{"id":"https://openalex.org/W2887833842","doi":"https://doi.org/10.1137/18m1205959","title":"Density Estimation in Uncertainty Propagation Problems Using a Surrogate Model","display_name":"Density Estimation in Uncertainty Propagation Problems Using a Surrogate Model","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2887833842","doi":"https://doi.org/10.1137/18m1205959","mag":"2887833842"},"language":"en","primary_location":{"id":"doi:10.1137/18m1205959","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1205959","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1803.10991","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037955264","display_name":"Adi Ditkowski","orcid":"https://orcid.org/0000-0003-1202-5072"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Adi Ditkowski","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065691928","display_name":"Gadi Fibich","orcid":"https://orcid.org/0000-0002-0173-7560"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gadi Fibich","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-0173-7560","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5031661439","display_name":"Amir Sagiv","orcid":"https://orcid.org/0000-0002-0831-216X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Amir Sagiv","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5037955264"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1699,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.58100233,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"8","issue":"1","first_page":"261","last_page":"300"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":1.0,"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":1.0,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9973999857902527,"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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.7192280292510986},{"id":"https://openalex.org/keywords/density-estimation","display_name":"Density estimation","score":0.7102777361869812},{"id":"https://openalex.org/keywords/kernel-density-estimation","display_name":"Kernel density estimation","score":0.6841980814933777},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6121618151664734},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6115450859069824},{"id":"https://openalex.org/keywords/multivariate-kernel-density-estimation","display_name":"Multivariate kernel density estimation","score":0.5774683952331543},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.5698512196540833},{"id":"https://openalex.org/keywords/spline","display_name":"Spline (mechanical)","score":0.5616001486778259},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5581781268119812},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5516310334205627},{"id":"https://openalex.org/keywords/surrogate-model","display_name":"Surrogate model","score":0.4653967320919037},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.390512615442276},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.383955717086792},{"id":"https://openalex.org/keywords/variable-kernel-density-estimation","display_name":"Variable kernel density estimation","score":0.3314337134361267},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.25382739305496216},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.21859228610992432},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19205006957054138},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15440192818641663},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08702105283737183},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.0862065851688385}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7192280292510986},{"id":"https://openalex.org/C189508267","wikidata":"https://www.wikidata.org/wiki/Q17088227","display_name":"Density estimation","level":3,"score":0.7102777361869812},{"id":"https://openalex.org/C71134354","wikidata":"https://www.wikidata.org/wiki/Q458825","display_name":"Kernel density estimation","level":3,"score":0.6841980814933777},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6121618151664734},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6115450859069824},{"id":"https://openalex.org/C84894716","wikidata":"https://www.wikidata.org/wiki/Q6935135","display_name":"Multivariate kernel density estimation","level":5,"score":0.5774683952331543},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.5698512196540833},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.5616001486778259},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5581781268119812},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5516310334205627},{"id":"https://openalex.org/C131675550","wikidata":"https://www.wikidata.org/wiki/Q7646884","display_name":"Surrogate model","level":2,"score":0.4653967320919037},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.390512615442276},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.383955717086792},{"id":"https://openalex.org/C195699287","wikidata":"https://www.wikidata.org/wiki/Q7915722","display_name":"Variable kernel density estimation","level":4,"score":0.3314337134361267},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.25382739305496216},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.21859228610992432},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19205006957054138},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15440192818641663},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08702105283737183},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0862065851688385},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/18m1205959","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1205959","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1803.10991","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1803.10991","pdf_url":"https://arxiv.org/pdf/1803.10991","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":null,"raw_type":"text"},{"id":"mag:2887833842","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1803.10991","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1803.10991","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1803.10991","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:1803.10991","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1803.10991","pdf_url":"https://arxiv.org/pdf/1803.10991","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5164851507","display_name":null,"funder_award_id":"2016197","funder_id":"https://openalex.org/F4320308960","funder_display_name":"United States - Israel Binational Science Foundation"},{"id":"https://openalex.org/G8392339385","display_name":null,"funder_award_id":"177/13","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320308960","display_name":"United States - Israel Binational Science Foundation","ror":"https://ror.org/00j8z2m73"},{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2887833842.pdf","grobid_xml":"https://content.openalex.org/works/W2887833842.grobid-xml"},"referenced_works_count":59,"referenced_works":["https://openalex.org/W9270277","https://openalex.org/W196710731","https://openalex.org/W253307310","https://openalex.org/W1511694993","https://openalex.org/W1538934584","https://openalex.org/W1548879090","https://openalex.org/W1585641754","https://openalex.org/W1593038947","https://openalex.org/W1635622277","https://openalex.org/W1880751280","https://openalex.org/W1965555277","https://openalex.org/W1973924921","https://openalex.org/W1981936413","https://openalex.org/W1988793248","https://openalex.org/W2003223511","https://openalex.org/W2004814202","https://openalex.org/W2018159038","https://openalex.org/W2021718677","https://openalex.org/W2024408299","https://openalex.org/W2024448661","https://openalex.org/W2029289838","https://openalex.org/W2030351330","https://openalex.org/W2034008227","https://openalex.org/W2037916768","https://openalex.org/W2055081012","https://openalex.org/W2064517598","https://openalex.org/W2065015198","https://openalex.org/W2069848868","https://openalex.org/W2070335948","https://openalex.org/W2071134051","https://openalex.org/W2072227363","https://openalex.org/W2083044431","https://openalex.org/W2084216171","https://openalex.org/W2089205960","https://openalex.org/W2092589298","https://openalex.org/W2096045964","https://openalex.org/W2108001913","https://openalex.org/W2139798157","https://openalex.org/W2143591652","https://openalex.org/W2146766088","https://openalex.org/W2159555138","https://openalex.org/W2162870748","https://openalex.org/W2168170318","https://openalex.org/W2268201048","https://openalex.org/W2332607870","https://openalex.org/W2483714367","https://openalex.org/W2485771012","https://openalex.org/W2547374341","https://openalex.org/W2608192427","https://openalex.org/W2610903070","https://openalex.org/W2735484855","https://openalex.org/W2790231963","https://openalex.org/W2798909945","https://openalex.org/W2888649834","https://openalex.org/W2964177109","https://openalex.org/W3038165843","https://openalex.org/W3101211521","https://openalex.org/W3147513489","https://openalex.org/W3215037115"],"related_works":["https://openalex.org/W2974127650","https://openalex.org/W2615086650","https://openalex.org/W2336764469","https://openalex.org/W3119113059","https://openalex.org/W1982521055","https://openalex.org/W2149649559","https://openalex.org/W2420900836","https://openalex.org/W2056132268","https://openalex.org/W1972274727","https://openalex.org/W2033474637","https://openalex.org/W2885665095","https://openalex.org/W3022344114","https://openalex.org/W2067338210","https://openalex.org/W1908411054","https://openalex.org/W2949431998","https://openalex.org/W3011226793","https://openalex.org/W2617860789","https://openalex.org/W1569602402","https://openalex.org/W2903213216","https://openalex.org/W2098605271"],"abstract_inverted_index":{"The":[0],"effect":[1],"of":[2,9,36,100,103,110,141,183],"uncertainties":[3],"and":[4,105,150,185,200],"noise":[5],"on":[6],"a":[7,31,116],"quantity":[8,102,109,182],"interest":[10,104,111,184],"(model":[11],"output)":[12],"is":[13,30,87,128,137,162],"often":[14],"better":[15,138],"described":[16],"by":[17,24],"its":[18,25,186],"probability":[19],"density":[20,28,42,89,121,144,152,173],"function":[21],"(PDF)":[22],"than":[23,139],"moments.":[26],"Although":[27],"estimation":[29,43,90,122,145,174],"common":[32],"task,":[33],"the":[34,50,80,93,98,101,108,131,163,169,181],"adequacy":[35],"approximation":[37],"methods":[38,146],"(surrogate":[39],"models)":[40],"for":[41,72,83,120,172,195],"has":[44],"not":[45,106],"been":[46],"analyzed":[47],"before":[48],"in":[49,126,130,188,197],"uncertainty-quantification":[51],"literature.":[52],"In":[53],"this":[54],"paper,":[55],"we":[56,114,167,191],"first":[57],"show":[58],"that":[59,92,140,179],"standard":[60,142],"surrogate":[61,94,177],"models":[62],"(such":[63,147],"as":[64,148],"generalized":[65],"polynomial":[66,129],"chaos),":[67],"which":[68],"are":[69],"highly":[70],"accurate":[71],"moment":[73],"estimation,":[74],"might":[75],"completely":[76],"fail":[77],"to":[78],"approximate":[79,97],"PDF,":[81],"even":[82],"one-dimensional":[84],"noise.":[85],"This":[86,134],"because":[88],"requires":[91],"model":[95,178],"accurately":[96],"gradient":[99,187],"just":[107],"itself.":[112],"Hence,":[113],"develop":[115],"novel":[117],"spline-based":[118],"algorithm":[119,194],"whose":[123],"convergence":[124,135,170],"rate":[125,136,171],"$L^q$":[127],"sampling":[132],"resolution.":[133],"statistical":[143],"histograms":[149],"kernel":[151],"estimators)":[153],"at":[154],"dimensions":[155],"$1":[156],"\\leq":[157],"d\\leq":[158],"\\frac{5}{2}m$,":[159],"where":[160],"$m$":[161],"spline":[164],"order.":[165],"Furthermore,":[166],"obtain":[168],"with":[175],"any":[176],"approximates":[180],"$L^{\\infty}$.":[189],"Finally,":[190],"demonstrate":[192],"our":[193],"problems":[196],"nonlinear":[198],"optics":[199],"fluid":[201],"dynamics.":[202]},"counts_by_year":[{"year":2024,"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"}
