{"id":"https://openalex.org/W4393041455","doi":"https://doi.org/10.1007/s00366-024-01957-5","title":"Physics informed neural networks for an inverse problem in peridynamic models","display_name":"Physics informed neural networks for an inverse problem in peridynamic models","publication_year":2024,"publication_date":"2024-03-21","ids":{"openalex":"https://openalex.org/W4393041455","doi":"https://doi.org/10.1007/s00366-024-01957-5"},"language":"en","primary_location":{"id":"doi:10.1007/s00366-024-01957-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00366-024-01957-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00366-024-01957-5.pdf","source":{"id":"https://openalex.org/S89333158","display_name":"Engineering With Computers","issn_l":"0177-0667","issn":["0177-0667","1435-5663"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Engineering with Computers","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00366-024-01957-5.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047215262","display_name":"Fabio V. Difonzo","orcid":"https://orcid.org/0000-0003-0101-3391"},"institutions":[{"id":"https://openalex.org/I4210106125","display_name":"Istituto per le Applicazioni del Calcolo Mauro Picone","ror":"https://ror.org/00ygy3d85","country_code":"IT","type":"facility","lineage":["https://openalex.org/I4210106125","https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Fabio V. Difonzo","raw_affiliation_strings":["Istituto per le Applicazioni del Calcolo \u201cMauro Picone\u201d, Consiglio Nazionale delle Ricerche, Via G. Amendola 122/I, 70126, Bari, Italy","Istituto per le Applicazioni del Calcolo \"Mauro Picone\", Consiglio Nazionale delle Ricerche, Via G. Amendola 122/I, 70126, Bari, Italy"],"affiliations":[{"raw_affiliation_string":"Istituto per le Applicazioni del Calcolo \u201cMauro Picone\u201d, Consiglio Nazionale delle Ricerche, Via G. Amendola 122/I, 70126, Bari, Italy","institution_ids":["https://openalex.org/I4210106125"]},{"raw_affiliation_string":"Istituto per le Applicazioni del Calcolo \"Mauro Picone\", Consiglio Nazionale delle Ricerche, Via G. Amendola 122/I, 70126, Bari, Italy","institution_ids":["https://openalex.org/I4210106125"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014483726","display_name":"L. Lopez","orcid":"https://orcid.org/0000-0001-5083-5151"},"institutions":[{"id":"https://openalex.org/I5561750","display_name":"University of Bari Aldo Moro","ror":"https://ror.org/027ynra39","country_code":"IT","type":"education","lineage":["https://openalex.org/I5561750"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Luciano Lopez","raw_affiliation_strings":["Dipartimento di Matematica, Universit\u00e0 degli Studi di Bari Aldo Moro, Via E. Orabona 4, 70125, Bari, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Universit\u00e0 degli Studi di Bari Aldo Moro, Via E. Orabona 4, 70125, Bari, Italy","institution_ids":["https://openalex.org/I5561750"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085898599","display_name":"Sabrina Francesca Pellegrino","orcid":"https://orcid.org/0000-0002-6482-1938"},"institutions":[{"id":"https://openalex.org/I68618741","display_name":"Polytechnic University of Bari","ror":"https://ror.org/03c44v465","country_code":"IT","type":"education","lineage":["https://openalex.org/I68618741"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Sabrina F. Pellegrino","raw_affiliation_strings":["Dipartimento di Ingegneria Elettrica e dell\u2019Informazione, Politecnico di Bari, Via E. Orabona 4, 70125, Bari, Italy","Dipartimento di Ingegneria Elettrica e dell'Informazione, Politecnico di Bari, Via E. Orabona 4, 70125, Bari, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria Elettrica e dell\u2019Informazione, Politecnico di Bari, Via E. Orabona 4, 70125, Bari, Italy","institution_ids":["https://openalex.org/I68618741"]},{"raw_affiliation_string":"Dipartimento di Ingegneria Elettrica e dell'Informazione, Politecnico di Bari, Via E. Orabona 4, 70125, Bari, Italy","institution_ids":["https://openalex.org/I68618741"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5047215262"],"corresponding_institution_ids":["https://openalex.org/I4210106125"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":8.1494,"has_fulltext":true,"cited_by_count":31,"citation_normalized_percentile":{"value":0.98850301,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"41","issue":"6","first_page":"4003","last_page":"4012"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9983000159263611,"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"}},"topics":[{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9983000159263611,"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"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9940000176429749,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9754999876022339,"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/peridynamics","display_name":"Peridynamics","score":0.726116955280304},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.6185923218727112},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5201473832130432},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4802004098892212},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.4642624855041504},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41278672218322754},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3690407872200012},{"id":"https://openalex.org/keywords/theoretical-physics","display_name":"Theoretical physics","score":0.3386014699935913},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33756619691848755},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31583529710769653},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.3155785799026489},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.26047414541244507},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21213224530220032},{"id":"https://openalex.org/keywords/continuum-mechanics","display_name":"Continuum mechanics","score":0.1327514350414276},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12798142433166504},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.06095772981643677}],"concepts":[{"id":"https://openalex.org/C142600616","wikidata":"https://www.wikidata.org/wiki/Q4351291","display_name":"Peridynamics","level":3,"score":0.726116955280304},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.6185923218727112},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5201473832130432},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4802004098892212},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.4642624855041504},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41278672218322754},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3690407872200012},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.3386014699935913},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33756619691848755},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31583529710769653},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3155785799026489},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26047414541244507},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21213224530220032},{"id":"https://openalex.org/C84035572","wikidata":"https://www.wikidata.org/wiki/Q193463","display_name":"Continuum mechanics","level":2,"score":0.1327514350414276},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12798142433166504},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.06095772981643677},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00366-024-01957-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00366-024-01957-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00366-024-01957-5.pdf","source":{"id":"https://openalex.org/S89333158","display_name":"Engineering With Computers","issn_l":"0177-0667","issn":["0177-0667","1435-5663"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Engineering with Computers","raw_type":"journal-article"},{"id":"pmh:oai:ricerca.uniba.it:11586/464942","is_oa":true,"landing_page_url":"https://hdl.handle.net/11586/464942","pdf_url":null,"source":{"id":"https://openalex.org/S4377196296","display_name":"CINECA IRIS Institutional Research Information System (University of Bari Aldo Moro)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I5561750","host_organization_name":"University of Bari Aldo Moro","host_organization_lineage":["https://openalex.org/I5561750"],"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":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s00366-024-01957-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00366-024-01957-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00366-024-01957-5.pdf","source":{"id":"https://openalex.org/S89333158","display_name":"Engineering With Computers","issn_l":"0177-0667","issn":["0177-0667","1435-5663"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Engineering with Computers","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1515584085","display_name":null,"funder_award_id":"REFIN Project, grant number D1AB726C","funder_id":"https://openalex.org/F4320326082","funder_display_name":"Regione Puglia"},{"id":"https://openalex.org/G2020143847","display_name":null,"funder_award_id":"E53C22001930001","funder_id":"https://openalex.org/F4320334079","funder_display_name":"Gruppo Nazionale per il Calcolo Scientifico"},{"id":"https://openalex.org/G4772130973","display_name":null,"funder_award_id":"E53C23001670001","funder_id":"https://openalex.org/F4320334079","funder_display_name":"Gruppo Nazionale per il Calcolo Scientifico"},{"id":"https://openalex.org/G5456286744","display_name":null,"funder_award_id":"E53C22001930001","funder_id":"https://openalex.org/F4320311030","funder_display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\""},{"id":"https://openalex.org/G5488169599","display_name":null,"funder_award_id":"E53C23001670001","funder_id":"https://openalex.org/F4320311030","funder_display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\""},{"id":"https://openalex.org/G734517595","display_name":null,"funder_award_id":"REFIN Project, grant number 812E4967","funder_id":"https://openalex.org/F4320326082","funder_display_name":"Regione Puglia"},{"id":"https://openalex.org/G7741705016","display_name":null,"funder_award_id":"CUP_E53C23001670001","funder_id":"https://openalex.org/F4320334079","funder_display_name":"Gruppo Nazionale per il Calcolo Scientifico"},{"id":"https://openalex.org/G800213781","display_name":null,"funder_award_id":"REFIN","funder_id":"https://openalex.org/F4320326082","funder_display_name":"Regione Puglia"},{"id":"https://openalex.org/G8278854977","display_name":null,"funder_award_id":"INdAM-GNCS 2023 Project, grant number CUP_E53C22001930001","funder_id":"https://openalex.org/F4320334079","funder_display_name":"Gruppo Nazionale per il Calcolo Scientifico"}],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320322651","display_name":"Consiglio Nazionale delle Ricerche","ror":"https://ror.org/04zaypm56"},{"id":"https://openalex.org/F4320326082","display_name":"Regione Puglia","ror":"https://ror.org/039k11f95"},{"id":"https://openalex.org/F4320334079","display_name":"Gruppo Nazionale per il Calcolo Scientifico","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4393041455.pdf"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W1993215954","https://openalex.org/W1993499036","https://openalex.org/W2008086878","https://openalex.org/W2012828992","https://openalex.org/W2029410933","https://openalex.org/W2071636135","https://openalex.org/W2204986623","https://openalex.org/W2395151902","https://openalex.org/W2481312347","https://openalex.org/W2554789187","https://openalex.org/W2769262245","https://openalex.org/W2899283552","https://openalex.org/W2944516342","https://openalex.org/W2966419255","https://openalex.org/W2993158195","https://openalex.org/W3031879091","https://openalex.org/W3089129046","https://openalex.org/W3099057226","https://openalex.org/W3101572174","https://openalex.org/W3169767944","https://openalex.org/W3183994952","https://openalex.org/W3188203211","https://openalex.org/W3217139884","https://openalex.org/W4225995462","https://openalex.org/W4288039037","https://openalex.org/W4293569036","https://openalex.org/W4312222006","https://openalex.org/W4313531672","https://openalex.org/W4321465178","https://openalex.org/W4366976333","https://openalex.org/W4368353915","https://openalex.org/W4380906878","https://openalex.org/W4381687077","https://openalex.org/W4385561992","https://openalex.org/W4387223604","https://openalex.org/W4387299841","https://openalex.org/W4387363324","https://openalex.org/W4387451198","https://openalex.org/W4388510538","https://openalex.org/W4388626571"],"related_works":["https://openalex.org/W2132729321","https://openalex.org/W3013043199","https://openalex.org/W1993403100","https://openalex.org/W2895843456","https://openalex.org/W2956918742","https://openalex.org/W2308035364","https://openalex.org/W3013142834","https://openalex.org/W4380203312","https://openalex.org/W2331917905","https://openalex.org/W3155039083"],"abstract_inverted_index":{"Abstract":[0],"Deep":[1],"learning":[2],"is":[3,90],"a":[4],"powerful":[5],"tool":[6],"for":[7],"solving":[8,22],"data":[9],"driven":[10],"differential":[11],"problems":[12,26],"and":[13,24,113],"has":[14],"come":[15],"out":[16],"to":[17,41,58,92,123],"have":[18],"successful":[19],"applications":[20],"in":[21,31,50,68,77],"direct":[23],"inverse":[25,61],"described":[27],"by":[28,103],"PDEs,":[29],"even":[30],"presence":[32],"of":[33,63,72,87],"integral":[34],"terms.":[35],"In":[36],"this":[37],"paper,":[38],"we":[39,79],"propose":[40],"apply":[42],"radial":[43],"basis":[44],"functions":[45,49],"(RBFs)":[46],"as":[47],"activation":[48],"suitably":[51],"designed":[52],"Physics":[53],"Informed":[54],"Neural":[55],"Networks":[56],"(PINNs)":[57],"solve":[59],"the":[60,65,69,85,99,104,116,120,124],"problem":[62],"computing":[64],"perydinamic":[66],"kernel":[67],"nonlocal":[70],"formulation":[71],"classical":[73],"wave":[74],"equation,":[75],"resulting":[76],"what":[78],"call":[80],"RBF-iPINN.":[81],"We":[82,106],"show":[83],"that":[84,96],"selection":[86],"an":[88],"RBF":[89],"necessary":[91],"achieve":[93],"meaningful":[94],"solutions,":[95],"agree":[97],"with":[98,110,119],"physical":[100],"expectations":[101],"carried":[102],"data.":[105],"support":[107],"our":[108],"results":[109],"numerical":[111],"examples":[112],"experiments,":[114],"comparing":[115],"solution":[117],"obtained":[118],"proposed":[121],"RBF-iPINN":[122],"exact":[125],"solutions.":[126]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":21},{"year":2024,"cited_by_count":6}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}