{"id":"https://openalex.org/W2613465422","doi":"https://doi.org/10.1137/16m1082688","title":"A Multilevel, Hierarchical Sampling Technique for Spatially Correlated Random Fields","display_name":"A Multilevel, Hierarchical Sampling Technique for Spatially Correlated Random Fields","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2613465422","doi":"https://doi.org/10.1137/16m1082688","mag":"2613465422"},"language":"en","primary_location":{"id":"doi:10.1137/16m1082688","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1082688","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":true,"oa_status":"green","oa_url":"https://www.osti.gov/biblio/1438756","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020792389","display_name":"Sarah Osborn","orcid":"https://orcid.org/0000-0003-3256-3337"},"institutions":[{"id":"https://openalex.org/I1282311441","display_name":"Lawrence Livermore National Laboratory","ror":"https://ror.org/041nk4h53","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282311441","https://openalex.org/I1330989302","https://openalex.org/I198811213","https://openalex.org/I4210138311"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Sarah Osborn","raw_affiliation_strings":["Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scienti\fc Computing"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scienti\fc Computing","institution_ids":["https://openalex.org/I1282311441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027636165","display_name":"Panayot S. Vassilevski","orcid":"https://orcid.org/0000-0002-5294-7242"},"institutions":[{"id":"https://openalex.org/I1282311441","display_name":"Lawrence Livermore National Laboratory","ror":"https://ror.org/041nk4h53","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282311441","https://openalex.org/I1330989302","https://openalex.org/I198811213","https://openalex.org/I4210138311"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Panayot S. Vassilevski","raw_affiliation_strings":["Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scienti\fc Computing"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scienti\fc Computing","institution_ids":["https://openalex.org/I1282311441"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083076229","display_name":"Umberto Villa","orcid":"https://orcid.org/0000-0002-5142-2559"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Umberto Villa","raw_affiliation_strings":["Univ. of Texas, Austin, TX (United States). Institute for Computational Engineering and Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ. of Texas, Austin, TX (United States). Institute for Computational Engineering and Sciences","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5020792389"],"corresponding_institution_ids":["https://openalex.org/I1282311441"],"apc_list":null,"apc_paid":null,"fwci":2.013,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.87680961,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"39","issue":"5","first_page":"S543","last_page":"S562"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9998000264167786,"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":0.9998000264167786,"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/T10894","display_name":"Groundwater flow and contamination studies","score":0.9959999918937683,"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/T10770","display_name":"Soil Geostatistics and Mapping","score":0.9932000041007996,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6088457107543945},{"id":"https://openalex.org/keywords/random-field","display_name":"Random field","score":0.5772512555122375},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.5346981883049011},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49930644035339355},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4742569029331207},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.46330079436302185},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45162007212638855},{"id":"https://openalex.org/keywords/gaussian-random-field","display_name":"Gaussian random field","score":0.43939048051834106},{"id":"https://openalex.org/keywords/parametrization","display_name":"Parametrization (atmospheric modeling)","score":0.4175834059715271},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.41441529989242554},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.38268810510635376},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3106750249862671},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.2920383810997009},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1771899163722992},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12442845106124878}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6088457107543945},{"id":"https://openalex.org/C130402806","wikidata":"https://www.wikidata.org/wiki/Q5361768","display_name":"Random field","level":2,"score":0.5772512555122375},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.5346981883049011},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49930644035339355},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4742569029331207},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.46330079436302185},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45162007212638855},{"id":"https://openalex.org/C51267290","wikidata":"https://www.wikidata.org/wiki/Q5527848","display_name":"Gaussian random field","level":4,"score":0.43939048051834106},{"id":"https://openalex.org/C202887219","wikidata":"https://www.wikidata.org/wiki/Q3895221","display_name":"Parametrization (atmospheric modeling)","level":3,"score":0.4175834059715271},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.41441529989242554},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.38268810510635376},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3106750249862671},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.2920383810997009},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1771899163722992},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12442845106124878},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0},{"id":"https://openalex.org/C74902906","wikidata":"https://www.wikidata.org/wiki/Q1190858","display_name":"Radiative transfer","level":2,"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/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/16m1082688","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1082688","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"},{"id":"pmh:oai:osti.gov:1438756","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1438756","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"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":null}],"best_oa_location":{"id":"pmh:oai:osti.gov:1438756","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1438756","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"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":null},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1445618291","https://openalex.org/W1747046542","https://openalex.org/W1837874438","https://openalex.org/W1973312823","https://openalex.org/W1980053021","https://openalex.org/W1998290124","https://openalex.org/W2010804587","https://openalex.org/W2018843168","https://openalex.org/W2050206349","https://openalex.org/W2070232376","https://openalex.org/W2072282162","https://openalex.org/W2079321251","https://openalex.org/W2082312113","https://openalex.org/W2089139137","https://openalex.org/W2112280313","https://openalex.org/W2128563079","https://openalex.org/W2135459060","https://openalex.org/W2138486270","https://openalex.org/W2149498546","https://openalex.org/W2163715525","https://openalex.org/W2962707560"],"related_works":["https://openalex.org/W3101730079","https://openalex.org/W4285599464","https://openalex.org/W2010794544","https://openalex.org/W2397703052","https://openalex.org/W4226280513","https://openalex.org/W2101272603","https://openalex.org/W4211052589","https://openalex.org/W4225610176","https://openalex.org/W2262012800","https://openalex.org/W1489542724"],"abstract_inverted_index":{"We":[0,78],"propose":[1,79],"an":[2],"alternative":[3],"method":[4,124],"to":[5,16,67,87,117],"generate":[6],"samples":[7,30],"of":[8,22,83,101,121,130],"a":[9,42,63,80,96,102,107,136],"spatially":[10],"correlated":[11],"random":[12],"field":[13,86],"with":[14,106],"applications":[15],"large-scale":[17,52],"problems":[18],"for":[19,27,51,89,135],"forward":[20],"propagation":[21],"uncertainty.":[23],"A":[24],"classical":[25],"approach":[26],"generating":[28],"these":[29],"is":[31,47,75],"the":[32,37,72,84,119,122,143],"Karhunen--Lo\u00e8ve":[33],"(KL)":[34],"decomposition.":[35],"However,":[36],"KL":[38],"expansion":[39],"requires":[40],"solving":[41,95],"dense":[43],"eigenvalue":[44],"problem":[45],"and":[46],"therefore":[48],"computationally":[49],"infeasible":[50],"problems.":[53],"Sampling":[54],"methods":[55],"based":[56,93],"on":[57,94],"stochastic":[58,85,103],"partial":[59],"differential":[60],"equations":[61],"provide":[62],"highly":[64],"scalable":[65],"way":[66],"sample":[68],"Gaussian":[69],"fields,":[70],"but":[71],"resulting":[73],"parametrization":[74],"mesh":[76],"dependent.":[77],"multilevel":[81,131],"decomposition":[82],"allow":[88],"scalable,":[90],"hierarchical":[91],"sampling":[92,123,145],"mixed":[97],"finite":[98],"element":[99],"formulation":[100],"reaction-diffusion":[104],"equation":[105],"random,":[108],"white":[109],"noise":[110],"source":[111],"function.":[112],"Numerical":[113],"experiments":[114],"are":[115],"presented":[116],"demonstrate":[118],"scalability":[120],"as":[125,127],"well":[126],"numerical":[128],"results":[129],"Monte":[132],"Carlo":[133],"simulations":[134],"subsurface":[137],"porous":[138],"media":[139],"flow":[140],"application":[141],"using":[142],"proposed":[144],"method.":[146]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-10T08:33:47.465468","created_date":"2025-10-10T00:00:00"}
