{"id":"https://openalex.org/W4399152082","doi":"https://doi.org/10.1186/s40323-025-00285-7","title":"Deterministic and statistical calibration of constitutive models from full-field data with parametric physics-informed neural networks","display_name":"Deterministic and statistical calibration of constitutive models from full-field data with parametric physics-informed neural networks","publication_year":2025,"publication_date":"2025-05-29","ids":{"openalex":"https://openalex.org/W4399152082","doi":"https://doi.org/10.1186/s40323-025-00285-7"},"language":"en","primary_location":{"id":"doi:10.1186/s40323-025-00285-7","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s40323-025-00285-7","pdf_url":"https://amses-journal.springeropen.com/counter/pdf/10.1186/s40323-025-00285-7","source":{"id":"https://openalex.org/S3034486266","display_name":"Advanced Modeling and Simulation in Engineering Sciences","issn_l":"2213-7467","issn":["2213-7467"],"is_oa":true,"is_in_doaj":true,"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advanced Modeling and Simulation in Engineering Sciences","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://amses-journal.springeropen.com/counter/pdf/10.1186/s40323-025-00285-7","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103109772","display_name":"David Anton","orcid":"https://orcid.org/0000-0002-0888-0220"},"institutions":[{"id":"https://openalex.org/I94509681","display_name":"Technische Universit\u00e4t Braunschweig","ror":"https://ror.org/010nsgg66","country_code":"DE","type":"education","lineage":["https://openalex.org/I94509681"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"David Anton","raw_affiliation_strings":["Institute of Applied Mechanics, Technische Universit\u00e4t Braunschweig, Pockelsstra\u00dfe 3, 38106, Braunschweig, Germany"],"raw_orcid":"https://orcid.org/0000-0002-0888-0220","affiliations":[{"raw_affiliation_string":"Institute of Applied Mechanics, Technische Universit\u00e4t Braunschweig, Pockelsstra\u00dfe 3, 38106, Braunschweig, Germany","institution_ids":["https://openalex.org/I94509681"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034391450","display_name":"Jendrik\u2010Alexander Tr\u00f6ger","orcid":"https://orcid.org/0000-0002-4999-4558"},"institutions":[{"id":"https://openalex.org/I43980791","display_name":"Clausthal University of Technology","ror":"https://ror.org/04qb8nc58","country_code":"DE","type":"education","lineage":["https://openalex.org/I43980791"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Jendrik-Alexander Tr\u00f6ger","raw_affiliation_strings":["Institute of Applied Mechanics, Clausthal University of Technology, Adolph-Roemer-Stra\u00dfe 2A, 38678, Clausthal-Zellerfeld, Germany"],"raw_orcid":"https://orcid.org/0000-0002-4999-4558","affiliations":[{"raw_affiliation_string":"Institute of Applied Mechanics, Clausthal University of Technology, Adolph-Roemer-Stra\u00dfe 2A, 38678, Clausthal-Zellerfeld, Germany","institution_ids":["https://openalex.org/I43980791"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078524162","display_name":"Henning Wessels","orcid":"https://orcid.org/0000-0002-2542-1130"},"institutions":[{"id":"https://openalex.org/I94509681","display_name":"Technische Universit\u00e4t Braunschweig","ror":"https://ror.org/010nsgg66","country_code":"DE","type":"education","lineage":["https://openalex.org/I94509681"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Henning Wessels","raw_affiliation_strings":["Institute of Applied Mechanics, Technische Universit\u00e4t Braunschweig, Pockelsstra\u00dfe 3, 38106, Braunschweig, Germany"],"raw_orcid":"https://orcid.org/0000-0002-2542-1130","affiliations":[{"raw_affiliation_string":"Institute of Applied Mechanics, Technische Universit\u00e4t Braunschweig, Pockelsstra\u00dfe 3, 38106, Braunschweig, Germany","institution_ids":["https://openalex.org/I94509681"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025553101","display_name":"Ulrich R\u00f6mer","orcid":"https://orcid.org/0000-0002-1277-7509"},"institutions":[{"id":"https://openalex.org/I94509681","display_name":"Technische Universit\u00e4t Braunschweig","ror":"https://ror.org/010nsgg66","country_code":"DE","type":"education","lineage":["https://openalex.org/I94509681"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ulrich R\u00f6mer","raw_affiliation_strings":["Institute for Acoustics and Dynamics, Technische Universit\u00e4t Braunschweig, Langer Kamp 19, 38106, Braunschweig, Germany"],"raw_orcid":"https://orcid.org/0000-0002-1277-7509","affiliations":[{"raw_affiliation_string":"Institute for Acoustics and Dynamics, Technische Universit\u00e4t Braunschweig, Langer Kamp 19, 38106, Braunschweig, Germany","institution_ids":["https://openalex.org/I94509681"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012113972","display_name":"Alexander Henkes","orcid":"https://orcid.org/0000-0003-4615-9271"},"institutions":[{"id":"https://openalex.org/I2799323385","display_name":"Board of the Swiss Federal Institutes of Technology","ror":"https://ror.org/01rvn4p91","country_code":"CH","type":"government","lineage":["https://openalex.org/I2799323385"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Alexander Henkes","raw_affiliation_strings":["Computational Mechanics Group, Eidgen\u00f6ssische Technische Hochschule Z\u00fcrich, Tannenstrasse 3, 8092, Z\u00fcrich, Switzerland"],"raw_orcid":"https://orcid.org/0000-0003-4615-9271","affiliations":[{"raw_affiliation_string":"Computational Mechanics Group, Eidgen\u00f6ssische Technische Hochschule Z\u00fcrich, Tannenstrasse 3, 8092, Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I2799323385"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001932535","display_name":"Stefan Hartmann","orcid":"https://orcid.org/0000-0003-1849-0784"},"institutions":[{"id":"https://openalex.org/I43980791","display_name":"Clausthal University of Technology","ror":"https://ror.org/04qb8nc58","country_code":"DE","type":"education","lineage":["https://openalex.org/I43980791"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Stefan Hartmann","raw_affiliation_strings":["Institute of Applied Mechanics, Clausthal University of Technology, Adolph-Roemer-Stra\u00dfe 2A, 38678, Clausthal-Zellerfeld, Germany"],"raw_orcid":"https://orcid.org/0000-0003-1849-0784","affiliations":[{"raw_affiliation_string":"Institute of Applied Mechanics, Clausthal University of Technology, Adolph-Roemer-Stra\u00dfe 2A, 38678, Clausthal-Zellerfeld, Germany","institution_ids":["https://openalex.org/I43980791"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5103109772"],"corresponding_institution_ids":["https://openalex.org/I94509681"],"apc_list":{"value":990,"currency":"GBP","value_usd":1214},"apc_paid":{"value":990,"currency":"GBP","value_usd":1214},"fwci":2.2657,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.8504618,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"12","issue":"1","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":0.9958999752998352,"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":0.9958999752998352,"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/T10876","display_name":"Fault Detection and Control Systems","score":0.9641000032424927,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T11201","display_name":"Metallurgy and Material Forming","score":0.9625999927520752,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/calibration","display_name":"Calibration","score":0.719061017036438},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.7131897807121277},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.6338946223258972},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.6251561045646667},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.563924252986908},{"id":"https://openalex.org/keywords/parametric-model","display_name":"Parametric model","score":0.4601195156574249},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4456327259540558},{"id":"https://openalex.org/keywords/experimental-data","display_name":"Experimental data","score":0.4206458628177643},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.3861994743347168},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3798789978027344},{"id":"https://openalex.org/keywords/theoretical-physics","display_name":"Theoretical physics","score":0.33827584981918335},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3372606635093689},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.27244478464126587},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.23888280987739563},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.13164618611335754}],"concepts":[{"id":"https://openalex.org/C165838908","wikidata":"https://www.wikidata.org/wiki/Q736777","display_name":"Calibration","level":2,"score":0.719061017036438},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.7131897807121277},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.6338946223258972},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.6251561045646667},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.563924252986908},{"id":"https://openalex.org/C24574437","wikidata":"https://www.wikidata.org/wiki/Q7135228","display_name":"Parametric model","level":3,"score":0.4601195156574249},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4456327259540558},{"id":"https://openalex.org/C55037315","wikidata":"https://www.wikidata.org/wiki/Q5421151","display_name":"Experimental data","level":2,"score":0.4206458628177643},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3861994743347168},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3798789978027344},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.33827584981918335},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3372606635093689},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.27244478464126587},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.23888280987739563},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.13164618611335754},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1186/s40323-025-00285-7","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s40323-025-00285-7","pdf_url":"https://amses-journal.springeropen.com/counter/pdf/10.1186/s40323-025-00285-7","source":{"id":"https://openalex.org/S3034486266","display_name":"Advanced Modeling and Simulation in Engineering Sciences","issn_l":"2213-7467","issn":["2213-7467"],"is_oa":true,"is_in_doaj":true,"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advanced Modeling and Simulation in Engineering Sciences","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2405.18311","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2405.18311","pdf_url":"https://arxiv.org/pdf/2405.18311","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:f56b82d0e9e44feda1e00665895cd6c1","is_oa":true,"landing_page_url":"https://doaj.org/article/f56b82d0e9e44feda1e00665895cd6c1","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Advanced Modeling and Simulation in Engineering Sciences, Vol 12, Iss 1, Pp 1-34 (2025)","raw_type":"article"},{"id":"doi:10.48550/arxiv.2405.18311","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2405.18311","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1186/s40323-025-00285-7","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s40323-025-00285-7","pdf_url":"https://amses-journal.springeropen.com/counter/pdf/10.1186/s40323-025-00285-7","source":{"id":"https://openalex.org/S3034486266","display_name":"Advanced Modeling and Simulation in Engineering Sciences","issn_l":"2213-7467","issn":["2213-7467"],"is_oa":true,"is_in_doaj":true,"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advanced Modeling and Simulation in Engineering Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1169211201","display_name":null,"funder_award_id":"255042459","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G1588815991","display_name":"Monitoringdatengetriebenes Lebensdauermanagement mit AR auf Basis einer adaptiven, KIgest\u00fctzen Korrosionsprognose f\u00fcr Infrastrukturbauwerke aus Stahlbeton unter kombinierten Einwirkungen","funder_award_id":"501798687","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G3120031080","display_name":null,"funder_award_id":"GRK2075","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G3270688909","display_name":null,"funder_award_id":"DFG 255042459","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4399152082.pdf","grobid_xml":"https://content.openalex.org/works/W4399152082.grobid-xml"},"referenced_works_count":66,"referenced_works":["https://openalex.org/W298568565","https://openalex.org/W3127735129","https://openalex.org/W4229489487","https://openalex.org/W1967851970","https://openalex.org/W2065195341","https://openalex.org/W2995629075","https://openalex.org/W1985621820","https://openalex.org/W2883270908","https://openalex.org/W2899283552","https://openalex.org/W3163993681","https://openalex.org/W1968326286","https://openalex.org/W2158985775","https://openalex.org/W1853291804","https://openalex.org/W4401250870","https://openalex.org/W4200119169","https://openalex.org/W4323262590","https://openalex.org/W4213199992","https://openalex.org/W3137392741","https://openalex.org/W4309443782","https://openalex.org/W3084024723","https://openalex.org/W4311726227","https://openalex.org/W4362450348","https://openalex.org/W4285226320","https://openalex.org/W4365505884","https://openalex.org/W4400424910","https://openalex.org/W3212815395","https://openalex.org/W6948735089","https://openalex.org/W6948613625","https://openalex.org/W6911271437","https://openalex.org/W601713258","https://openalex.org/W6666698583","https://openalex.org/W2899253534","https://openalex.org/W1991462738","https://openalex.org/W2046930772","https://openalex.org/W2103496339","https://openalex.org/W2137983211","https://openalex.org/W2009566405","https://openalex.org/W2770250658","https://openalex.org/W4255949318","https://openalex.org/W3200673624","https://openalex.org/W6631190155","https://openalex.org/W2051434435","https://openalex.org/W2103111465","https://openalex.org/W2078409719","https://openalex.org/W4230107568","https://openalex.org/W4241367446","https://openalex.org/W1542343170","https://openalex.org/W2075665712","https://openalex.org/W4238789798","https://openalex.org/W4248681815","https://openalex.org/W2101687185","https://openalex.org/W2063397409","https://openalex.org/W2165429502","https://openalex.org/W2093625674","https://openalex.org/W1998235272","https://openalex.org/W4294912042","https://openalex.org/W4211049957","https://openalex.org/W1973333099","https://openalex.org/W2525748878","https://openalex.org/W2889523591","https://openalex.org/W3157127629","https://openalex.org/W3044248863","https://openalex.org/W2763532150","https://openalex.org/W2596961269","https://openalex.org/W3092743582","https://openalex.org/W4226480439"],"related_works":["https://openalex.org/W2289718384","https://openalex.org/W1995675544","https://openalex.org/W2509524819","https://openalex.org/W2012121796","https://openalex.org/W2068427817","https://openalex.org/W2952090425","https://openalex.org/W2538333368","https://openalex.org/W3127866798","https://openalex.org/W4294845631","https://openalex.org/W1518153952"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"calibration":[2,67,123,168,203],"of":[3,27,39,89,124,158,165,201],"constitutive":[4,65,133],"models":[5],"from":[6,68,135],"full-field":[7,18,69],"data":[8,71,180],"has":[9],"recently":[10],"gained":[11],"increasing":[12],"interest":[13],"due":[14],"to":[15,23,52,84,150,197],"improvements":[16],"in":[17,112,187,207,215],"measurement":[19],"capabilities.":[20],"In":[21,74,95],"addition":[22],"the":[24,90,96,100,109,116,120,152,159,162,166,171,184,198],"experimental":[25,179],"characterization":[26],"novel":[28],"materials,":[29],"continuous":[30],"structural":[31],"health":[32],"monitoring":[33,43],"is":[34,38,44,174,212],"another":[35],"application":[36],"that":[37,170,183],"great":[40],"interest.":[41],"However,":[42],"usually":[45],"associated":[46],"with":[47,54,190],"severe":[48],"time":[49],"constraints,":[50],"difficult":[51],"meet":[53],"standard":[55],"numerical":[56],"approaches.":[57],"Therefore,":[58],"parametric":[59,79,101],"physics-informed":[60],"neural":[61],"networks":[62],"(PINNs)":[63],"for":[64,108,119],"model":[66,134],"displacement":[70,138],"are":[72,186],"investigated.":[73],"an":[75],"offline":[76],"stage,":[77,99],"a":[78,86,106,125,131,191],"PINN":[80,102],"can":[81,204],"be":[82,205],"trained":[83],"learn":[85],"parameterized":[87],"solution":[88],"underlying":[91],"partial":[92],"differential":[93],"equation.":[94],"subsequent":[97],"online":[98],"then":[103],"acts":[104],"as":[105,128,130,219],"surrogate":[107],"parameters-to-state":[110],"map":[111],"calibration.":[113,195],"We":[114,140],"test":[115],"proposed":[117],"approach":[118],"deterministic":[121,167],"least-squares":[122],"linear":[126],"elastic":[127],"well":[129],"hyperelastic":[132],"noisy":[136],"synthetic":[137],"data.":[139],"further":[141],"carry":[142],"out":[143],"Markov":[144,220],"chain":[145,221],"Monte":[146,222],"Carlo-based":[147,223],"Bayesian":[148,224],"inference":[149],"quantify":[151],"uncertainty.":[153],"A":[154],"proper":[155],"statistical":[156],"evaluation":[157,200],"results":[160,185],"underlines":[161],"high":[163],"accuracy":[164],"and":[169,181],"estimated":[172],"uncertainty":[173],"valid.":[175],"Finally,":[176],"we":[177],"consider":[178],"show":[182],"good":[188],"agreement":[189],"finite":[192],"element":[193],"method-based":[194],"Due":[196],"fast":[199],"PINNs,":[202],"performed":[206],"near":[208],"real-time.":[209],"This":[210],"advantage":[211],"particularly":[213],"evident":[214],"many-query":[216],"applications":[217],"such":[218],"inference.":[225]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2024-05-30T00:00:00"}