{"id":"https://openalex.org/W4391994496","doi":"https://doi.org/10.1080/00401706.2024.2320211","title":"Mesh-Clustered Gaussian Process Emulator for Partial Differential Equation Boundary Value Problems","display_name":"Mesh-Clustered Gaussian Process Emulator for Partial Differential Equation Boundary Value Problems","publication_year":2024,"publication_date":"2024-02-21","ids":{"openalex":"https://openalex.org/W4391994496","doi":"https://doi.org/10.1080/00401706.2024.2320211"},"language":"en","primary_location":{"id":"doi:10.1080/00401706.2024.2320211","is_oa":true,"landing_page_url":"https://doi.org/10.1080/00401706.2024.2320211","pdf_url":"https://www.tandfonline.com/doi/pdf/10.1080/00401706.2024.2320211?needAccess=true","source":{"id":"https://openalex.org/S985303","display_name":"Technometrics","issn_l":"0040-1706","issn":["0040-1706","1537-2723"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Technometrics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.tandfonline.com/doi/pdf/10.1080/00401706.2024.2320211?needAccess=true","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038691222","display_name":"Chih\u2010Li Sung","orcid":"https://orcid.org/0000-0003-4622-5195"},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Chih-Li Sung","raw_affiliation_strings":["Michigan State University, East Lansing, MI"],"raw_orcid":"https://orcid.org/0000-0003-4622-5195","affiliations":[{"raw_affiliation_string":"Michigan State University, East Lansing, MI","institution_ids":["https://openalex.org/I87216513"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100655526","display_name":"Wenjia Wang","orcid":"https://orcid.org/0000-0001-9219-0494"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wenjia Wang","raw_affiliation_strings":["Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027478572","display_name":"Liang Ding","orcid":"https://orcid.org/0000-0003-3998-3860"},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liang Ding","raw_affiliation_strings":["Fudan University, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fudan University, Shanghai, China","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100694628","display_name":"Xingjian Wang","orcid":"https://orcid.org/0000-0001-6704-3097"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xingjian Wang","raw_affiliation_strings":["Tsinghua University, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5038691222"],"corresponding_institution_ids":["https://openalex.org/I87216513"],"apc_list":null,"apc_paid":null,"fwci":1.3245,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.82263104,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"66","issue":"3","first_page":"406","last_page":"421"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9980999827384949,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9966999888420105,"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/computer-science","display_name":"Computer science","score":0.6483665704727173},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.604052722454071},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.5354658961296082},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.46376630663871765},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4481557309627533},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.433268278837204},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.43260711431503296},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4293064773082733},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3745362162590027},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.3672332763671875},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.354946494102478},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15268388390541077},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1062515377998352}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6483665704727173},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.604052722454071},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.5354658961296082},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.46376630663871765},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4481557309627533},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.433268278837204},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.43260711431503296},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4293064773082733},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3745362162590027},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.3672332763671875},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.354946494102478},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15268388390541077},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1062515377998352},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00401706.2024.2320211","is_oa":true,"landing_page_url":"https://doi.org/10.1080/00401706.2024.2320211","pdf_url":"https://www.tandfonline.com/doi/pdf/10.1080/00401706.2024.2320211?needAccess=true","source":{"id":"https://openalex.org/S985303","display_name":"Technometrics","issn_l":"0040-1706","issn":["0040-1706","1537-2723"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Technometrics","raw_type":"journal-article"},{"id":"pmh:oai:repository.hkust.edu.hk:1783.1-139494","is_oa":false,"landing_page_url":"http://repository.hkust.edu.hk/ir/Record/1783.1-139494","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"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":"Article"}],"best_oa_location":{"id":"doi:10.1080/00401706.2024.2320211","is_oa":true,"landing_page_url":"https://doi.org/10.1080/00401706.2024.2320211","pdf_url":"https://www.tandfonline.com/doi/pdf/10.1080/00401706.2024.2320211?needAccess=true","source":{"id":"https://openalex.org/S985303","display_name":"Technometrics","issn_l":"0040-1706","issn":["0040-1706","1537-2723"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Technometrics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1529976661","display_name":null,"funder_award_id":"12101149","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G472926795","display_name":null,"funder_award_id":"DMS 2113407","funder_id":"https://openalex.org/F4320320373","funder_display_name":"National Stroke Foundation"}],"funders":[{"id":"https://openalex.org/F4320320373","display_name":"National Stroke Foundation","ror":"https://ror.org/004ckc033"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4391994496.pdf"},"referenced_works_count":79,"referenced_works":["https://openalex.org/W16794263","https://openalex.org/W29489373","https://openalex.org/W55912154","https://openalex.org/W112187595","https://openalex.org/W1516111018","https://openalex.org/W1573186872","https://openalex.org/W1581043462","https://openalex.org/W1601795611","https://openalex.org/W1601829011","https://openalex.org/W1627001989","https://openalex.org/W1855169650","https://openalex.org/W1964490787","https://openalex.org/W1976870403","https://openalex.org/W2006984640","https://openalex.org/W2019180174","https://openalex.org/W2020462115","https://openalex.org/W2025720061","https://openalex.org/W2040932457","https://openalex.org/W2065392216","https://openalex.org/W2065817392","https://openalex.org/W2069429561","https://openalex.org/W2072169887","https://openalex.org/W2072844193","https://openalex.org/W2076474160","https://openalex.org/W2078454401","https://openalex.org/W2080972498","https://openalex.org/W2092250306","https://openalex.org/W2095849032","https://openalex.org/W2098949458","https://openalex.org/W2111683289","https://openalex.org/W2111857777","https://openalex.org/W2118276286","https://openalex.org/W2120636621","https://openalex.org/W2127498532","https://openalex.org/W2145911539","https://openalex.org/W2150705946","https://openalex.org/W2151967501","https://openalex.org/W2152172226","https://openalex.org/W2156614992","https://openalex.org/W2160299137","https://openalex.org/W2163614729","https://openalex.org/W2201048008","https://openalex.org/W2225156818","https://openalex.org/W2524866123","https://openalex.org/W2582743722","https://openalex.org/W2593789309","https://openalex.org/W2618462867","https://openalex.org/W2732719471","https://openalex.org/W2782911365","https://openalex.org/W2962717448","https://openalex.org/W2963207825","https://openalex.org/W2989768142","https://openalex.org/W2990138404","https://openalex.org/W2993623579","https://openalex.org/W3036314241","https://openalex.org/W3043876737","https://openalex.org/W3045751695","https://openalex.org/W3095900652","https://openalex.org/W3105020499","https://openalex.org/W3116299394","https://openalex.org/W3123229529","https://openalex.org/W3156809662","https://openalex.org/W3198776453","https://openalex.org/W3204708751","https://openalex.org/W4221149570","https://openalex.org/W4229945461","https://openalex.org/W4235606958","https://openalex.org/W4237236652","https://openalex.org/W4292156489","https://openalex.org/W4293052541","https://openalex.org/W4312190934","https://openalex.org/W4392655579","https://openalex.org/W6632908801","https://openalex.org/W6674468447","https://openalex.org/W6674660115","https://openalex.org/W6677658955","https://openalex.org/W6678007500","https://openalex.org/W6682569104","https://openalex.org/W6786151208"],"related_works":["https://openalex.org/W4298130764","https://openalex.org/W2804364458","https://openalex.org/W2132641928","https://openalex.org/W4310225030","https://openalex.org/W2090259340","https://openalex.org/W1926736923","https://openalex.org/W2158836806","https://openalex.org/W2393816671","https://openalex.org/W1964286703","https://openalex.org/W2169866437"],"abstract_inverted_index":{"Partial":[0],"differential":[1],"equations":[2,15],"(PDEs)":[3],"have":[4],"become":[5],"an":[6,55,201],"essential":[7],"tool":[8],"for":[9,194],"modeling":[10],"complex":[11],"physical":[12,184],"systems.":[13],"Such":[14],"are":[16,38,155],"typically":[17],"solved":[18],"numerically":[19],"via":[20,105],"mesh-based":[21],"methods,":[22,27],"such":[23,186],"as":[24,187],"finite":[25],"element":[26],"with":[28,67,115,171],"solutions":[29,37,62],"over":[30,63],"the":[31,43,61,64,77,82,85,90,95,99,116,127,131,142,195],"spatial":[32,65],"domain.":[33],"However,":[34],"obtaining":[35],"these":[36],"often":[39],"prohibitively":[40],"costly,":[41],"limiting":[42],"feasibility":[44],"of":[45,70,76,84,121,141,179],"exploring":[46],"parameters":[47],"in":[48,81,119,200],"PDEs.":[49],"In":[50,93],"this":[51],"article,":[52],"we":[53],"propose":[54],"efficient":[56],"emulator":[57],"that":[58,145,159,182],"simultaneously":[59],"predicts":[60],"domain,":[66],"theoretical":[68],"justification":[69],"its":[71,168],"uncertainty":[72],"quantification.":[73],"The":[74],"novelty":[75],"proposed":[78,96,132,161,196],"method":[79,97,133,162],"lies":[80],"incorporation":[83],"mesh":[86,100,180],"node":[87],"coordinates":[88],"into":[89,102,138],"statistical":[91],"model.":[92],"particular,":[94],"segments":[98],"nodes":[101,181],"multiple":[103],"clusters":[104,178],"a":[106],"Dirichlet":[107],"process":[108,113],"prior":[109],"and":[110,175],"fits":[111],"Gaussian":[112],"models":[114],"same":[117],"hyperparameters":[118],"each":[120],"them.":[122],"Most":[123],"importantly,":[124],"by":[125],"revealing":[126],"underlying":[128],"clustering":[129],"structures,":[130],"can":[134,146],"provide":[135],"valuable":[136],"insights":[137],"qualitative":[139],"features":[140],"resulting":[143],"dynamics":[144],"be":[147],"used":[148],"to":[149,157],"guide":[150],"further":[151],"investigations.":[152],"Real":[153],"examples":[154],"demonstrated":[156],"show":[158],"our":[160],"has":[163],"smaller":[164],"prediction":[165],"errors":[166],"than":[167],"main":[169],"competitors,":[170],"competitive":[172],"computation":[173],"time,":[174],"identifies":[176],"interesting":[177],"possess":[183],"significance,":[185],"satisfying":[188],"boundary":[189],"conditions.":[190],"An":[191],"R":[192],"package":[193],"methodology":[197],"is":[198],"provided":[199],"open":[202],"repository.":[203]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
