{"id":"https://openalex.org/W4411763512","doi":"https://doi.org/10.1007/978-3-031-97626-1_5","title":"Tensorial Implementation for\u00a0Robust Variational Physics-Informed Neural Networks","display_name":"Tensorial Implementation for\u00a0Robust Variational Physics-Informed Neural Networks","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4411763512","doi":"https://doi.org/10.1007/978-3-031-97626-1_5"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-031-97626-1_5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-031-97626-1_5","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://bird.bcamath.org/bitstream/20.500.11824/2046/1/Tensorial_VPINNs.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5117809543","display_name":"Askold Vilkha","orcid":"https://orcid.org/0000-0001-9272-9082"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Askold Vilkha","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-9272-9082","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075508918","display_name":"C. Uriarte","orcid":"https://orcid.org/0000-0002-6962-6883"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Carlos Uriarte","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-6962-6883","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048015876","display_name":"Pawe\u0142 Maczuga","orcid":"https://orcid.org/0000-0002-5111-6981"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pawe\u0142 Maczuga","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-5111-6981","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084873757","display_name":"Tomasz S\u0142u\u017calec","orcid":"https://orcid.org/0000-0001-6217-4274"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tomasz S\u0142u\u017calec","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-6217-4274","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5075191779","display_name":"Maciej Paszy\u0144ski","orcid":"https://orcid.org/0000-0001-7766-6052"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Maciej Paszy\u0144ski","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-7766-6052","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5117809543"],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.30977342,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"61","last_page":"75"},"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/T12560","display_name":"Nuclear Engineering Thermal-Hydraulics","score":0.9891999959945679,"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"}},{"id":"https://openalex.org/T11254","display_name":"Fluid Dynamics and Vibration Analysis","score":0.9879000186920166,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6982506513595581},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6004748344421387},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3606099784374237},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3267155885696411},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.11176103353500366}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6982506513595581},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6004748344421387},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3606099784374237},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3267155885696411},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.11176103353500366}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-3-031-97626-1_5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-031-97626-1_5","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:bird.bcamath.org:20.500.11824/2046","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11824/2046","pdf_url":"https://bird.bcamath.org/bitstream/20.500.11824/2046/1/Tensorial_VPINNs.pdf","source":{"id":"https://openalex.org/S4306401608","display_name":"BIRD (Basque Center for Applied Mathematics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2802176441","host_organization_name":"Basque Center for Applied Mathematics","host_organization_lineage":["https://openalex.org/I2802176441"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:bird.bcamath.org:20.500.11824/2046","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11824/2046","pdf_url":"https://bird.bcamath.org/bitstream/20.500.11824/2046/1/Tensorial_VPINNs.pdf","source":{"id":"https://openalex.org/S4306401608","display_name":"BIRD (Basque Center for Applied Mathematics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2802176441","host_organization_name":"Basque Center for Applied Mathematics","host_organization_lineage":["https://openalex.org/I2802176441"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1643949827","display_name":null,"funder_award_id":"AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G2003458463","display_name":null,"funder_award_id":"BERC 2022-2025 program","funder_id":"https://openalex.org/F4320321705","funder_display_name":"Eusko Jaurlaritza"},{"id":"https://openalex.org/G2262748287","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G2550080368","display_name":null,"funder_award_id":"MICIU/AEI/ 10.13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G2601397997","display_name":null,"funder_award_id":"10.13039/501100011033","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G300979063","display_name":null,"funder_award_id":"10.13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3081656539","display_name":null,"funder_award_id":"CEX2021-001142-S","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3412273058","display_name":null,"funder_award_id":"AEI/ 10.13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3480869486","display_name":null,"funder_award_id":"13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3681454997","display_name":null,"funder_award_id":"13039/501100011033","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G4042783231","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G4079952795","display_name":null,"funder_award_id":"MICIU/AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G4488079590","display_name":null,"funder_award_id":"BERC 2022-2025","funder_id":"https://openalex.org/F4320321705","funder_display_name":"Eusko Jaurlaritza"},{"id":"https://openalex.org/G5080475149","display_name":null,"funder_award_id":"10.13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G5914213083","display_name":null,"funder_award_id":"MICIU/AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320321705","funder_display_name":"Eusko Jaurlaritza"},{"id":"https://openalex.org/G6294024929","display_name":null,"funder_award_id":"CEX2021-001142-S","funder_id":"https://openalex.org/F4320328444","funder_display_name":"Basque Center for Applied Mathematics"},{"id":"https://openalex.org/G6391922461","display_name":null,"funder_award_id":"MICIU/AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G6823456974","display_name":null,"funder_award_id":"AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G7084143925","display_name":null,"funder_award_id":"AEI/10","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7266728691","display_name":null,"funder_award_id":"13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7436716198","display_name":null,"funder_award_id":"BERC 2022-2025","funder_id":"https://openalex.org/F4320328444","funder_display_name":"Basque Center for Applied Mathematics"},{"id":"https://openalex.org/G7535663061","display_name":null,"funder_award_id":"AEI/10.","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7748812462","display_name":null,"funder_award_id":"2022-2025","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G7829631415","display_name":"Real-time inversion using self-explainable deep learning driven by expert knowledge","funder_award_id":"101119556","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8939903727","display_name":null,"funder_award_id":"2022-2025","funder_id":"https://openalex.org/F4320321705","funder_display_name":"Eusko Jaurlaritza"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320321705","display_name":"Eusko Jaurlaritza","ror":"https://ror.org/00pz2fp31"},{"id":"https://openalex.org/F4320328444","display_name":"Basque Center for Applied Mathematics","ror":"https://ror.org/03b21sh32"},{"id":"https://openalex.org/F4320334322","display_name":"HORIZON EUROPE Framework Programme","ror":null},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4411763512.pdf"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W1592730613","https://openalex.org/W1601517105","https://openalex.org/W1980493061","https://openalex.org/W2495211843","https://openalex.org/W2534240011","https://openalex.org/W2899283552","https://openalex.org/W2900369848","https://openalex.org/W2948230027","https://openalex.org/W2978281981","https://openalex.org/W2997814214","https://openalex.org/W2998366519","https://openalex.org/W3011806874","https://openalex.org/W3111557793","https://openalex.org/W3128157635","https://openalex.org/W3170606933","https://openalex.org/W3176116059","https://openalex.org/W3177439049","https://openalex.org/W3187773598","https://openalex.org/W3196894304","https://openalex.org/W4220717841","https://openalex.org/W4220929409","https://openalex.org/W4225142395","https://openalex.org/W4226244456","https://openalex.org/W4239704419","https://openalex.org/W4312915956","https://openalex.org/W4379386863","https://openalex.org/W4382406482","https://openalex.org/W4383374400","https://openalex.org/W4383956635","https://openalex.org/W4387443591","https://openalex.org/W4392905622"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-05-09T13:55:54.758798","created_date":"2025-10-10T00:00:00"}
