{"id":"https://openalex.org/W2085298086","doi":"https://doi.org/10.1137/130940517","title":"Weighted Reduced Basis Method for Stochastic Optimal Control Problems with Elliptic PDE Constraint","display_name":"Weighted Reduced Basis Method for Stochastic Optimal Control Problems with Elliptic PDE Constraint","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2085298086","doi":"https://doi.org/10.1137/130940517","mag":"2085298086"},"language":"en","primary_location":{"id":"doi:10.1137/130940517","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130940517","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":"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/A5100338488","display_name":"Peng Chen","orcid":"https://orcid.org/0000-0003-4215-9901"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Peng Chen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5013754088","display_name":"Alfio Quarteroni","orcid":"https://orcid.org/0000-0002-5947-6885"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alfio Quarteroni","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.2649,"has_fulltext":false,"cited_by_count":59,"citation_normalized_percentile":{"value":0.97178707,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"2","issue":"1","first_page":"364","last_page":"396"},"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":0.9987999796867371,"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"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9973999857902527,"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/discretization","display_name":"Discretization","score":0.7358945608139038},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6691117286682129},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.5766229629516602},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.5542647838592529},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5438414812088013},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5143436193466187},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5088256001472473},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.5064562559127808},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5036877989768982},{"id":"https://openalex.org/keywords/stochastic-control","display_name":"Stochastic control","score":0.4927535355091095},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.470140278339386},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4570593237876892},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.45196303725242615},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.4399900734424591},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.41787779331207275},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23564955592155457},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16952061653137207}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7358945608139038},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6691117286682129},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.5766229629516602},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.5542647838592529},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5438414812088013},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5143436193466187},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5088256001472473},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5064562559127808},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5036877989768982},{"id":"https://openalex.org/C170131372","wikidata":"https://www.wikidata.org/wiki/Q7617811","display_name":"Stochastic control","level":3,"score":0.4927535355091095},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.470140278339386},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4570593237876892},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.45196303725242615},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4399900734424591},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.41787779331207275},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23564955592155457},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16952061653137207},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/130940517","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130940517","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:re.public.polimi.it:11311/1016624","is_oa":false,"landing_page_url":"http://hdl.handle.net/11311/1016624","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"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":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1506304142","https://openalex.org/W1555557982","https://openalex.org/W1558333494","https://openalex.org/W1708679080","https://openalex.org/W1820125862","https://openalex.org/W1966886095","https://openalex.org/W1967011851","https://openalex.org/W1970476229","https://openalex.org/W1982421072","https://openalex.org/W1983156129","https://openalex.org/W2010916308","https://openalex.org/W2021411519","https://openalex.org/W2022176369","https://openalex.org/W2022977680","https://openalex.org/W2027362114","https://openalex.org/W2031567600","https://openalex.org/W2034942773","https://openalex.org/W2039055345","https://openalex.org/W2040960244","https://openalex.org/W2052690618","https://openalex.org/W2062993069","https://openalex.org/W2067780150","https://openalex.org/W2070999115","https://openalex.org/W2082406229","https://openalex.org/W2083845086","https://openalex.org/W2092622790","https://openalex.org/W2112649070","https://openalex.org/W2116478899","https://openalex.org/W2116621195","https://openalex.org/W2128702576","https://openalex.org/W2143591652","https://openalex.org/W2162221417","https://openalex.org/W2341548236","https://openalex.org/W3040267042"],"related_works":["https://openalex.org/W2943897807","https://openalex.org/W3120484221","https://openalex.org/W4366198066","https://openalex.org/W3047748938","https://openalex.org/W2358522863","https://openalex.org/W4386034604","https://openalex.org/W278441094","https://openalex.org/W3099285423","https://openalex.org/W4381248241","https://openalex.org/W2336173978"],"abstract_inverted_index":{"In":[0,86],"this":[1],"paper":[2],"we":[3,63,93],"develop":[4,94],"and":[5,34,75,118],"analyze":[6],"an":[7,19],"efficient":[8],"computational":[9,91],"method":[10,68,79],"for":[11,69,80],"solving":[12],"stochastic":[13,47,57,77],"optimal":[14,38,43],"control":[15],"problems":[16],"constrained":[17],"by":[18],"elliptic":[20],"partial":[21],"differential":[22],"equation":[23],"(PDE)":[24],"with":[25],"random":[26,84],"input":[27],"data.":[28],"We":[29],"first":[30],"prove":[31],"both":[32],"existence":[33],"uniqueness":[35],"of":[36,41,53,56,72,83,111],"the":[37,42,46,54,70,81,90,112],"solution.":[39],"Regularity":[40],"solution":[44],"in":[45,51],"space":[48],"is":[49,115],"studied":[50],"view":[52],"analysis":[55,110],"approximation":[58,114],"error.":[59],"For":[60],"numerical":[61,113,120],"approximation,":[62],"employ":[64],"a":[65,76,95,102],"finite":[66],"element":[67],"discretization":[71,82],"physical":[73],"variables,":[74],"collocation":[78],"variables.":[85],"order":[87,97],"to":[88,124],"alleviate":[89],"effort,":[92],"model":[96],"reduction":[98],"strategy":[99],"based":[100],"on":[101],"weighted":[103],"reduced":[104],"basis":[105],"method.":[106],"A":[107],"global":[108],"error":[109],"carried":[116],"out,":[117],"several":[119],"tests":[121],"are":[122],"performed":[123],"verify":[125],"our":[126],"analysis.":[127]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
