{"id":"https://openalex.org/W3045668026","doi":"https://doi.org/10.1137/19m1277485","title":"A Data-Driven Approach for Multiscale Elliptic PDEs with Random Coefficients Based on Intrinsic Dimension Reduction","display_name":"A Data-Driven Approach for Multiscale Elliptic PDEs with Random Coefficients Based on Intrinsic Dimension Reduction","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3045668026","doi":"https://doi.org/10.1137/19m1277485","mag":"3045668026"},"language":"en","primary_location":{"id":"doi:10.1137/19m1277485","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1277485","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling & Simulation","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/A5101836520","display_name":"Sijing Li","orcid":"https://orcid.org/0000-0001-6703-4377"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sijing Li","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100611977","display_name":"Zhiwen Zhang","orcid":"https://orcid.org/0000-0002-3123-8885"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhiwen Zhang","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-3123-8885","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5069922005","display_name":"Hongkai Zhao","orcid":"https://orcid.org/0000-0002-2358-9028"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hongkai Zhao","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":1.5203,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.86533625,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"18","issue":"3","first_page":"1242","last_page":"1271"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9986000061035156,"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"}},{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9983999729156494,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.6891039609909058},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.6094805598258972},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.600267767906189},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5965082049369812},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.5536540150642395},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5423160791397095},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5370951890945435},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.4950224757194519},{"id":"https://openalex.org/keywords/truncation-error","display_name":"Truncation error","score":0.42150694131851196},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37941208481788635},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37498557567596436},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37388163805007935},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2668322026729584},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.073324054479599}],"concepts":[{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.6891039609909058},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.6094805598258972},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.600267767906189},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5965082049369812},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.5536540150642395},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5423160791397095},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5370951890945435},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.4950224757194519},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.42150694131851196},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37941208481788635},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37498557567596436},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37388163805007935},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2668322026729584},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.073324054479599},{"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1277485","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1277485","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling & Simulation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1657889736","display_name":"Theory and practice for exploiting the underlying structure of probability models in big data analysis","funder_award_id":"1622490","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2184393679","display_name":"Adaptive numerical methods for long-time integration and model reduction with applications in computing effective diffusivity and Anderson localization","funder_award_id":"17300817","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"},{"id":"https://openalex.org/G4454691053","display_name":"Efficient methods for exploring low-dimensional structures and solving multiscale stochastic elliptic PDEs and Helmholtz equations in random media","funder_award_id":"17300318","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"},{"id":"https://openalex.org/G446662411","display_name":"Intrinsic Complexity of Random Fields and Its Connections to Random Matrices and Stochastic Differential Equations","funder_award_id":"1821010","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5137264589","display_name":"Efficient computational methods for stochastic convection-dominated and multiscale flow problems","funder_award_id":"27300616","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"},{"id":"https://openalex.org/G6349937024","display_name":null,"funder_award_id":"JCYJ20180307151603959","funder_id":"https://openalex.org/F4320326705","funder_display_name":"Science, Technology and Innovation Commission of Shenzhen Municipality"},{"id":"https://openalex.org/G6647141808","display_name":null,"funder_award_id":"11601457","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321592","display_name":"Research Grants Council, University Grants Committee","ror":"https://ror.org/00djwmt25"},{"id":"https://openalex.org/F4320322170","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86"},{"id":"https://openalex.org/F4320326705","display_name":"Science, Technology and Innovation Commission of Shenzhen Municipality","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W1633869374","https://openalex.org/W1964773554","https://openalex.org/W1966606705","https://openalex.org/W1972576201","https://openalex.org/W1978744409","https://openalex.org/W1983156129","https://openalex.org/W1993422094","https://openalex.org/W1993900609","https://openalex.org/W2010384911","https://openalex.org/W2011083881","https://openalex.org/W2022264564","https://openalex.org/W2047591100","https://openalex.org/W2051344283","https://openalex.org/W2052271668","https://openalex.org/W2053695265","https://openalex.org/W2055460625","https://openalex.org/W2064332562","https://openalex.org/W2070460788","https://openalex.org/W2081210755","https://openalex.org/W2083845086","https://openalex.org/W2087257783","https://openalex.org/W2101948461","https://openalex.org/W2105425058","https://openalex.org/W2108001913","https://openalex.org/W2112823474","https://openalex.org/W2117756735","https://openalex.org/W2119334003","https://openalex.org/W2136602340","https://openalex.org/W2143591652","https://openalex.org/W2144144515","https://openalex.org/W2144389445","https://openalex.org/W2149498546","https://openalex.org/W2152896489","https://openalex.org/W2156164638","https://openalex.org/W2767757270","https://openalex.org/W2804813293","https://openalex.org/W2962840746","https://openalex.org/W2963798430","https://openalex.org/W2963874263","https://openalex.org/W4236965008","https://openalex.org/W4255975175"],"related_works":["https://openalex.org/W2006953814","https://openalex.org/W2040666836","https://openalex.org/W2542637001","https://openalex.org/W2238041693","https://openalex.org/W2112774109","https://openalex.org/W125347959","https://openalex.org/W1990789772","https://openalex.org/W138907054","https://openalex.org/W2536422707","https://openalex.org/W24145419"],"abstract_inverted_index":{"We":[0,119],"propose":[1],"a":[2,38,71],"data-driven":[3,64,135],"approach":[4],"to":[5,49,69,143],"solve":[6,70],"multiscale":[7,73],"elliptic":[8,23,74],"PDEs":[9],"with":[10],"random":[11,107],"coefficients":[12],"based":[13,88,123],"on":[14,89,124],"the":[15,21,35,55,59,62,94,103,106,125,129,134,145,150],"intrinsic":[16],"approximate":[17,80],"low-dimensional":[18,39,81],"structure":[19,82],"of":[20,29,79,93,102,149],"underlying":[22,95],"differential":[24],"operators.":[25],"Our":[26],"method":[27],"consists":[28],"offline":[30,36],"and":[31,41,98,128,147],"online":[32,60,110],"stages.":[33],"At":[34,58],"stage,":[37,61],"space":[40],"its":[42],"basis":[43,65],"are":[44,113],"extracted":[45,63],"from":[46],"solution":[47,56],"samples":[48],"achieve":[50],"significant":[51],"dimension":[52],"reduction":[53],"in":[54,85,105,132],"space.":[57],"will":[66],"be":[67],"used":[68],"new":[72],"PDE":[75],"efficiently.":[76],"The":[77],"existence":[78],"is":[83],"established":[84],"two":[86],"scenarios":[87],"(1)":[90],"high":[91],"separability":[92],"Green's":[96],"functions,":[97],"(2)":[99],"smooth":[100],"dependence":[101],"parameters":[104],"coefficients.":[108],"Various":[109],"construction":[111],"methods":[112],"proposed":[114,151],"for":[115],"different":[116],"problem":[117],"setups.":[118],"provide":[120],"error":[121,127],"analysis":[122],"sampling":[126],"truncation":[130],"threshold":[131],"building":[133],"basis.":[136],"Finally,":[137],"we":[138],"present":[139],"extensive":[140],"numerical":[141],"examples":[142],"demonstrate":[144],"accuracy":[146],"efficiency":[148],"method.":[152]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":1}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}