{"id":"https://openalex.org/W3157216123","doi":"https://doi.org/10.1061/(asce)cp.1943-5487.0000965","title":"Uncertainty Quantification of Locally Nonlinear Dynamical Systems Using Neural Networks","display_name":"Uncertainty Quantification of Locally Nonlinear Dynamical Systems Using Neural Networks","publication_year":2021,"publication_date":"2021-04-30","ids":{"openalex":"https://openalex.org/W3157216123","doi":"https://doi.org/10.1061/(asce)cp.1943-5487.0000965","mag":"3157216123"},"language":"en","primary_location":{"id":"doi:10.1061/(asce)cp.1943-5487.0000965","is_oa":false,"landing_page_url":"https://doi.org/10.1061/(asce)cp.1943-5487.0000965","pdf_url":null,"source":{"id":"https://openalex.org/S176637136","display_name":"Journal of Computing in Civil Engineering","issn_l":"0887-3801","issn":["0887-3801","1943-5487"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315747","host_organization_name":"American Society of Civil Engineers","host_organization_lineage":["https://openalex.org/P4310315747"],"host_organization_lineage_names":["American Society of Civil Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computing in Civil Engineering","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011838459","display_name":"Subhayan De","orcid":"https://orcid.org/0000-0002-1974-6123"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]},{"id":"https://openalex.org/I4210142152","display_name":"ORCID","ror":"https://ror.org/04fa4r544","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210142152"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Subhayan De","raw_affiliation_strings":["Postdoctoral Associate, Smead Dept. of Aerospace Engineering Sciences, Univ. of Colorado, Boulder, CO 80303. ORCID: ","Postdoctoral Associate, Smead Dept. of Aerospace Engineering Sciences, Univ. of Colorado, Boulder, CO 80303. ORCID: https://orcid.org/0000-0002-1974-6123"],"raw_orcid":"https://orcid.org/0000-0002-1974-6123","affiliations":[{"raw_affiliation_string":"Postdoctoral Associate, Smead Dept. of Aerospace Engineering Sciences, Univ. of Colorado, Boulder, CO 80303. ORCID: ","institution_ids":["https://openalex.org/I188538660"]},{"raw_affiliation_string":"Postdoctoral Associate, Smead Dept. of Aerospace Engineering Sciences, Univ. of Colorado, Boulder, CO 80303. ORCID: https://orcid.org/0000-0002-1974-6123","institution_ids":["https://openalex.org/I188538660","https://openalex.org/I4210142152"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5011838459"],"corresponding_institution_ids":["https://openalex.org/I188538660","https://openalex.org/I4210142152"],"apc_list":null,"apc_paid":null,"fwci":0.7102,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.84190101,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"35","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9998999834060669,"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/T10534","display_name":"Structural Health Monitoring Techniques","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9987999796867371,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/uncertainty-quantification","display_name":"Uncertainty quantification","score":0.7218435406684875},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7037491202354431},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.625410795211792},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.5683954358100891},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5568568706512451},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5527445673942566},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.5015196800231934},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.472639262676239},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.47100913524627686},{"id":"https://openalex.org/keywords/importance-sampling","display_name":"Importance sampling","score":0.44747281074523926},{"id":"https://openalex.org/keywords/physical-system","display_name":"Physical system","score":0.4334411025047302},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.27522045373916626},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.24408751726150513},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.17593291401863098}],"concepts":[{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.7218435406684875},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7037491202354431},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.625410795211792},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.5683954358100891},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5568568706512451},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5527445673942566},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.5015196800231934},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.472639262676239},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.47100913524627686},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.44747281074523926},{"id":"https://openalex.org/C116672817","wikidata":"https://www.wikidata.org/wiki/Q1454986","display_name":"Physical system","level":2,"score":0.4334411025047302},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.27522045373916626},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.24408751726150513},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.17593291401863098},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"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/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1061/(asce)cp.1943-5487.0000965","is_oa":false,"landing_page_url":"https://doi.org/10.1061/(asce)cp.1943-5487.0000965","pdf_url":null,"source":{"id":"https://openalex.org/S176637136","display_name":"Journal of Computing in Civil Engineering","issn_l":"0887-3801","issn":["0887-3801","1943-5487"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315747","host_organization_name":"American Society of Civil Engineers","host_organization_lineage":["https://openalex.org/P4310315747"],"host_organization_lineage_names":["American Society of Civil Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computing in Civil Engineering","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/17","score":0.41999998688697815,"display_name":"Partnerships for the goals"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":66,"referenced_works":["https://openalex.org/W1508147193","https://openalex.org/W1522301498","https://openalex.org/W1538934584","https://openalex.org/W1746819321","https://openalex.org/W1806891645","https://openalex.org/W1904365287","https://openalex.org/W1982886636","https://openalex.org/W1983067771","https://openalex.org/W1983156129","https://openalex.org/W1990562007","https://openalex.org/W1997512975","https://openalex.org/W2014208555","https://openalex.org/W2016059496","https://openalex.org/W2018159038","https://openalex.org/W2025669880","https://openalex.org/W2025782392","https://openalex.org/W2027197837","https://openalex.org/W2036729857","https://openalex.org/W2038669746","https://openalex.org/W2045325874","https://openalex.org/W2055746248","https://openalex.org/W2061028639","https://openalex.org/W2069072065","https://openalex.org/W2087524586","https://openalex.org/W2126849813","https://openalex.org/W2165698076","https://openalex.org/W2194775991","https://openalex.org/W2194820107","https://openalex.org/W2346026520","https://openalex.org/W2402144811","https://openalex.org/W2471488293","https://openalex.org/W2482051381","https://openalex.org/W2557283755","https://openalex.org/W2621213434","https://openalex.org/W2745110207","https://openalex.org/W2766298346","https://openalex.org/W2791547487","https://openalex.org/W2795982117","https://openalex.org/W2890968382","https://openalex.org/W2897628882","https://openalex.org/W2899283552","https://openalex.org/W2899771611","https://openalex.org/W2909614798","https://openalex.org/W2915854813","https://openalex.org/W2919958648","https://openalex.org/W2922073063","https://openalex.org/W2946752227","https://openalex.org/W2950883932","https://openalex.org/W2963595769","https://openalex.org/W2963687058","https://openalex.org/W2989144367","https://openalex.org/W3007264146","https://openalex.org/W3014009018","https://openalex.org/W3022399480","https://openalex.org/W3022953487","https://openalex.org/W3034609614","https://openalex.org/W3035952341","https://openalex.org/W3040786507","https://openalex.org/W3047494561","https://openalex.org/W3083834825","https://openalex.org/W3089040801","https://openalex.org/W3101378293","https://openalex.org/W3123883114","https://openalex.org/W4211049957","https://openalex.org/W6632535845","https://openalex.org/W6654151595"],"related_works":["https://openalex.org/W2186864281","https://openalex.org/W1991093342","https://openalex.org/W4255427455","https://openalex.org/W1966025497","https://openalex.org/W68941528","https://openalex.org/W4206451355","https://openalex.org/W2765903009","https://openalex.org/W301916688","https://openalex.org/W3186041451","https://openalex.org/W1983960451"],"abstract_inverted_index":{"Models":[0],"are":[1,54,280],"often":[2,65,113],"given":[3],"in":[4,35,121,212],"terms":[5],"of":[6,16,20,23,33,47,50,69,78,95,143,151,154,173,221,229,262,276],"differential":[7,73,99],"equations":[8,74,100],"to":[9,218,234,257,271],"represent":[10],"physical":[11,52],"systems.":[12],"In":[13,38,106,199],"the":[14,21,27,31,36,48,70,79,93,96,141,144,167,187,194,213,219,227,236,240,248,251,263,274],"presence":[15],"uncertainty,":[17],"accurate":[18],"prediction":[19],"behavior":[22],"these":[24,51,58,87],"systems":[25,53,103],"using":[26,247],"models":[28],"requires":[29],"understanding":[30],"effect":[32],"uncertainty":[34,39,119,133,152,197],"response.":[37,145],"quantification,":[40],"statistics":[41,142,275],"such":[42,102],"as":[43,92,224,226],"mean":[44],"and":[45,179,196,242,265],"variance":[46],"response":[49,168,172,188,261,279],"sought.":[55,281],"To":[56,146],"estimate":[57,235],"statistics,":[59],"sampling-based":[60,130],"methods":[61,88,131],"like":[62],"Monte":[63],"Carlo":[64],"require":[66],"many":[67],"evaluations":[68],"models\u2019":[71,97],"governing":[72,98],"for":[75,82,101,127,132,139,208],"multiple":[76],"realizations":[77],"uncertainty.":[80],"However,":[81],"large":[83],"complex":[84],"engineering":[85],"systems,":[86,159],"become":[89],"computationally":[90],"burdensome":[91],"solution":[94],"is":[104,162,186,232,245,269],"expensive.":[105],"structural":[107],"engineering,":[108],"an":[109],"otherwise":[110],"linear":[111,177],"structure":[112],"contains":[114,193],"spatially":[115],"local":[116],"nonlinearities":[117],"with":[118,129],"present":[120],"them.":[122],"A":[123],"standard":[124],"nonlinear":[125,157,241],"solver":[126],"them":[128],"quantification":[134,153],"incurs":[135],"significant":[136],"computational":[137,149,222],"cost":[138],"estimating":[140],"ease":[147],"this":[148,200],"burden":[150],"large-scale":[155],"locally":[156],"dynamical":[158],"a":[160,174,180,190,204,259,277],"method":[161],"proposed":[163],"herein":[164],"that":[165,192],"decomposes":[166],"into":[169],"two":[170],"parts:":[171],"deterministic":[175],"nominal":[176],"system":[178],"corrective":[181,184],"term.":[182],"This":[183],"term":[185],"from":[189],"pseudoforce":[191,244],"nonlinearity":[195],"information.":[198],"paper,":[201],"neural":[202,249],"network,":[203],"recently":[205],"popular":[206],"tool":[207],"universal":[209],"function":[210],"approximation":[211],"scientific":[214],"machine-learning":[215],"community":[216],"due":[217],"advancement":[220],"capability":[223],"well":[225],"availability":[228],"open-source":[230],"packages,":[231],"used":[233,256],"pseudoforce.":[237],"Since":[238],"only":[239],"uncertain":[243],"modeled":[246],"networks,":[250],"same":[252],"network":[253,268],"can":[254],"be":[255],"predict":[258],"different":[260,278],"system,":[264],"no":[266],"new":[267],"required":[270],"train":[272],"if":[273]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
