{"id":"https://openalex.org/W4321337769","doi":"https://doi.org/10.48550/arxiv.2302.08216","title":"Uncertainty quantification for nonlinear solid mechanics using reduced order models with Gaussian process regression","display_name":"Uncertainty quantification for nonlinear solid mechanics using reduced order models with Gaussian process regression","publication_year":2023,"publication_date":"2023-02-16","ids":{"openalex":"https://openalex.org/W4321337769","doi":"https://doi.org/10.48550/arxiv.2302.08216"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2302.08216","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2302.08216","pdf_url":"https://arxiv.org/pdf/2302.08216","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2302.08216","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005197459","display_name":"Ludovica Cicci","orcid":"https://orcid.org/0000-0002-2544-9889"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]},{"id":"https://openalex.org/I183935753","display_name":"King's College London","ror":"https://ror.org/0220mzb33","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I183935753"]}],"countries":["GB","IT"],"is_corresponding":true,"raw_author_name":"Cicci, Ludovica","raw_affiliation_strings":["Politecnico di Milano","King's College London"],"affiliations":[{"raw_affiliation_string":"Politecnico di Milano","institution_ids":["https://openalex.org/I93860229"]},{"raw_affiliation_string":"King's College London","institution_ids":["https://openalex.org/I183935753"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040645637","display_name":"Stefania Fresca","orcid":"https://orcid.org/0000-0001-8599-6588"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Fresca, Stefania","raw_affiliation_strings":["Politecnico di Milano"],"affiliations":[{"raw_affiliation_string":"Politecnico di Milano","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005525255","display_name":"Mengwu Guo","orcid":"https://orcid.org/0000-0002-5541-437X"},"institutions":[{"id":"https://openalex.org/I94624287","display_name":"University of Twente","ror":"https://ror.org/006hf6230","country_code":"NL","type":"education","lineage":["https://openalex.org/I94624287"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Guo, Mengwu","raw_affiliation_strings":["University of Twente"],"affiliations":[{"raw_affiliation_string":"University of Twente","institution_ids":["https://openalex.org/I94624287"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082126056","display_name":"Andrea Manzoni","orcid":"https://orcid.org/0000-0001-8277-2802"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Manzoni, Andrea","raw_affiliation_strings":["Politecnico di Milano"],"affiliations":[{"raw_affiliation_string":"Politecnico di Milano","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038341430","display_name":"Paolo Zunino","orcid":"https://orcid.org/0000-0002-2470-0189"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Zunino, Paolo","raw_affiliation_strings":["Politecnico di Milano"],"affiliations":[{"raw_affiliation_string":"Politecnico di Milano","institution_ids":["https://openalex.org/I93860229"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5005197459"],"corresponding_institution_ids":["https://openalex.org/I183935753","https://openalex.org/I93860229"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.9984999895095825,"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":0.9984999895095825,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9742000102996826,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11372","display_name":"Hydraulic and Pneumatic Systems","score":0.9506000280380249,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/uncertainty-quantification","display_name":"Uncertainty quantification","score":0.6506227254867554},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6308484077453613},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.572433352470398},{"id":"https://openalex.org/keywords/kriging","display_name":"Kriging","score":0.5462649464607239},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5005474090576172},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.45915594696998596},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3915102183818817},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3228432536125183},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.24936065077781677},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.19775396585464478}],"concepts":[{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.6506227254867554},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6308484077453613},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.572433352470398},{"id":"https://openalex.org/C81692654","wikidata":"https://www.wikidata.org/wiki/Q225926","display_name":"Kriging","level":2,"score":0.5462649464607239},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5005474090576172},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.45915594696998596},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3915102183818817},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3228432536125183},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.24936065077781677},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.19775396585464478},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:arXiv.org:2302.08216","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2302.08216","pdf_url":"https://arxiv.org/pdf/2302.08216","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:ris.utwente.nl:openaire/55cf2815-10c2-454c-9821-964cacd9c6e9","is_oa":true,"landing_page_url":"https://research.utwente.nl/en/publications/55cf2815-10c2-454c-9821-964cacd9c6e9","pdf_url":null,"source":{"id":"https://openalex.org/S4406922991","display_name":"University of Twente Research Information","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Cicci, L, Fresca, S, Guo, M, Manzoni, A & Zunino, P 2023 'Uncertainty quantification for nonlinear solid mechanics using reduced order models with Gaussian process regression' ArXiv.org. https://doi.org/10.48550/arXiv.2302.08216","raw_type":"info:eu-repo/semantics/preprint"},{"id":"pmh:oai:ris.utwente.nl:publications/fcefa72a-3dbb-492e-aafc-94de6128f9ee","is_oa":true,"landing_page_url":"https://research.utwente.nl/en/publications/fcefa72a-3dbb-492e-aafc-94de6128f9ee","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"doi:10.48550/arxiv.2302.08216","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2302.08216","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2302.08216","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2302.08216","pdf_url":"https://arxiv.org/pdf/2302.08216","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1464101492","display_name":null,"funder_award_id":"FESR 2014-2020","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G453067482","display_name":null,"funder_award_id":"014-2020","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G5527288744","display_name":null,"funder_award_id":"2014-2020","funder_id":"https://openalex.org/F4320326078","funder_display_name":"Regione Lombardia"},{"id":"https://openalex.org/G5634946813","display_name":null,"funder_award_id":"2014-2020","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G6262740336","display_name":null,"funder_award_id":"POR FESR 2014-2020","funder_id":"https://openalex.org/F4320326078","funder_display_name":"Regione Lombardia"},{"id":"https://openalex.org/G72824567","display_name":null,"funder_award_id":"POR FESR 2014-2020","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G779831060","display_name":null,"funder_award_id":"FESR 2014-2020","funder_id":"https://openalex.org/F4320326078","funder_display_name":"Regione Lombardia"},{"id":"https://openalex.org/G8195099764","display_name":null,"funder_award_id":"NEWMED","funder_id":"https://openalex.org/F4320326078","funder_display_name":"Regione Lombardia"},{"id":"https://openalex.org/G8570012161","display_name":null,"funder_award_id":"unknown","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"}],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320326078","display_name":"Regione Lombardia","ror":null},{"id":"https://openalex.org/F4320334079","display_name":"Gruppo Nazionale per il Calcolo Scientifico","ror":null},{"id":"https://openalex.org/F4320335322","display_name":"European Regional Development Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4321337769.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1968523686","https://openalex.org/W298893735","https://openalex.org/W2199291344","https://openalex.org/W2211316729","https://openalex.org/W2167342507","https://openalex.org/W4221140712","https://openalex.org/W4247222564","https://openalex.org/W3123323883","https://openalex.org/W2151794096","https://openalex.org/W2922348557"],"abstract_inverted_index":{"Uncertainty":[0],"quantification":[1],"(UQ)":[2],"tasks,":[3],"such":[4,43],"as":[5,44,127],"sensitivity":[6,203],"analysis":[7,204],"and":[8,161,179,209,212,225],"parameter":[9,213],"estimation,":[10],"entail":[11],"a":[12,84,100,128,152,156,176,180,186],"huge":[13],"computational":[14,61,223],"complexity":[15,62],"when":[16,73,114],"dealing":[17],"with":[18,78],"input-output":[19],"maps":[20],"involving":[21],"the":[22,30,45,55,60,97,125,168,195],"solution":[23],"of":[24,29,63,158,188],"nonlinear":[25,106],"differential":[26,80],"problems,":[27,107],"because":[28],"need":[31],"to":[32,58,96,136,150,166,200,230],"query":[33],"expensive":[34],"numerical":[35],"solvers":[36],"repeatedly.":[37],"Projection-based":[38],"reduced":[39,153],"order":[40,67],"models":[41,68],"(ROMs),":[42],"Galerkin-reduced":[46],"basis":[47,154],"(RB)":[48],"method,":[49],"have":[50,132],"been":[51,133],"extensively":[52],"developed":[53,135],"in":[54],"last":[56],"decades":[57],"overcome":[59,137],"high":[64],"fidelity":[65],"full":[66],"(FOMs),":[69],"providing":[70],"remarkable":[71,222],"speedups":[72,224],"addressing":[74],"UQ":[75],"tasks":[76],"related":[77],"parameterized":[79],"problems.":[81],"Nonetheless,":[82],"constructing":[83],"projection-based":[85],"ROM":[86,197],"that":[87],"can":[88],"be":[89],"efficiently":[90],"queried":[91],"usually":[92],"requires":[93],"extensive":[94],"modifications":[95],"original":[98],"code,":[99],"task":[101],"which":[102,122],"is":[103,117,198],"non-trivial":[104],"for":[105],"or":[108],"even":[109],"not":[110],"possible":[111],"at":[112],"all":[113],"proprietary":[115],"software":[116],"used.":[118],"Non-intrusive":[119],"ROMs":[120,145],"-":[121,131],"rely":[123],"on":[124,185,206],"FOM":[126,159],"black":[129],"box":[130],"recently":[134],"this":[138,141],"issue.":[139],"In":[140],"work,":[142],"we":[143],"consider":[144],"exploiting":[146],"proper":[147],"orthogonal":[148],"decomposition":[149],"construct":[151],"from":[155],"set":[157,187],"snapshots,":[160],"Gaussian":[162],"process":[163],"regression":[164],"(GPR)":[165],"approximate":[167],"RB":[169],"projection":[170],"coefficients.":[171],"Two":[172],"different":[173],"approaches,":[174],"namely":[175],"global":[177,202],"GPR":[178],"tensor-decomposition-based":[181],"GPR,":[182],"are":[183],"explored":[184],"3D":[189],"time-dependent":[190],"solid":[191],"mechanics":[192],"examples.":[193],"Finally,":[194],"non-intrusive":[196],"exploited":[199],"perform":[201],"(relying":[205],"both":[207],"screening":[208],"variance-based":[210],"methods)":[211],"estimation":[214],"(through":[215],"Markov":[216],"chain":[217],"Monte":[218],"Carlo":[219],"methods),":[220],"showing":[221],"very":[226],"good":[227],"accuracy":[228],"compared":[229],"high-fidelity":[231],"FOMs.":[232]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-04-20T07:46:08.049788","created_date":"2023-02-19T00:00:00"}
