{"id":"https://openalex.org/W3083513911","doi":"https://doi.org/10.3390/e22090985","title":"Generalized Nonlinear Least Squares Method for the Calibration of Complex Computer Code Using a Gaussian Process Surrogate","display_name":"Generalized Nonlinear Least Squares Method for the Calibration of Complex Computer Code Using a Gaussian Process Surrogate","publication_year":2020,"publication_date":"2020-09-04","ids":{"openalex":"https://openalex.org/W3083513911","doi":"https://doi.org/10.3390/e22090985","mag":"3083513911","pmid":"https://pubmed.ncbi.nlm.nih.gov/33286754"},"language":"en","primary_location":{"id":"doi:10.3390/e22090985","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e22090985","pdf_url":"https://www.mdpi.com/1099-4300/22/9/985/pdf?version=1599214706","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/22/9/985/pdf?version=1599214706","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074467421","display_name":"Youngsaeng Lee","orcid":"https://orcid.org/0000-0001-7457-2579"},"institutions":[{"id":"https://openalex.org/I111277659","display_name":"Chonnam National University","ror":"https://ror.org/05kzjxq56","country_code":"KR","type":"education","lineage":["https://openalex.org/I111277659"]},{"id":"https://openalex.org/I198972184","display_name":"Korea Electric Power Corporation (South Korea)","ror":"https://ror.org/04fperw70","country_code":"KR","type":"company","lineage":["https://openalex.org/I198972184"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Youngsaeng Lee","raw_affiliation_strings":["Data Science Lab, Korea Electric Power Corporation, Seoul 60732, Korea","Department of Statistics, Chonnam National University, Gwangju 61186, Korea"],"raw_orcid":"https://orcid.org/0000-0001-7457-2579","affiliations":[{"raw_affiliation_string":"Data Science Lab, Korea Electric Power Corporation, Seoul 60732, Korea","institution_ids":["https://openalex.org/I198972184"]},{"raw_affiliation_string":"Department of Statistics, Chonnam National University, Gwangju 61186, Korea","institution_ids":["https://openalex.org/I111277659"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087029604","display_name":"Jeong\u2010Soo Park","orcid":"https://orcid.org/0000-0002-8460-4869"},"institutions":[{"id":"https://openalex.org/I111277659","display_name":"Chonnam National University","ror":"https://ror.org/05kzjxq56","country_code":"KR","type":"education","lineage":["https://openalex.org/I111277659"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Jeong-Soo Park","raw_affiliation_strings":["Department of Statistics, Chonnam National University, Gwangju 61186, Korea"],"raw_orcid":"https://orcid.org/0000-0002-8460-4869","affiliations":[{"raw_affiliation_string":"Department of Statistics, Chonnam National University, Gwangju 61186, Korea","institution_ids":["https://openalex.org/I111277659"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5087029604"],"corresponding_institution_ids":["https://openalex.org/I111277659"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.4373,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.69707676,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"22","issue":"9","first_page":"985","last_page":"985"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9976999759674072,"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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9976999759674072,"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":0.9919000267982483,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9814000129699707,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6344194412231445},{"id":"https://openalex.org/keywords/heteroscedasticity","display_name":"Heteroscedasticity","score":0.6246325969696045},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5527070760726929},{"id":"https://openalex.org/keywords/variance-function","display_name":"Variance function","score":0.5059449076652527},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.48760977387428284},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.48223528265953064},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.48182740807533264},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4594050943851471},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4438713788986206},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.43873798847198486},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.4200684130191803},{"id":"https://openalex.org/keywords/surrogate-model","display_name":"Surrogate model","score":0.4149138927459717},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41055893898010254},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40837562084198},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4029008746147156},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2647569477558136},{"id":"https://openalex.org/keywords/regression-analysis","display_name":"Regression analysis","score":0.14381560683250427}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6344194412231445},{"id":"https://openalex.org/C101104100","wikidata":"https://www.wikidata.org/wiki/Q1063540","display_name":"Heteroscedasticity","level":2,"score":0.6246325969696045},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5527070760726929},{"id":"https://openalex.org/C120488996","wikidata":"https://www.wikidata.org/wiki/Q17016064","display_name":"Variance function","level":3,"score":0.5059449076652527},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.48760977387428284},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.48223528265953064},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.48182740807533264},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4594050943851471},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4438713788986206},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.43873798847198486},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.4200684130191803},{"id":"https://openalex.org/C131675550","wikidata":"https://www.wikidata.org/wiki/Q7646884","display_name":"Surrogate model","level":2,"score":0.4149138927459717},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41055893898010254},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40837562084198},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4029008746147156},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2647569477558136},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.14381560683250427},{"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},{"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/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e22090985","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e22090985","pdf_url":"https://www.mdpi.com/1099-4300/22/9/985/pdf?version=1599214706","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:33286754","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33286754","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:8285916cd7ff4a4389969a78cb3961a3","is_oa":true,"landing_page_url":"https://doaj.org/article/8285916cd7ff4a4389969a78cb3961a3","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 22, Iss 9, p 985 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/22/9/985/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e22090985","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy; Volume 22; Issue 9; Pages: 985","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7597302","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7597302","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e22090985","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e22090985","pdf_url":"https://www.mdpi.com/1099-4300/22/9/985/pdf?version=1599214706","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5602793055","display_name":null,"funder_award_id":"2020R1I1A3069260","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G5856549105","display_name":null,"funder_award_id":"2016R1A2B4014518","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"}],"funders":[{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W113733777","https://openalex.org/W1840389249","https://openalex.org/W1915759647","https://openalex.org/W1973333099","https://openalex.org/W1977631358","https://openalex.org/W1991788899","https://openalex.org/W1992870395","https://openalex.org/W2018044188","https://openalex.org/W2036008353","https://openalex.org/W2040189105","https://openalex.org/W2043170151","https://openalex.org/W2044458183","https://openalex.org/W2056145269","https://openalex.org/W2067278522","https://openalex.org/W2078454401","https://openalex.org/W2094129114","https://openalex.org/W2098043077","https://openalex.org/W2119142031","https://openalex.org/W2119902028","https://openalex.org/W2137390208","https://openalex.org/W2158519240","https://openalex.org/W2165528241","https://openalex.org/W2403035479","https://openalex.org/W2497151737","https://openalex.org/W2742425491","https://openalex.org/W2798972612","https://openalex.org/W2803204571","https://openalex.org/W2886288701","https://openalex.org/W2889346967","https://openalex.org/W2962851339","https://openalex.org/W2978269572","https://openalex.org/W3007474926","https://openalex.org/W3101044315","https://openalex.org/W3101048699","https://openalex.org/W3105788762","https://openalex.org/W4235606958","https://openalex.org/W4237236652","https://openalex.org/W6742695105"],"related_works":["https://openalex.org/W2111861869","https://openalex.org/W2026556990","https://openalex.org/W2380616114","https://openalex.org/W2095094294","https://openalex.org/W981653334","https://openalex.org/W2960540998","https://openalex.org/W4237912051","https://openalex.org/W2903759548","https://openalex.org/W3022412718","https://openalex.org/W2050117464"],"abstract_inverted_index":{"The":[0,27,121],"approximated":[1],"nonlinear":[2],"least":[3],"squares":[4],"(ALS)":[5],"method":[6,191],"has":[7],"been":[8],"used":[9],"for":[10,149,195,207,262],"the":[11,17,32,37,56,63,82,92,95,98,116,124,130,139,150,156,162,169,174,187,212,217,225,233,239,246,249,253,260,263,283,289,295],"estimation":[12,172],"of":[13,76,81,97,119,123,211,229,286],"unknown":[14],"parameters":[15,163],"in":[16,67,94,202,288],"complex":[18,265],"computer":[19,33,44,99,179],"code":[20,34,70],"which":[21,152],"is":[22,84,127,134,153,276,280],"very":[23],"time-consuming":[24],"to":[25,129,138,271],"execute.":[26],"ALS":[28,64,83,112,190,247,290],"calibrates":[29],"or":[30,61],"tunes":[31],"by":[35,101,114,168,176,294],"minimizing":[36],"squared":[38],"difference":[39],"between":[40],"real":[41],"observations":[42],"and":[43,132,166,173,180,227,238,248,278],"output":[45],"using":[46,177],"a":[47,51,68,73,102,110,196,208,272],"surrogate":[48],"such":[49],"as":[50,155],"Gaussian":[52],"process":[53],"model.":[54],"When":[55],"differences":[57],"(residuals)":[58],"are":[59,164,205,241],"correlated":[60],"heteroscedastic,":[62],"may":[65],"result":[66],"distorted":[69],"tuning":[71,140],"with":[72,136],"large":[74],"variance":[75,228],"estimation.":[77],"Another":[78],"potential":[79],"drawback":[80],"that":[85,223,282],"it":[86,133,279],"does":[87],"not":[88],"take":[89],"into":[90],"account":[91],"uncertainty":[93],"approximation":[96],"model":[100],"surrogate.":[103],"To":[104],"address":[105],"these":[106],"problems,":[107],"we":[108,144,221],"propose":[109],"generalized":[111],"(GALS)":[113],"constructing":[115],"covariance":[117,125],"matrix":[118,126],"residuals.":[120],"inverse":[122],"multiplied":[128],"residuals,":[131],"minimized":[135],"respect":[137],"parameters.":[141],"In":[142,159],"addition,":[143],"consider":[145],"an":[146,269],"iterative":[147],"version":[148],"GALS,":[151,175],"called":[154],"max-minG":[157,254],"algorithm.":[158],"this":[160],"algorithm,":[161],"re-estimated":[165],"updated":[167],"maximum":[170],"likelihood":[171],"both":[178,224],"experimental":[181],"data":[182],"repeatedly":[183],"until":[184],"convergence.":[185],"Moreover,":[186],"iteratively":[188],"re-weighted":[189],"(IRWALS)":[192],"was":[193],"considered":[194],"comparison":[197],"purpose.":[198],"Five":[199],"test":[200,218,266],"functions":[201],"different":[203],"conditions":[204],"examined":[206],"comparative":[209],"analysis":[210],"four":[213],"methods.":[214,251,297],"Based":[215],"on":[216],"function":[219],"study,":[220],"find":[222],"bias":[226],"estimates":[230],"obtained":[231],"from":[232,245],"proposed":[234,296],"methods":[235],"(the":[236],"GALS":[237,261],"max-minG)":[240],"smaller":[242],"than":[243,257],"those":[244],"IRWALS":[250],"Especially,":[252],"works":[255],"better":[256],"others":[258],"including":[259],"relatively":[264],"functions.":[267],"Lastly,":[268],"application":[270],"nuclear":[273],"fusion":[274],"simulator":[275],"illustrated":[277],"shown":[281],"abnormal":[284],"pattern":[285],"residuals":[287],"can":[291],"be":[292],"resolved":[293]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}