{"id":"https://openalex.org/W2596028806","doi":"https://doi.org/10.1080/00207160.2017.1299861","title":"Application of local improvements to reduced-order models to sampling methods for nonlinear PDEs with noise","display_name":"Application of local improvements to reduced-order models to sampling methods for nonlinear PDEs with noise","publication_year":2017,"publication_date":"2017-03-16","ids":{"openalex":"https://openalex.org/W2596028806","doi":"https://doi.org/10.1080/00207160.2017.1299861","mag":"2596028806"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2017.1299861","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2017.1299861","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5012536010","display_name":"Maziar Raissi","orcid":"https://orcid.org/0000-0002-8467-4568"},"institutions":[{"id":"https://openalex.org/I162714631","display_name":"George Mason University","ror":"https://ror.org/02jqj7156","country_code":"US","type":"education","lineage":["https://openalex.org/I162714631"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"M. Raissi","raw_affiliation_strings":["Department of Mathematical Sciences, George Mason University, Fairfax, VA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, George Mason University, Fairfax, VA, USA","institution_ids":["https://openalex.org/I162714631"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029673753","display_name":"Padmanabhan Seshaiyer","orcid":"https://orcid.org/0000-0002-4303-4636"},"institutions":[{"id":"https://openalex.org/I162714631","display_name":"George Mason University","ror":"https://ror.org/02jqj7156","country_code":"US","type":"education","lineage":["https://openalex.org/I162714631"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"P. Seshaiyer","raw_affiliation_strings":["Department of Mathematical Sciences, George Mason University, Fairfax, VA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, George Mason University, Fairfax, VA, USA","institution_ids":["https://openalex.org/I162714631"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5012536010"],"corresponding_institution_ids":["https://openalex.org/I162714631"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.02619606,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"95","issue":"5","first_page":"870","last_page":"880"},"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/T12560","display_name":"Nuclear Engineering Thermal-Hydraulics","score":0.9853000044822693,"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":0.618781328201294},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.5515413880348206},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.5479151010513306},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5373572111129761},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5344437956809998},{"id":"https://openalex.org/keywords/model-order-reduction","display_name":"Model order reduction","score":0.5240398049354553},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5175966024398804},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48662933707237244},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.48165881633758545},{"id":"https://openalex.org/keywords/fidelity","display_name":"Fidelity","score":0.4510915279388428},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.42385274171829224},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4210435748100281},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3749057650566101},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3406233489513397},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08192148804664612},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07293084263801575}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.618781328201294},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.5515413880348206},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.5479151010513306},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5373572111129761},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5344437956809998},{"id":"https://openalex.org/C2779277453","wikidata":"https://www.wikidata.org/wiki/Q12202921","display_name":"Model order reduction","level":3,"score":0.5240398049354553},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5175966024398804},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48662933707237244},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.48165881633758545},{"id":"https://openalex.org/C2776459999","wikidata":"https://www.wikidata.org/wiki/Q2119376","display_name":"Fidelity","level":2,"score":0.4510915279388428},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.42385274171829224},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4210435748100281},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3749057650566101},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3406233489513397},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08192148804664612},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07293084263801575},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2017.1299861","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2017.1299861","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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":26,"referenced_works":["https://openalex.org/W145067746","https://openalex.org/W259723797","https://openalex.org/W1971099220","https://openalex.org/W1971508897","https://openalex.org/W1983156129","https://openalex.org/W1989951672","https://openalex.org/W1990568935","https://openalex.org/W1996568929","https://openalex.org/W2015431729","https://openalex.org/W2017745440","https://openalex.org/W2032733248","https://openalex.org/W2047947072","https://openalex.org/W2052272941","https://openalex.org/W2058544887","https://openalex.org/W2069754569","https://openalex.org/W2071128523","https://openalex.org/W2083845086","https://openalex.org/W2125301070","https://openalex.org/W2128341577","https://openalex.org/W2142863015","https://openalex.org/W2144144515","https://openalex.org/W2149493559","https://openalex.org/W2294798173","https://openalex.org/W2466218146","https://openalex.org/W2743229471","https://openalex.org/W4300875669"],"related_works":["https://openalex.org/W2370840338","https://openalex.org/W2388641108","https://openalex.org/W2381850946","https://openalex.org/W4380449851","https://openalex.org/W2368317224","https://openalex.org/W2370651559","https://openalex.org/W3125091513","https://openalex.org/W4318832338","https://openalex.org/W2383177152","https://openalex.org/W3000893075"],"abstract_inverted_index":{"In":[0,34],"this":[1,103],"work,":[2],"we":[3],"extend":[4],"upon":[5],"the":[6,39,50,68,100,116],"results":[7],"of":[8,52,99,102,115],"Raissi":[9,35,72],"and":[10,36,73],"Seshaiyer":[11,37,74],"[A":[12],"multi-fidelity":[13],"stochastic":[14,58],"collocation":[15],"method":[16,69],"for":[17],"parabolic":[18],"partial":[19],"differential":[20],"equations":[21],"with":[22],"random":[23],"input":[24],"data,":[25],"Int.":[26],"J.":[27],"Uncertain.":[28],"Quantif.":[29],"4(3)":[30],"(2014),":[31,38],"pp.":[32],"225\u2013242].":[33],"authors":[40],"propose":[41],"to":[42,48,63,66,76,83,91,107],"use":[43],"deterministic":[44],"model":[45],"reduction":[46],"techniques":[47],"enhance":[49],"performance":[51],"sampling":[53],"methods":[54],"like":[55],"Monte-Carlo":[56],"or":[57],"collocation.":[59],"However,":[60],"in":[61,71],"order":[62],"be":[64,84],"able":[65],"apply":[67],"proposed":[70],"(2014)":[75],"non-linear":[77],"problems":[78],"a":[79],"crucial":[80],"step":[81,87],"needs":[82],"taken.":[85],"This":[86,94],"involves":[88],"local":[89],"improvements":[90,106],"reduced-order":[92,108],"models.":[93],"paper":[95],"is":[96],"an":[97],"illustration":[98],"importance":[101],"step.":[104],"Local":[105],"models":[109],"are":[110],"achieved":[111],"using":[112],"sensitivity":[113],"analysis":[114],"proper":[117],"orthogonal":[118],"decomposition.":[119]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2}],"updated_date":"2026-03-26T15:22:09.906841","created_date":"2025-10-10T00:00:00"}
