{"id":"https://openalex.org/W4390671307","doi":"https://doi.org/10.1115/1.4064449","title":"Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks and Operators in Scientific Computing: Fluid and Solid Mechanics","display_name":"Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks and Operators in Scientific Computing: Fluid and Solid Mechanics","publication_year":2024,"publication_date":"2024-01-08","ids":{"openalex":"https://openalex.org/W4390671307","doi":"https://doi.org/10.1115/1.4064449"},"language":"en","primary_location":{"id":"doi:10.1115/1.4064449","is_oa":false,"landing_page_url":"https://doi.org/10.1115/1.4064449","pdf_url":null,"source":{"id":"https://openalex.org/S173178594","display_name":"Journal of Computing and Information Science in Engineering","issn_l":"1530-9827","issn":["1530-9827","1944-7078"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310316053","host_organization_name":"ASM International","host_organization_lineage":["https://openalex.org/P4310316053"],"host_organization_lineage_names":["ASM International"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computing and Information Science in Engineering","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/A5046183234","display_name":"Salah A. Faroughi","orcid":"https://orcid.org/0000-0002-6543-1691"},"institutions":[{"id":"https://openalex.org/I13511017","display_name":"Texas State University","ror":"https://ror.org/05h9q1g27","country_code":"US","type":"education","lineage":["https://openalex.org/I13511017"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Salah A. Faroughi","raw_affiliation_strings":["Texas State University Geo-Intelligence Laboratory, Ingram School of Engineering, , San Marcos, TX 78666"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Texas State University Geo-Intelligence Laboratory, Ingram School of Engineering, , San Marcos, TX 78666","institution_ids":["https://openalex.org/I13511017"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079315042","display_name":"Nikhil M. Pawar","orcid":"https://orcid.org/0000-0002-1161-3289"},"institutions":[{"id":"https://openalex.org/I13511017","display_name":"Texas State University","ror":"https://ror.org/05h9q1g27","country_code":"US","type":"education","lineage":["https://openalex.org/I13511017"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nikhil M. Pawar","raw_affiliation_strings":["Texas State University Geo-Intelligence Laboratory, Ingram School of Engineering, , San Marcos, TX 78666"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Texas State University Geo-Intelligence Laboratory, Ingram School of Engineering, , San Marcos, TX 78666","institution_ids":["https://openalex.org/I13511017"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078610236","display_name":"C\u00e9lio Fernandes","orcid":"https://orcid.org/0000-0002-0340-3556"},"institutions":[{"id":"https://openalex.org/I13511017","display_name":"Texas State University","ror":"https://ror.org/05h9q1g27","country_code":"US","type":"education","lineage":["https://openalex.org/I13511017"]},{"id":"https://openalex.org/I99682543","display_name":"University of Minho","ror":"https://ror.org/037wpkx04","country_code":"PT","type":"education","lineage":["https://openalex.org/I99682543"]}],"countries":["PT","US"],"is_corresponding":false,"raw_author_name":"C\u00e9lio Fernandes","raw_affiliation_strings":["Texas State University Geo-Intelligence Laboratory, Ingram School of Engineering, , San Marcos, TX 78666 ; Centre of Mathematics (CMAT), , Campus of Gualtar, 4710-057 Braga ,","University of Minho Geo-Intelligence Laboratory, Ingram School of Engineering, , San Marcos, TX 78666 ; Centre of Mathematics (CMAT), , Campus of Gualtar, 4710-057 Braga ,","Rua Dr. Roberto Frias s/n Porto, 4200-465 Portugal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Texas State University Geo-Intelligence Laboratory, Ingram School of Engineering, , San Marcos, TX 78666 ; Centre of Mathematics (CMAT), , Campus of Gualtar, 4710-057 Braga ,","institution_ids":["https://openalex.org/I13511017"]},{"raw_affiliation_string":"University of Minho Geo-Intelligence Laboratory, Ingram School of Engineering, , San Marcos, TX 78666 ; Centre of Mathematics (CMAT), , Campus of Gualtar, 4710-057 Braga ,","institution_ids":["https://openalex.org/I99682543"]},{"raw_affiliation_string":"Rua Dr. Roberto Frias s/n Porto, 4200-465 Portugal","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012536010","display_name":"Maziar Raissi","orcid":"https://orcid.org/0000-0002-8467-4568"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Maziar Raissi","raw_affiliation_strings":["University of Colorado Boulder Department of Applied Mathematics, , Boulder, CO 610101"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Colorado Boulder Department of Applied Mathematics, , Boulder, CO 610101","institution_ids":["https://openalex.org/I188538660"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053621729","display_name":"Subasish Das","orcid":"https://orcid.org/0000-0002-1671-2753"},"institutions":[{"id":"https://openalex.org/I13511017","display_name":"Texas State University","ror":"https://ror.org/05h9q1g27","country_code":"US","type":"education","lineage":["https://openalex.org/I13511017"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Subasish Das","raw_affiliation_strings":["Texas State University Artificial Intelligence in Transportation Lab, Ingram School of Engineering, , San Marcos, TX 78666"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Texas State University Artificial Intelligence in Transportation Lab, Ingram School of Engineering, , San Marcos, TX 78666","institution_ids":["https://openalex.org/I13511017"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037113425","display_name":"Nima K. Kalantari","orcid":null},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nima K. Kalantari","raw_affiliation_strings":["Texas A&M University Computer Science and Engineering Department, , College Station, TX 77843"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Texas A&M University Computer Science and Engineering Department, , College Station, TX 77843","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054870315","display_name":"Seyed Kourosh Mahjour","orcid":"https://orcid.org/0000-0001-7825-9707"},"institutions":[{"id":"https://openalex.org/I13511017","display_name":"Texas State University","ror":"https://ror.org/05h9q1g27","country_code":"US","type":"education","lineage":["https://openalex.org/I13511017"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Seyed Kourosh Mahjour","raw_affiliation_strings":["Texas State University Geo-Intelligence Laboratory, Ingram School of Engineering, , San Marcos, TX 78666"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Texas State University Geo-Intelligence Laboratory, Ingram School of Engineering, , San Marcos, TX 78666","institution_ids":["https://openalex.org/I13511017"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5046183234"],"corresponding_institution_ids":["https://openalex.org/I13511017"],"apc_list":null,"apc_paid":null,"fwci":47.0941,"has_fulltext":false,"cited_by_count":180,"citation_normalized_percentile":{"value":0.9996828,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"24","issue":"4","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":0.9998000264167786,"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":0.9998000264167786,"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/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10104","display_name":"Nanofluid Flow and Heat Transfer","score":0.9914000034332275,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/multiphysics","display_name":"Multiphysics","score":0.7588468790054321},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6712073087692261},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5620222687721252},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.5166947841644287},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4867513179779053},{"id":"https://openalex.org/keywords/nervous-system-network-models","display_name":"Nervous system network models","score":0.425792932510376},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.34273675084114075},{"id":"https://openalex.org/keywords/recurrent-neural-network","display_name":"Recurrent neural network","score":0.3302440047264099},{"id":"https://openalex.org/keywords/types-of-artificial-neural-networks","display_name":"Types of artificial neural networks","score":0.2971814274787903},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2907300889492035},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.1500166654586792}],"concepts":[{"id":"https://openalex.org/C46435376","wikidata":"https://www.wikidata.org/wiki/Q1829750","display_name":"Multiphysics","level":3,"score":0.7588468790054321},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6712073087692261},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5620222687721252},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.5166947841644287},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4867513179779053},{"id":"https://openalex.org/C173079777","wikidata":"https://www.wikidata.org/wiki/Q4299350","display_name":"Nervous system network models","level":5,"score":0.425792932510376},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.34273675084114075},{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.3302440047264099},{"id":"https://openalex.org/C177973122","wikidata":"https://www.wikidata.org/wiki/Q7860946","display_name":"Types of artificial neural networks","level":4,"score":0.2971814274787903},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2907300889492035},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.1500166654586792},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1115/1.4064449","is_oa":false,"landing_page_url":"https://doi.org/10.1115/1.4064449","pdf_url":null,"source":{"id":"https://openalex.org/S173178594","display_name":"Journal of Computing and Information Science in Engineering","issn_l":"1530-9827","issn":["1530-9827","1944-7078"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310316053","host_organization_name":"ASM International","host_organization_lineage":["https://openalex.org/P4310316053"],"host_organization_lineage_names":["ASM International"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computing and Information Science in Engineering","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.46000000834465027,"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure"}],"awards":[{"id":"https://openalex.org/G1536945442","display_name":null,"funder_award_id":"66452-DNI9","funder_id":"https://openalex.org/F4320332454","funder_display_name":"American Chemical Society Petroleum Research Fund"},{"id":"https://openalex.org/G3244154915","display_name":null,"funder_award_id":"DE-SC0023044","funder_id":"https://openalex.org/F4320337509","funder_display_name":"Biological and Environmental Research"},{"id":"https://openalex.org/G6552381984","display_name":null,"funder_award_id":"DMR-2122041","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G76585310","display_name":null,"funder_award_id":"MIRG-9000003028","funder_id":"https://openalex.org/F4320310830","funder_display_name":"Texas State University"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320310830","display_name":"Texas State University","ror":"https://ror.org/009ey6w22"},{"id":"https://openalex.org/F4320332454","display_name":"American Chemical Society Petroleum Research Fund","ror":"https://ror.org/059dqb057"},{"id":"https://openalex.org/F4320337509","display_name":"Biological and Environmental Research","ror":"https://ror.org/0114b2m14"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":427,"referenced_works":["https://openalex.org/W171432391","https://openalex.org/W175001303","https://openalex.org/W298249810","https://openalex.org/W574962919","https://openalex.org/W581347801","https://openalex.org/W1262895620","https://openalex.org/W1485009520","https://openalex.org/W1497534795","https://openalex.org/W1498436455","https://openalex.org/W1597927018","https://openalex.org/W1853291804","https://openalex.org/W1856502440","https://openalex.org/W1886421468","https://openalex.org/W1940872118","https://openalex.org/W1969696351","https://openalex.org/W1970454553","https://openalex.org/W1982151782","https://openalex.org/W1984426476","https://openalex.org/W1991832796","https://openalex.org/W1995791682","https://openalex.org/W1998646770","https://openalex.org/W2003361850","https://openalex.org/W2007233074","https://openalex.org/W2015588933","https://openalex.org/W2021960576","https://openalex.org/W2027053193","https://openalex.org/W2029083633","https://openalex.org/W2030676195","https://openalex.org/W2034997378","https://openalex.org/W2043979833","https://openalex.org/W2049141364","https://openalex.org/W2050962398","https://openalex.org/W2053635242","https://openalex.org/W2072566913","https://openalex.org/W2073775990","https://openalex.org/W2074616700","https://openalex.org/W2075473759","https://openalex.org/W2079263908","https://openalex.org/W2080977367","https://openalex.org/W2095705004","https://openalex.org/W2104070031","https://openalex.org/W2110493966","https://openalex.org/W2111072639","https://openalex.org/W2112796928","https://openalex.org/W2114424556","https://openalex.org/W2116341502","https://openalex.org/W2121713565","https://openalex.org/W2132622721","https://openalex.org/W2139923370","https://openalex.org/W2164699887","https://openalex.org/W2170612190","https://openalex.org/W2183351193","https://openalex.org/W2194775991","https://openalex.org/W2220999736","https://openalex.org/W2291618559","https://openalex.org/W2302255633","https://openalex.org/W2334591577","https://openalex.org/W2356652130","https://openalex.org/W2476548250","https://openalex.org/W2501995758","https://openalex.org/W2502067955","https://openalex.org/W2534240011","https://openalex.org/W2553754377","https://openalex.org/W2574952845","https://openalex.org/W2574963492","https://openalex.org/W2585298970","https://openalex.org/W2594632285","https://openalex.org/W2595317701","https://openalex.org/W2736092219","https://openalex.org/W2752032793","https://openalex.org/W2765811365","https://openalex.org/W2772097715","https://openalex.org/W2784350055","https://openalex.org/W2784733489","https://openalex.org/W2785024182","https://openalex.org/W2785071288","https://openalex.org/W2800872951","https://openalex.org/W2803594690","https://openalex.org/W2807841289","https://openalex.org/W2808943413","https://openalex.org/W2809078955","https://openalex.org/W2811815171","https://openalex.org/W2884430236","https://openalex.org/W2885195348","https://openalex.org/W2887432454","https://openalex.org/W2891039272","https://openalex.org/W2896796166","https://openalex.org/W2898456550","https://openalex.org/W2899283552","https://openalex.org/W2902809050","https://openalex.org/W2903166210","https://openalex.org/W2907522752","https://openalex.org/W2908541468","https://openalex.org/W2913467712","https://openalex.org/W2913594191","https://openalex.org/W2917178248","https://openalex.org/W2919115771","https://openalex.org/W2924210888","https://openalex.org/W2936357167","https://openalex.org/W2939407295","https://openalex.org/W2946771678","https://openalex.org/W2947047078","https://openalex.org/W2949547603","https://openalex.org/W2951392159","https://openalex.org/W2962727772","https://openalex.org/W2963755523","https://openalex.org/W2972267209","https://openalex.org/W2972758939","https://openalex.org/W2973119841","https://openalex.org/W2973886134","https://openalex.org/W2976793329","https://openalex.org/W2977796156","https://openalex.org/W2979017369","https://openalex.org/W2979786244","https://openalex.org/W2980435522","https://openalex.org/W2982417218","https://openalex.org/W2984973432","https://openalex.org/W2985383053","https://openalex.org/W2990714382","https://openalex.org/W2993795140","https://openalex.org/W2994408221","https://openalex.org/W2996028791","https://openalex.org/W2997814214","https://openalex.org/W2998004632","https://openalex.org/W2998366519","https://openalex.org/W2998830881","https://openalex.org/W3004619146","https://openalex.org/W3004857598","https://openalex.org/W3005106966","https://openalex.org/W3005172792","https://openalex.org/W3008419421","https://openalex.org/W3010415407","https://openalex.org/W3010839048","https://openalex.org/W3010849941","https://openalex.org/W3012518767","https://openalex.org/W3012591061","https://openalex.org/W3014009018","https://openalex.org/W3014468003","https://openalex.org/W3015078075","https://openalex.org/W3015865829","https://openalex.org/W3016481759","https://openalex.org/W3017130883","https://openalex.org/W3020102814","https://openalex.org/W3021027692","https://openalex.org/W3021457401","https://openalex.org/W3025017190","https://openalex.org/W3026669735","https://openalex.org/W3028928637","https://openalex.org/W3029817982","https://openalex.org/W3031879091","https://openalex.org/W3033526262","https://openalex.org/W3033937423","https://openalex.org/W3034021666","https://openalex.org/W3036412988","https://openalex.org/W3036843665","https://openalex.org/W3037588546","https://openalex.org/W3040226701","https://openalex.org/W3040508529","https://openalex.org/W3047245470","https://openalex.org/W3047326826","https://openalex.org/W3080930191","https://openalex.org/W3084024723","https://openalex.org/W3085463724","https://openalex.org/W3087644732","https://openalex.org/W3088666270","https://openalex.org/W3091986675","https://openalex.org/W3092743582","https://openalex.org/W3092923133","https://openalex.org/W3093786597","https://openalex.org/W3093821973","https://openalex.org/W3094142577","https://openalex.org/W3094424025","https://openalex.org/W3095154255","https://openalex.org/W3096161794","https://openalex.org/W3096831136","https://openalex.org/W3098546160","https://openalex.org/W3103787556","https://openalex.org/W3105245152","https://openalex.org/W3105469151","https://openalex.org/W3106023117","https://openalex.org/W3109445814","https://openalex.org/W3109864797","https://openalex.org/W3111914315","https://openalex.org/W3113317199","https://openalex.org/W3115418185","https://openalex.org/W3119943851","https://openalex.org/W3120374370","https://openalex.org/W3121733470","https://openalex.org/W3123608446","https://openalex.org/W3124695286","https://openalex.org/W3124856606","https://openalex.org/W3126393581","https://openalex.org/W3127215704","https://openalex.org/W3127451557","https://openalex.org/W3128991244","https://openalex.org/W3130494174","https://openalex.org/W3130945614","https://openalex.org/W3131921307","https://openalex.org/W3134515731","https://openalex.org/W3134811368","https://openalex.org/W3135391574","https://openalex.org/W3137392741","https://openalex.org/W3144438719","https://openalex.org/W3151535550","https://openalex.org/W3153315752","https://openalex.org/W3153522897","https://openalex.org/W3154575637","https://openalex.org/W3157259013","https://openalex.org/W3159218436","https://openalex.org/W3160518394","https://openalex.org/W3161192096","https://openalex.org/W3161200675","https://openalex.org/W3162045419","https://openalex.org/W3162304445","https://openalex.org/W3163993681","https://openalex.org/W3164032021","https://openalex.org/W3164919902","https://openalex.org/W3166414150","https://openalex.org/W3170347025","https://openalex.org/W3172050125","https://openalex.org/W3173358212","https://openalex.org/W3173549089","https://openalex.org/W3175061452","https://openalex.org/W3178566976","https://openalex.org/W3178968719","https://openalex.org/W3179444763","https://openalex.org/W3179621946","https://openalex.org/W3180490621","https://openalex.org/W3185095713","https://openalex.org/W3186224863","https://openalex.org/W3186285864","https://openalex.org/W3187481252","https://openalex.org/W3192242357","https://openalex.org/W3193726109","https://openalex.org/W3193909976","https://openalex.org/W3197308578","https://openalex.org/W3197694049","https://openalex.org/W3197818013","https://openalex.org/W3198848420","https://openalex.org/W3199632382","https://openalex.org/W3200372603","https://openalex.org/W3200673624","https://openalex.org/W3201666041","https://openalex.org/W3201958666","https://openalex.org/W3202433620","https://openalex.org/W3205073660","https://openalex.org/W3208498987","https://openalex.org/W3208953217","https://openalex.org/W3211723343","https://openalex.org/W3214040539","https://openalex.org/W3214220788","https://openalex.org/W3214496267","https://openalex.org/W3214795678","https://openalex.org/W4200119169","https://openalex.org/W4200462984","https://openalex.org/W4200603639","https://openalex.org/W4205717954","https://openalex.org/W4205834965","https://openalex.org/W4207022452","https://openalex.org/W4210336314","https://openalex.org/W4210423197","https://openalex.org/W4211029392","https://openalex.org/W4211052067","https://openalex.org/W4213199992","https://openalex.org/W4213444041","https://openalex.org/W4214504644","https://openalex.org/W4214863413","https://openalex.org/W4220696910","https://openalex.org/W4220717841","https://openalex.org/W4220725955","https://openalex.org/W4221019179","https://openalex.org/W4221107806","https://openalex.org/W4221153224","https://openalex.org/W4221156259","https://openalex.org/W4221158603","https://openalex.org/W4224007003","https://openalex.org/W4224285428","https://openalex.org/W4225422786","https://openalex.org/W4225619856","https://openalex.org/W4225696772","https://openalex.org/W4225752825","https://openalex.org/W4225995462","https://openalex.org/W4226030434","https://openalex.org/W4226106627","https://openalex.org/W4226191973","https://openalex.org/W4226478851","https://openalex.org/W4226480439","https://openalex.org/W4229459060","https://openalex.org/W4235892290","https://openalex.org/W4242376272","https://openalex.org/W4281480322","https://openalex.org/W4281620757","https://openalex.org/W4281711890","https://openalex.org/W4281727527","https://openalex.org/W4281740368","https://openalex.org/W4283170975","https://openalex.org/W4283204116","https://openalex.org/W4283321413","https://openalex.org/W4284666812","https://openalex.org/W4285384919","https://openalex.org/W4285483984","https://openalex.org/W4286909924","https://openalex.org/W4286988446","https://openalex.org/W4287023463","https://openalex.org/W4287671439","https://openalex.org/W4288039037","https://openalex.org/W4288067189","https://openalex.org/W4288734997","https://openalex.org/W4289699964","https://openalex.org/W4289703354","https://openalex.org/W4292178981","https://openalex.org/W4292622286","https://openalex.org/W4292824053","https://openalex.org/W4294170298","https://openalex.org/W4294653590","https://openalex.org/W4296363099","https://openalex.org/W4296468671","https://openalex.org/W4296657845","https://openalex.org/W4297841718","https://openalex.org/W4297846984","https://openalex.org/W4297921849","https://openalex.org/W4298000212","https://openalex.org/W4298155841","https://openalex.org/W4304086854","https://openalex.org/W4307570062","https://openalex.org/W4308052476","https://openalex.org/W4308194133","https://openalex.org/W4309522700","https://openalex.org/W4310980593","https://openalex.org/W4311728648","https://openalex.org/W4312222837","https://openalex.org/W4313419889","https://openalex.org/W4319347409","https://openalex.org/W4320013936","https://openalex.org/W4320062096","https://openalex.org/W4367674997","https://openalex.org/W4372319591","https://openalex.org/W4382138811","https://openalex.org/W4383851868","https://openalex.org/W4385686902","https://openalex.org/W4386366778","https://openalex.org/W4387812071","https://openalex.org/W4388418991","https://openalex.org/W4390176157","https://openalex.org/W4394649112","https://openalex.org/W4399647672","https://openalex.org/W6628254996","https://openalex.org/W6628877408","https://openalex.org/W6629849204","https://openalex.org/W6638908295","https://openalex.org/W6640362995","https://openalex.org/W6657612527","https://openalex.org/W6668562388","https://openalex.org/W6674330103","https://openalex.org/W6687483927","https://openalex.org/W6698183232","https://openalex.org/W6720887540","https://openalex.org/W6724307092","https://openalex.org/W6730344855","https://openalex.org/W6732503498","https://openalex.org/W6734922100","https://openalex.org/W6746731892","https://openalex.org/W6748177122","https://openalex.org/W6752231694","https://openalex.org/W6752307458","https://openalex.org/W6753012237","https://openalex.org/W6753700359","https://openalex.org/W6753817354","https://openalex.org/W6757391552","https://openalex.org/W6758969245","https://openalex.org/W6761080300","https://openalex.org/W6761271948","https://openalex.org/W6767573681","https://openalex.org/W6768147225","https://openalex.org/W6769531570","https://openalex.org/W6770130613","https://openalex.org/W6770910452","https://openalex.org/W6774119754","https://openalex.org/W6774402226","https://openalex.org/W6775127026","https://openalex.org/W6776009139","https://openalex.org/W6776142728","https://openalex.org/W6779456492","https://openalex.org/W6779674755","https://openalex.org/W6780179280","https://openalex.org/W6780640948","https://openalex.org/W6781544064","https://openalex.org/W6782707356","https://openalex.org/W6783048280","https://openalex.org/W6783678127","https://openalex.org/W6784227514","https://openalex.org/W6784288912","https://openalex.org/W6784732000","https://openalex.org/W6785328185","https://openalex.org/W6788657042","https://openalex.org/W6789412200","https://openalex.org/W6790339181","https://openalex.org/W6790910904","https://openalex.org/W6793867231","https://openalex.org/W6795000047","https://openalex.org/W6796306510","https://openalex.org/W6798564201","https://openalex.org/W6800169315","https://openalex.org/W6800781246","https://openalex.org/W6801551493","https://openalex.org/W6802015701","https://openalex.org/W6804070175","https://openalex.org/W6804257718","https://openalex.org/W6804467878","https://openalex.org/W6804625228","https://openalex.org/W6804951855","https://openalex.org/W6805681846","https://openalex.org/W6805822973","https://openalex.org/W6810168066","https://openalex.org/W6810376456","https://openalex.org/W6810641295","https://openalex.org/W6811235180","https://openalex.org/W6839004550","https://openalex.org/W6839038296","https://openalex.org/W6839123454","https://openalex.org/W6842622385","https://openalex.org/W6843754093","https://openalex.org/W6845980154","https://openalex.org/W6849714529","https://openalex.org/W6864195360","https://openalex.org/W6869608176","https://openalex.org/W6929334658"],"related_works":["https://openalex.org/W3008584592","https://openalex.org/W2765937093","https://openalex.org/W615938567","https://openalex.org/W180587397","https://openalex.org/W4292953721","https://openalex.org/W2282306231","https://openalex.org/W1584270863","https://openalex.org/W1538193578","https://openalex.org/W2085961337","https://openalex.org/W4214632534"],"abstract_inverted_index":{"Abstract":[0],"Advancements":[1],"in":[2,22,44,70,141,202,223],"computing":[3,20,204],"power":[4],"have":[5],"recently":[6],"made":[7],"it":[8],"possible":[9],"to":[10,17,49,83,100,148,185],"utilize":[11],"machine":[12],"learning":[13,16,237],"and":[14,60,73,115,174,199,209,217,232,235],"deep":[15,236],"push":[18],"scientific":[19,72,203,234],"forward":[21],"a":[23,80,187],"range":[24],"of":[25,38,131,158,189,225],"disciplines,":[26],"such":[27],"as":[28],"fluid":[29],"mechanics,":[30,32],"solid":[31,81],"materials":[33],"science,":[34],"etc.":[35],"The":[36,206],"incorporation":[37],"neural":[39,54,77,97,107,112,118,142,192],"networks":[40,55,78,108,113,119],"is":[41,67,162],"particularly":[42],"crucial":[43],"this":[45],"hybridization":[46],"process.":[47],"Due":[48],"their":[50,170,210],"intrinsic":[51],"architecture,":[52],"conventional":[53],"cannot":[56],"be":[57],"successfully":[58],"trained":[59],"scoped":[61],"when":[62,154],"data":[63],"are":[64,94,212,215,221],"sparse,":[65],"which":[66],"the":[68,102,128,138,155,190],"case":[69],"many":[71],"engineering":[74],"domains.":[75],"Nonetheless,":[76],"provide":[79,123],"foundation":[82],"respect":[84],"physics-driven":[85],"or":[86],"knowledge-based":[87],"constraints":[88],"during":[89],"training.":[90],"Generally":[91],"speaking,":[92],"there":[93],"three":[95],"distinct":[96,124],"network":[98,193],"frameworks":[99,194],"enforce":[101],"underlying":[103],"physics:":[104],"(i)":[105],"physics-guided":[106],"(PgNNs),":[109],"(ii)":[110],"physics-informed":[111],"(PiNNs),":[114],"(iii)":[116],"physics-encoded":[117],"(PeNNs).":[120],"These":[121],"methods":[122],"advantages":[125],"for":[126,178],"accelerating":[127],"numerical":[129],"modeling":[130],"complex":[132,159],"multiscale":[133],"multiphysics":[134,160],"phenomena.":[135],"In":[136],"addition,":[137],"recent":[139],"developments":[140],"operators":[143],"(NOs)":[144],"add":[145],"another":[146],"dimension":[147],"these":[149,165],"new":[150],"simulation":[151],"paradigms,":[152],"especially":[153],"real-time":[156],"prediction":[157],"systems":[161],"required.":[163],"All":[164],"models":[166],"also":[167],"come":[168],"with":[169],"own":[171],"unique":[172],"drawbacks":[173],"limitations":[175,214],"that":[176],"call":[177],"further":[179],"fundamental":[180],"research.":[181,205],"This":[182],"study":[183],"aims":[184],"present":[186],"review":[188],"four":[191],"(i.e.,":[195],"PgNNs,":[196],"PiNNs,":[197],"PeNNs,":[198],"NOs)":[200],"used":[201],"state-of-the-art":[207],"architectures":[208],"applications":[211],"reviewed,":[213],"discussed,":[216],"future":[218],"research":[219],"opportunities":[220],"presented":[222],"terms":[224],"improving":[226],"algorithms,":[227],"considering":[228],"causalities,":[229],"expanding":[230],"applications,":[231],"coupling":[233],"solvers.":[238]},"counts_by_year":[{"year":2026,"cited_by_count":37},{"year":2025,"cited_by_count":106},{"year":2024,"cited_by_count":36},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-09T13:55:54.758798","created_date":"2025-10-10T00:00:00"}
