{"id":"https://openalex.org/W1984114259","doi":"https://doi.org/10.1137/100817498","title":"Refinement Criteria for Simplex Stochastic Collocation with Local Extremum Diminishing Robustness","display_name":"Refinement Criteria for Simplex Stochastic Collocation with Local Extremum Diminishing Robustness","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1984114259","doi":"https://doi.org/10.1137/100817498","mag":"1984114259"},"language":"en","primary_location":{"id":"doi:10.1137/100817498","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100817498","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/A5020618592","display_name":"Jeroen Witteveen","orcid":"https://orcid.org/0000-0002-7459-0774"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jeroen A. S. Witteveen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5047377841","display_name":"Gianluca Iaccarino","orcid":"https://orcid.org/0000-0003-3659-7745"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gianluca Iaccarino","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":4.1194,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.94582846,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"34","issue":"3","first_page":"A1522","last_page":"A1543"},"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":0.9927999973297119,"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":0.9919000267982483,"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/mathematics","display_name":"Mathematics","score":0.7960355281829834},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.7246042490005493},{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.5893672108650208},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5214383006095886},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45699211955070496},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.4126974940299988},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10577484965324402}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7960355281829834},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.7246042490005493},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.5893672108650208},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5214383006095886},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45699211955070496},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.4126974940299988},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10577484965324402},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/100817498","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100817498","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1634277530","https://openalex.org/W1966827182","https://openalex.org/W1972020904","https://openalex.org/W1978744409","https://openalex.org/W1982421072","https://openalex.org/W1983156129","https://openalex.org/W1996687420","https://openalex.org/W1998830482","https://openalex.org/W2004814202","https://openalex.org/W2015628091","https://openalex.org/W2018159038","https://openalex.org/W2039150507","https://openalex.org/W2044390636","https://openalex.org/W2048874176","https://openalex.org/W2052196828","https://openalex.org/W2055460625","https://openalex.org/W2061604462","https://openalex.org/W2062163080","https://openalex.org/W2070335948","https://openalex.org/W2083845086","https://openalex.org/W2096969866","https://openalex.org/W2103452908","https://openalex.org/W2105596596","https://openalex.org/W2108001913","https://openalex.org/W2112548197","https://openalex.org/W2139798157","https://openalex.org/W2140951396","https://openalex.org/W2143591652","https://openalex.org/W2147927632","https://openalex.org/W2153789649","https://openalex.org/W2161783230","https://openalex.org/W2167720109"],"related_works":["https://openalex.org/W4296209631","https://openalex.org/W2063021680","https://openalex.org/W2561617217","https://openalex.org/W2357922472","https://openalex.org/W4294811468","https://openalex.org/W2384278689","https://openalex.org/W2355801475","https://openalex.org/W2170062176","https://openalex.org/W2386777115","https://openalex.org/W88330805"],"abstract_inverted_index":{"The":[0,17,83],"simplex":[1],"stochastic":[2],"collocation":[3],"method":[4,88],"is":[5,22,70,89,118],"developed":[6],"for":[7,65,108],"adaptive":[8,20,87],"uncertainty":[9],"quantification":[10],"in":[11,74],"computational":[12],"problems":[13],"with":[14,81],"random":[15],"inputs.":[16],"effectiveness":[18],"of":[19,59,79,85],"formulations":[21],"determined":[23],"to":[24,98,121],"a":[25,76],"large":[26],"extent":[27],"by":[28,91],"both":[29,113],"the":[30,36,55,60,66,86,92,102,115,122,130],"$h$-":[31],"and":[32,35,43,124,128],"$p$-refinement":[33],"measures":[34,46,132],"stopping":[37,41,116],"criterion.":[38],"An":[39],"improved":[40],"criterion":[42,117],"different":[44],"$h$-refinement":[45],"are":[47],"derived":[48],"from":[49],"an":[50],"error":[51,126],"estimate":[52],"based":[53],"on":[54],"root":[56],"mean":[57],"square":[58],"hierarchical":[61],"surpluses.":[62],"A":[63],"$p$-criterion":[64],"polynomial":[67],"degree":[68],"$p$":[69],"established":[71],"that":[72,114,129],"achieves,":[73],"principle,":[75],"constant":[77],"order":[78],"convergence":[80],"dimensionality.":[82],"robustness":[84],"guaranteed":[90],"local":[93,104],"extremum":[94,105],"diminishing":[95],"concept":[96],"extended":[97],"probability":[99],"space":[100],"using":[101],"introduced":[103],"conserving":[106],"limiter":[107],"$p$.":[109],"Numerical":[110],"results":[111],"show":[112],"reliable":[119],"owing":[120],"accurate":[123],"conservative":[125],"estimate,":[127],"refinement":[131],"outperform":[133],"uniform":[134],"refinement.":[135]},"counts_by_year":[{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":7}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
