-3032"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Academic Journal of Science and Technology","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4391963294.pdf","grobid_xml":"https://content.openalex.org/works/W4391963294.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W279073656","https://openalex.org/W1600371943","https://openalex.org/W1856502440","https://openalex.org/W1970454553","https://openalex.org/W1978075626","https://openalex.org/W2745110207","https://openalex.org/W2770250658","https://openalex.org/W2886364848","https://openalex.org/W2899283552","https://openalex.org/W2902028058","https://openalex.org/W2948449500","https://openalex.org/W2955939954","https://openalex.org/W3010145426","https://openalex.org/W3080475323","https://openalex.org/W3097739104","https://openalex.org/W3101260193","https://openalex.org/W3131579400","https://openalex.org/W3136841107","https://openalex.org/W3169194923","https://openalex.org/W3176116059","https://openalex.org/W3205073660","https://openalex.org/W4200560982","https://openalex.org/W4224235076","https://openalex.org/W4224621006","https://openalex.org/W4224903982","https://openalex.org/W4287378181","https://openalex.org/W4318465483","https://openalex.org/W4323557148","https://openalex.org/W4323828899","https://openalex.org/W4385343761","https://openalex.org/W4385767688","https://openalex.org/W4387185421","https://openalex.org/W4390874033","https://openalex.org/W6600248585","https://openalex.org/W6600339963","https://openalex.org/W6604381581","https://openalex.org/W6605114435","https://openalex.org/W6641950794","https://openalex.org/W7133190560"],"related_works":["https://openalex.org/W4288039037","https://openalex.org/W7134113974","https://openalex.org/W7125404100","https://openalex.org/W4410082238","https://openalex.org/W7204037396","https://openalex.org/W4409990577","https://openalex.org/W4409396987","https://openalex.org/W4410111481","https://openalex.org/W4406782206","https://openalex.org/W4415405371"],"abstract_inverted_index":{"Physics-Informed":[0],"Neural":[1],"Networks":[2],"(PINNs)":[3],"represent":[4],"a":[5,44,90,125],"groundbreaking":[6],"approach":[7],"wherein":[8],"neural":[9,96,107,144],"networks":[10,108],"(NNs)":[11],"integrate":[12],"model":[13],"equations,":[14,37,39],"such":[15],"as":[16],"Partial":[17],"Differential":[18],"Equations":[19],"(PDEs),":[20],"within":[21],"their":[22,72],"architecture.":[23],"This":[24,61],"innovation":[25],"has":[26],"become":[27],"instrumental":[28],"in":[29,128,168],"solving":[30],"diverse":[31,134],"problem":[32],"sets":[33],"including":[34],"PDEs,":[35],"fractional":[36],"integral-differential":[38],"and":[40,75,112,147,191],"stochastic":[41],"PDEs.":[42],"It's":[43],"versatile":[45],"multi-task":[46],"learning":[47],"framework":[48],"that":[49,184],"tasks":[50],"NNs":[51],"with":[52],"fitting":[53],"observed":[54],"data":[55],"while":[56],"simultaneously":[57],"minimizing":[58],"PDE":[59],"residuals.":[60],"paper":[62],"delves":[63],"into":[64],"the":[65,79,100,153,171,188],"landscape":[66],"of":[67,82,93,119,193],"PINNs,":[68,158],"aiming":[69],"to":[70,88],"delineate":[71],"inherent":[73],"strengths":[74],"weaknesses.":[76],"Beyond":[77],"exploring":[78],"fundamental":[80],"characteristics":[81],"these":[83],"networks,":[84,97],"this":[85,120,194],"review":[86,172],"endeavors":[87],"encompass":[89],"wider":[91],"spectrum":[92],"collocation-based":[94],"physics-informed":[95],"extending":[98],"beyond":[99],"core":[101],"PINN":[102,114],"model.":[103],"Variants":[104],"like":[105,163],"physics-constrained":[106],"(PCNN),":[109],"variational":[110],"hp-VPINN,":[111],"conservative":[113],"(CPINN)":[115],"constitute":[116],"pivotal":[117],"aspects":[118],"exploration.":[121],"The":[122],"study":[123],"accentuates":[124],"predominant":[126],"focus":[127],"research":[129],"on":[130],"tailoring":[131],"PINNs":[132],"through":[133],"strategies:":[135],"adapting":[136],"activation":[137],"functions,":[138],"refining":[139],"gradient":[140],"optimization":[141],"techniques,":[142],"innovating":[143],"network":[145],"structures,":[146],"enhancing":[148],"loss":[149],"function":[150],"architectures.":[151],"Despite":[152],"extensive":[154],"applicability":[155],"demonstrated":[156],"by":[157],"surpassing":[159],"classical":[160],"numerical":[161],"methods":[162],"Finite":[164],"Element":[165],"Method":[166],"(FEM)":[167],"certain":[169],"contexts,":[170],"highlights":[173],"ongoing":[174],"opportunities":[175],"for":[176],"advancement.":[177],"Notably,":[178],"there":[179],"are":[180],"persisting":[181],"theoretical":[182],"challenges":[183],"demand":[185],"resolution,":[186],"ensuring":[187],"continued":[189],"evolution":[190],"refinement":[192],"revolutionary":[195],"approach.":[196]},"counts_by_year":[{"year":2026,"cited_by_count":15},{"year":2025,"cited_by_count":19},{"year":2024,"cited_by_count":6}],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2024-02-21T00:00:00"}