{"id":"https://openalex.org/W4402234893","doi":"https://doi.org/10.1017/s0962492923000089","title":"Numerical analysis of physics-informed neural networks and related models in physics-informed machine learning","display_name":"Numerical analysis of physics-informed neural networks and related models in physics-informed machine learning","publication_year":2024,"publication_date":"2024-07-01","ids":{"openalex":"https://openalex.org/W4402234893","doi":"https://doi.org/10.1017/s0962492923000089"},"language":"en","primary_location":{"id":"doi:10.1017/s0962492923000089","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0962492923000089","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A059C6E13478F0F7C70EC7C976716F9F/S0962492923000089a.pdf/div-class-title-numerical-analysis-of-physics-informed-neural-networks-and-related-models-in-physics-informed-machine-learning-div.pdf","source":{"id":"https://openalex.org/S124973578","display_name":"Acta Numerica","issn_l":"0962-4929","issn":["0962-4929","1474-0508"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Acta Numerica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A059C6E13478F0F7C70EC7C976716F9F/S0962492923000089a.pdf/div-class-title-numerical-analysis-of-physics-informed-neural-networks-and-related-models-in-physics-informed-machine-learning-div.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053556239","display_name":"Tim De Ryck","orcid":"https://orcid.org/0000-0001-6860-1345"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Tim De Ryck","raw_affiliation_strings":["Seminar for Applied Mathematics, ETH Z\u00fcrich, R\u00e4mistrasse 101, 8092 Z\u00fcrich, Switzerland E-mail:"],"raw_orcid":"https://orcid.org/0000-0001-6860-1345","affiliations":[{"raw_affiliation_string":"Seminar for Applied Mathematics, ETH Z\u00fcrich, R\u00e4mistrasse 101, 8092 Z\u00fcrich, Switzerland E-mail:","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101961582","display_name":"Siddhartha Mishra","orcid":"https://orcid.org/0000-0002-2665-5385"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]},{"id":"https://openalex.org/I4210090941","display_name":"Institute for Biomedical Engineering","ror":"https://ror.org/00baskk38","country_code":"CH","type":"facility","lineage":["https://openalex.org/I202697423","https://openalex.org/I2799323385","https://openalex.org/I35440088","https://openalex.org/I4210090941"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Siddhartha Mishra","raw_affiliation_strings":["Seminar for Applied Mathematics & ETH AI Center, ETH Z\u00fcrich, R\u00e4mistrasse 101, 8092 Z\u00fcrich, Switzerland E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Seminar for Applied Mathematics & ETH AI Center, ETH Z\u00fcrich, R\u00e4mistrasse 101, 8092 Z\u00fcrich, Switzerland E-mail:","institution_ids":["https://openalex.org/I35440088","https://openalex.org/I4210090941"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":12.7455,"has_fulltext":true,"cited_by_count":64,"citation_normalized_percentile":{"value":0.99462597,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"33","issue":null,"first_page":"633","last_page":"713"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9894999861717224,"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":0.9894999861717224,"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/T13650","display_name":"Computational Physics and Python Applications","score":0.9677000045776367,"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/T10597","display_name":"Nuclear reactor physics and engineering","score":0.9656999707221985,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/artificial-neural-network","display_name":"Artificial neural network","score":0.606393039226532},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5827259421348572},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.45121434330940247},{"id":"https://openalex.org/keywords/cognitive-science","display_name":"Cognitive science","score":0.4498611092567444},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.42022407054901123},{"id":"https://openalex.org/keywords/management-science","display_name":"Management science","score":0.3620968759059906},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3209910988807678},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2344740927219391},{"id":"https://openalex.org/keywords/psychology","display_name":"Psychology","score":0.14318394660949707},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.07614538073539734}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.606393039226532},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5827259421348572},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.45121434330940247},{"id":"https://openalex.org/C188147891","wikidata":"https://www.wikidata.org/wiki/Q147638","display_name":"Cognitive science","level":1,"score":0.4498611092567444},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.42022407054901123},{"id":"https://openalex.org/C539667460","wikidata":"https://www.wikidata.org/wiki/Q2414942","display_name":"Management science","level":1,"score":0.3620968759059906},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3209910988807678},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2344740927219391},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.14318394660949707},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.07614538073539734}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0962492923000089","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0962492923000089","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A059C6E13478F0F7C70EC7C976716F9F/S0962492923000089a.pdf/div-class-title-numerical-analysis-of-physics-informed-neural-networks-and-related-models-in-physics-informed-machine-learning-div.pdf","source":{"id":"https://openalex.org/S124973578","display_name":"Acta Numerica","issn_l":"0962-4929","issn":["0962-4929","1474-0508"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Acta Numerica","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1017/s0962492923000089","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0962492923000089","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A059C6E13478F0F7C70EC7C976716F9F/S0962492923000089a.pdf/div-class-title-numerical-analysis-of-physics-informed-neural-networks-and-related-models-in-physics-informed-machine-learning-div.pdf","source":{"id":"https://openalex.org/S124973578","display_name":"Acta Numerica","issn_l":"0962-4929","issn":["0962-4929","1474-0508"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Acta Numerica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4402234893.pdf","grobid_xml":"https://content.openalex.org/works/W4402234893.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2961085424","https://openalex.org/W2391251536","https://openalex.org/W2362198218","https://openalex.org/W1982750869","https://openalex.org/W2019521278","https://openalex.org/W1984922432","https://openalex.org/W2113077220","https://openalex.org/W2375008505","https://openalex.org/W2350679292","https://openalex.org/W2086348228"],"abstract_inverted_index":{"Physics-informed":[0],"neural":[1],"networks":[2],"(PINNs)":[3],"and":[4,23,48,96,99,110,129],"their":[5,100,130],"variants":[6],"have":[7],"been":[8],"very":[9],"popular":[10],"in":[11,64,77,134,165],"recent":[12],"years":[13],"as":[14,151],"algorithms":[15],"for":[16,26],"the":[17,43,53,68,72,105,108,111,114,121,124,127,135,145,159],"numerical":[18,44],"simulation":[19],"of":[20,38,46,55,67,71,90,107,113,123,126,162],"both":[21],"forward":[22],"inverse":[24],"problems":[25],"partial":[27],"differential":[28],"equations.":[29],"This":[30],"article":[31],"aims":[32],"to":[33,104,132,143],"provide":[34,60],"a":[35,61,87,152],"comprehensive":[36],"review":[37,89],"currently":[39],"available":[40,91],"results":[41,92,139],"on":[42,93],"analysis":[45,66],"PINNs":[47,76],"related":[49],"models":[50,164],"that":[51],"constitute":[52],"backbone":[54],"physics-informed":[56,166],"machine":[57,167],"learning.":[58,168],"We":[59,85,147],"unified":[62],"framework":[63],"which":[65,155],"various":[69,163],"components":[70],"error":[73,136],"incurred":[74],"by":[75],"approximating":[78],"PDEs":[79],"can":[80,156],"be":[81],"effectively":[82],"carried":[83],"out.":[84],"present":[86],"detailed":[88],"approximation,":[94],"generalization":[95],"training":[97,149],"errors":[98,150],"behaviour":[101],"with":[102],"respect":[103],"type":[106],"PDE":[109],"dimension":[112],"underlying":[115],"domain.":[116],"In":[117],"particular,":[118],"we":[119],"elucidate":[120],"role":[122],"regularity":[125],"solutions":[128],"stability":[131],"perturbations":[133],"analysis.":[137],"Numerical":[138],"are":[140],"also":[141],"presented":[142],"illustrate":[144],"theory.":[146],"identify":[148],"key":[153],"bottleneck":[154],"adversely":[157],"affect":[158],"overall":[160],"performance":[161]},"counts_by_year":[{"year":2026,"cited_by_count":38},{"year":2025,"cited_by_count":25},{"year":2024,"cited_by_count":1}],"updated_date":"2026-08-08T01:25:22.217667","created_date":"2024-09-05T00:00:00"}