{"id":"https://openalex.org/W2301535466","doi":"https://doi.org/10.1137/16m1056444","title":"An Ensemble-Proper Orthogonal Decomposition Method for the Nonstationary Navier--Stokes Equations","display_name":"An Ensemble-Proper Orthogonal Decomposition Method for the Nonstationary Navier--Stokes Equations","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2301535466","doi":"https://doi.org/10.1137/16m1056444","mag":"2301535466"},"language":"en","primary_location":{"id":"doi:10.1137/16m1056444","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1056444","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/1603.04777","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076283476","display_name":"Max Gunzburger","orcid":"https://orcid.org/0000-0003-0921-9079"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Max Gunzburger","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060285534","display_name":"Nan Jiang","orcid":"https://orcid.org/0000-0002-1080-258X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nan Jiang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5011820135","display_name":"Michael Schneier","orcid":"https://orcid.org/0000-0003-1101-4507"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael Schneier","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5076283476"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1733,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.44954319,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"55","issue":"1","first_page":"286","last_page":"304"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998999834060669,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.995199978351593,"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/T12560","display_name":"Nuclear Engineering Thermal-Hydraulics","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"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/mathematics","display_name":"Mathematics","score":0.586205005645752},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.584363579750061},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5648869276046753},{"id":"https://openalex.org/keywords/proper-orthogonal-decomposition","display_name":"Proper orthogonal decomposition","score":0.5581863522529602},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5524571537971497},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.545140266418457},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5248111486434937},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5238533020019531},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4966297745704651},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4713446795940399},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.41547682881355286},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30335864424705505},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.28804486989974976},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18626081943511963},{"id":"https://openalex.org/keywords/point-of-delivery","display_name":"Point of delivery","score":0.12142553925514221}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.586205005645752},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.584363579750061},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5648869276046753},{"id":"https://openalex.org/C2984998066","wikidata":"https://www.wikidata.org/wiki/Q105037988","display_name":"Proper orthogonal decomposition","level":3,"score":0.5581863522529602},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5524571537971497},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.545140266418457},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5248111486434937},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5238533020019531},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4966297745704651},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4713446795940399},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.41547682881355286},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30335864424705505},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28804486989974976},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18626081943511963},{"id":"https://openalex.org/C137776501","wikidata":"https://www.wikidata.org/wiki/Q7208270","display_name":"Point of delivery","level":2,"score":0.12142553925514221},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/16m1056444","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1056444","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1603.04777","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1603.04777","pdf_url":"https://arxiv.org/pdf/1603.04777","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:2301535466","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1603.04777.pdf","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.1603.04777","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1603.04777","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:1603.04777","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1603.04777","pdf_url":"https://arxiv.org/pdf/1603.04777","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/G1523888516","display_name":null,"funder_award_id":"FA9550-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G227703289","display_name":null,"funder_award_id":"FA9550-15-1-000","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G2553306785","display_name":null,"funder_award_id":"FA9550-15-1-0001","funder_id":"https://openalex.org/F4320332467","funder_display_name":"U.S. Air Force"},{"id":"https://openalex.org/G4635511262","display_name":null,"funder_award_id":"FA9550-15-1-0001","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G5809100787","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G609617663","display_name":null,"funder_award_id":"DE-SC0009324","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G6543358554","display_name":null,"funder_award_id":"FA9550-15-1-0001","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G7090116110","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320332467","funder_display_name":"U.S. Air Force"},{"id":"https://openalex.org/G8069151137","display_name":null,"funder_award_id":"DE-SC0010678","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320332359","display_name":"Office of Science","ror":"https://ror.org/00mmn6b08"},{"id":"https://openalex.org/F4320332467","display_name":"U.S. Air Force","ror":"https://ror.org/006gmme17"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2301535466.pdf","grobid_xml":"https://content.openalex.org/works/W2301535466.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W73123583","https://openalex.org/W134367920","https://openalex.org/W209265777","https://openalex.org/W1489519217","https://openalex.org/W1510334898","https://openalex.org/W1561569551","https://openalex.org/W1579236455","https://openalex.org/W1968541242","https://openalex.org/W1989951672","https://openalex.org/W2001027221","https://openalex.org/W2026123674","https://openalex.org/W2029309765","https://openalex.org/W2041243668","https://openalex.org/W2049741199","https://openalex.org/W2069824076","https://openalex.org/W2073594627","https://openalex.org/W2085551594","https://openalex.org/W2087755601","https://openalex.org/W2087778158","https://openalex.org/W2095041371","https://openalex.org/W2096345667","https://openalex.org/W2097652335","https://openalex.org/W2101743932","https://openalex.org/W2106090507","https://openalex.org/W2127843081","https://openalex.org/W2148105077","https://openalex.org/W2176150232","https://openalex.org/W2409648791","https://openalex.org/W2963056102"],"related_works":["https://openalex.org/W2754720210","https://openalex.org/W2625685423","https://openalex.org/W1994064939","https://openalex.org/W2188342050","https://openalex.org/W1964392002","https://openalex.org/W2985052740","https://openalex.org/W2964544862","https://openalex.org/W2067485895","https://openalex.org/W2010334931","https://openalex.org/W2751587025","https://openalex.org/W206853762","https://openalex.org/W2805131913","https://openalex.org/W2551923682","https://openalex.org/W3027732438","https://openalex.org/W760150438","https://openalex.org/W70134582","https://openalex.org/W1558506802","https://openalex.org/W2974791629","https://openalex.org/W2925064267","https://openalex.org/W646573028"],"abstract_inverted_index":{"The":[0,21,85,141],"definition":[1],"of":[2,11,23,28,52,59,76,90,103,120,124],"partial":[3],"differential":[4],"equation":[5],"models":[6],"usually":[7],"involves":[8],"a":[9,18,25,66,100,130],"set":[10,27,102],"parameters":[12],"whose":[13],"values":[14,30],"may":[15,31],"vary":[16],"over":[17],"wide":[19],"range.":[20],"solution":[22],"even":[24],"single":[26],"parameter":[29,53,83],"be":[32],"quite":[33],"expensive.":[34],"In":[35],"many":[36,50,82],"cases,":[37],"e.g.,":[38],"optimization,":[39],"control,":[40],"uncertainty":[41],"quantification,":[42],"and":[43,143],"other":[44],"settings,":[45],"solutions":[46,79,93,108,123],"are":[47,150],"needed":[48],"for":[49,64,72,146],"sets":[51],"values.":[54],"We":[55],"consider":[56],"the":[57,60,73,77,88,91,107,110,118,125,138,147,153],"case":[58],"time-dependent":[61],"Navier--Stokes":[62,126],"equations":[63,104],"which":[65],"recently":[67],"developed":[68],"ensemble-based":[69,139,148],"method":[70,86,149],"allows":[71],"efficient":[74],"determination":[75],"multiple":[78,92,122],"corresponding":[80],"to":[81,98,152],"sets.":[84],"uses":[87],"average":[89],"at":[94,109],"any":[95],"time":[96,112],"step":[97],"define":[99],"linear":[101],"that":[105],"determines":[106],"next":[111],"step.":[113],"To":[114],"significantly":[115],"further":[116],"reduce":[117],"costs":[119],"determining":[121],"equations,":[127],"we":[128],"incorporate":[129],"proper":[131],"orthogonal":[132],"decomposition":[133],"(POD)":[134],"reduced-order":[135],"model":[136],"into":[137],"method.":[140],"stability":[142],"convergence":[144],"results":[145],"extended":[151],"ensemble-POD":[154],"approach.":[155]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
