{"id":"https://openalex.org/W3175533034","doi":"https://doi.org/10.1137/20m1336515","title":"Polynomial Chaos as a Control Variate Method","display_name":"Polynomial Chaos as a Control Variate Method","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3175533034","doi":"https://doi.org/10.1137/20m1336515","mag":"3175533034"},"language":"en","primary_location":{"id":"doi:10.1137/20m1336515","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1336515","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Journal on Scientific Computing","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/A5019628027","display_name":"Jamie Fox","orcid":"https://orcid.org/0000-0001-9038-2361"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jamie Fox","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5090457966","display_name":"Giray \u00d6kten","orcid":"https://orcid.org/0000-0003-2594-1758"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Giray \u00d6kten","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5019628027"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5218,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.80504414,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"43","issue":"3","first_page":"A2268","last_page":"A2294"},"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/T11371","display_name":"Wind and Air Flow Studies","score":0.9399999976158142,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9314000010490417,"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/polynomial-chaos","display_name":"Polynomial chaos","score":0.9051876068115234},{"id":"https://openalex.org/keywords/sobol-sequence","display_name":"Sobol sequence","score":0.864936351776123},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.7032465934753418},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6742748022079468},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6512621641159058},{"id":"https://openalex.org/keywords/control-variates","display_name":"Control variates","score":0.6456509232521057},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5873436331748962},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5795835256576538},{"id":"https://openalex.org/keywords/sensitivity","display_name":"Sensitivity (control systems)","score":0.46600160002708435},{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.4240434765815735},{"id":"https://openalex.org/keywords/random-variate","display_name":"Random variate","score":0.42305833101272583},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3740348219871521},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.2493671178817749},{"id":"https://openalex.org/keywords/hybrid-monte-carlo","display_name":"Hybrid Monte Carlo","score":0.20418083667755127},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.166100412607193},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.13282498717308044},{"id":"https://openalex.org/keywords/markov-chain-monte-carlo","display_name":"Markov chain Monte Carlo","score":0.10908520221710205}],"concepts":[{"id":"https://openalex.org/C197656079","wikidata":"https://www.wikidata.org/wiki/Q17147719","display_name":"Polynomial chaos","level":3,"score":0.9051876068115234},{"id":"https://openalex.org/C49740808","wikidata":"https://www.wikidata.org/wiki/Q7550116","display_name":"Sobol sequence","level":3,"score":0.864936351776123},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.7032465934753418},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6742748022079468},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6512621641159058},{"id":"https://openalex.org/C121683094","wikidata":"https://www.wikidata.org/wiki/Q3554721","display_name":"Control variates","level":5,"score":0.6456509232521057},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5873436331748962},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5795835256576538},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.46600160002708435},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.4240434765815735},{"id":"https://openalex.org/C141547133","wikidata":"https://www.wikidata.org/wiki/Q7291996","display_name":"Random variate","level":3,"score":0.42305833101272583},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3740348219871521},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.2493671178817749},{"id":"https://openalex.org/C13153151","wikidata":"https://www.wikidata.org/wiki/Q1639846","display_name":"Hybrid Monte Carlo","level":4,"score":0.20418083667755127},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.166100412607193},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13282498717308044},{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.10908520221710205},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/20m1336515","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1336515","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Journal on Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1973492181","https://openalex.org/W1980609382","https://openalex.org/W2018159038","https://openalex.org/W2029767409","https://openalex.org/W2045355467","https://openalex.org/W2049774453","https://openalex.org/W2101589741","https://openalex.org/W2107880495","https://openalex.org/W2696437456","https://openalex.org/W2726925287","https://openalex.org/W2921426515"],"related_works":["https://openalex.org/W2965675185","https://openalex.org/W4352981514","https://openalex.org/W2372527200","https://openalex.org/W2321583666","https://openalex.org/W4301851442","https://openalex.org/W2133421790","https://openalex.org/W4289883505","https://openalex.org/W2761503845","https://openalex.org/W2015607830","https://openalex.org/W2163792679"],"abstract_inverted_index":{"We":[0,19,106],"introduce":[1,107],"a":[2,13,45,84,89],"control":[3,27,71,82,112],"variate":[4,28,72,113],"Monte":[5,41,129],"Carlo":[6,42,130],"method":[7],"to":[8,83,144],"estimate":[9],"$E[f(X)]$":[10],"based":[11],"on":[12],"polynomial":[14,35,59,85,110,137],"chaos":[15,36,60,86],"expansion":[16],"for":[17,115],"$f(X)$.":[18],"analyze":[20],"the":[21,26,31,34,51,58,64,67,70,77,81,95,99,116,149],"mean":[22],"square":[23],"error":[24],"of":[25,33,54,66,79,88,98,118,151],"estimator":[29],"when":[30],"coefficients":[32,61],"approximation":[37,87],"are":[38],"obtained":[39],"from":[40],"simulation.":[43],"For":[44],"fixed":[46],"computational":[47],"cost,":[48],"we":[49,75,140],"determine":[50],"optimal":[52],"allocation":[53],"cost":[55],"between":[56],"approximating":[57],"and":[62,122,131,147],"estimating":[63],"expectation":[65],"function":[68],"with":[69],"estimator.":[73],"Then,":[74],"examine":[76],"effects":[78],"setting":[80],"reduced":[90],"model,":[91],"formed":[92],"by":[93],"freezing":[94],"insignificant":[96],"inputs":[97],"original":[100],"model":[101],"using":[102],"global":[103],"sensitivity":[104,120],"analysis.":[105],"two":[108],"other":[109],"chaos-based":[111],"methods":[114,125],"calculation":[117],"Sobol'":[119],"indices,":[121],"compare":[123],"our":[124],"numerically":[126],"against":[127],"crude":[128],"an":[132],"approach":[133],"that":[134],"only":[135],"uses":[136],"chaos.":[138],"Finally,":[139],"present":[141],"some":[142],"applications":[143],"option":[145],"pricing,":[146],"compute":[148],"sensitivities":[150],"IEEE":[152],"14":[153],"busbar":[154],"power":[155],"system.":[156]},"counts_by_year":[{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-05T08:41:31.759640","created_date":"2025-10-10T00:00:00"}
