{"id":"https://openalex.org/W4220674352","doi":"https://doi.org/10.3390/a15030101","title":"Multi-Fidelity Sparse Polynomial Chaos and Kriging Surrogate Models Applied to Analytical Benchmark Problems","display_name":"Multi-Fidelity Sparse Polynomial Chaos and Kriging Surrogate Models Applied to Analytical Benchmark Problems","publication_year":2022,"publication_date":"2022-03-21","ids":{"openalex":"https://openalex.org/W4220674352","doi":"https://doi.org/10.3390/a15030101"},"language":"en","primary_location":{"id":"doi:10.3390/a15030101","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a15030101","pdf_url":"https://www.mdpi.com/1999-4893/15/3/101/pdf?version=1647920613","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/15/3/101/pdf?version=1647920613","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054806727","display_name":"Markus P. Rumpfkeil","orcid":null},"institutions":[{"id":"https://openalex.org/I127591826","display_name":"University of Dayton","ror":"https://ror.org/021v3qy27","country_code":"US","type":"education","lineage":["https://openalex.org/I127591826"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Markus P. Rumpfkeil","raw_affiliation_strings":["Department of Mechanical and Aerospace Engineering, University of Dayton, Dayton, OH 45469, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, University of Dayton, Dayton, OH 45469, USA","institution_ids":["https://openalex.org/I127591826"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088537317","display_name":"Dean E. Bryson","orcid":"https://orcid.org/0000-0002-8419-701X"},"institutions":[{"id":"https://openalex.org/I2799950915","display_name":"Wright-Patterson Air Force Base","ror":"https://ror.org/0097e1k27","country_code":"US","type":"other","lineage":["https://openalex.org/I1330347796","https://openalex.org/I2799950915","https://openalex.org/I4210089612","https://openalex.org/I4210102105"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dean Bryson","raw_affiliation_strings":["Air Force Research Laboratory, Wright-Patterson Air Force Base, OH 45433, USA"],"affiliations":[{"raw_affiliation_string":"Air Force Research Laboratory, Wright-Patterson Air Force Base, OH 45433, USA","institution_ids":["https://openalex.org/I2799950915"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027097641","display_name":"Phil Beran","orcid":null},"institutions":[{"id":"https://openalex.org/I2799950915","display_name":"Wright-Patterson Air Force Base","ror":"https://ror.org/0097e1k27","country_code":"US","type":"other","lineage":["https://openalex.org/I1330347796","https://openalex.org/I2799950915","https://openalex.org/I4210089612","https://openalex.org/I4210102105"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Phil Beran","raw_affiliation_strings":["Air Force Research Laboratory, Wright-Patterson Air Force Base, OH 45433, USA"],"affiliations":[{"raw_affiliation_string":"Air Force Research Laboratory, Wright-Patterson Air Force Base, OH 45433, USA","institution_ids":["https://openalex.org/I2799950915"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5054806727"],"corresponding_institution_ids":["https://openalex.org/I127591826"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.4338,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.83111609,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"15","issue":"3","first_page":"101","last_page":"101"},"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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9979000091552734,"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/T11798","display_name":"Optimal Experimental Design Methods","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"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/polynomial-chaos","display_name":"Polynomial chaos","score":0.8495528697967529},{"id":"https://openalex.org/keywords/surrogate-model","display_name":"Surrogate model","score":0.7943019270896912},{"id":"https://openalex.org/keywords/kriging","display_name":"Kriging","score":0.7891057729721069},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.7690056562423706},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6373297572135925},{"id":"https://openalex.org/keywords/fidelity","display_name":"Fidelity","score":0.6106997132301331},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6096128821372986},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5893623232841492},{"id":"https://openalex.org/keywords/uncertainty-quantification","display_name":"Uncertainty quantification","score":0.474779337644577},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.46583738923072815},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3915281891822815},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31582334637641907},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.20467162132263184},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09436434507369995}],"concepts":[{"id":"https://openalex.org/C197656079","wikidata":"https://www.wikidata.org/wiki/Q17147719","display_name":"Polynomial chaos","level":3,"score":0.8495528697967529},{"id":"https://openalex.org/C131675550","wikidata":"https://www.wikidata.org/wiki/Q7646884","display_name":"Surrogate model","level":2,"score":0.7943019270896912},{"id":"https://openalex.org/C81692654","wikidata":"https://www.wikidata.org/wiki/Q225926","display_name":"Kriging","level":2,"score":0.7891057729721069},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.7690056562423706},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6373297572135925},{"id":"https://openalex.org/C2776459999","wikidata":"https://www.wikidata.org/wiki/Q2119376","display_name":"Fidelity","level":2,"score":0.6106997132301331},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6096128821372986},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5893623232841492},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.474779337644577},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46583738923072815},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3915281891822815},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31582334637641907},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.20467162132263184},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09436434507369995},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"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/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.0},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/a15030101","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a15030101","pdf_url":"https://www.mdpi.com/1999-4893/15/3/101/pdf?version=1647920613","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:ae1c69cfce704476a2c407d8ac75f364","is_oa":true,"landing_page_url":"https://doaj.org/article/ae1c69cfce704476a2c407d8ac75f364","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 15, Iss 3, p 101 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1999-4893/15/3/101/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/a15030101","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":"Algorithms; Volume 15; Issue 3; Pages: 101","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/a15030101","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a15030101","pdf_url":"https://www.mdpi.com/1999-4893/15/3/101/pdf?version=1647920613","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4220674352.pdf","grobid_xml":"https://content.openalex.org/works/W4220674352.grobid-xml"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W1486164486","https://openalex.org/W1506962395","https://openalex.org/W1950691413","https://openalex.org/W1982886636","https://openalex.org/W1988706000","https://openalex.org/W1996804224","https://openalex.org/W2019389302","https://openalex.org/W2035665246","https://openalex.org/W2045355467","https://openalex.org/W2050297026","https://openalex.org/W2056558085","https://openalex.org/W2073016592","https://openalex.org/W2074984119","https://openalex.org/W2094763293","https://openalex.org/W2112372720","https://openalex.org/W2112985838","https://openalex.org/W2114459240","https://openalex.org/W2117929919","https://openalex.org/W2119142673","https://openalex.org/W2124012450","https://openalex.org/W2145096794","https://openalex.org/W2269678754","https://openalex.org/W2313924857","https://openalex.org/W2316673954","https://openalex.org/W2318332398","https://openalex.org/W2429108336","https://openalex.org/W2642249342","https://openalex.org/W2744517292","https://openalex.org/W2763090371","https://openalex.org/W2963889731","https://openalex.org/W2983638446","https://openalex.org/W2990237985","https://openalex.org/W2996933288","https://openalex.org/W3001287763","https://openalex.org/W3004945969","https://openalex.org/W3035274195","https://openalex.org/W3037761057","https://openalex.org/W4250955649","https://openalex.org/W4300263211","https://openalex.org/W4301584875","https://openalex.org/W6645938543","https://openalex.org/W6677217807","https://openalex.org/W6682335648","https://openalex.org/W6765685986"],"related_works":["https://openalex.org/W2931365531","https://openalex.org/W3014573403","https://openalex.org/W2517755966","https://openalex.org/W3215394929","https://openalex.org/W4381941132","https://openalex.org/W2169974588","https://openalex.org/W3038021552","https://openalex.org/W2108001913","https://openalex.org/W2084593435","https://openalex.org/W2963889731"],"abstract_inverted_index":{"In":[0,15],"this":[1],"article,":[2],"multi-fidelity":[3,27,65,101],"kriging":[4],"and":[5,82,157],"sparse":[6],"polynomial":[7,83],"chaos":[8],"expansion":[9],"(SPCE)":[10],"surrogate":[11,23,34,66],"models":[12,67,102],"are":[13,59,103,121],"constructed.":[14],"addition,":[16],"a":[17,26,43,97,116,128,154],"novel":[18],"combination":[19,143],"of":[20,46,85,130,139,144],"the":[21,110,145,149],"two":[22,131,146],"approaches":[24,147],"into":[25,148],"SPCE-Kriging":[28,150],"model":[29,151],"will":[30],"be":[31,39,69,127],"presented.":[32],"Accurate":[33],"models,":[35],"once":[36],"obtained,":[37],"can":[38,68],"employed":[40],"for":[41,48,109],"evaluating":[42],"large":[44],"number":[45],"designs":[47],"uncertainty":[49],"quantification,":[50],"optimization,":[51],"or":[52,132],"design":[53],"space":[54],"exploration.":[55],"Analytical":[56],"benchmark":[57],"problems":[58],"used":[60],"to":[61,126,153],"show":[62],"that":[63],"accurate":[64,105,156],"obtained":[70],"at":[71],"lower":[72,89],"computational":[73],"cost":[74],"than":[75,106,135],"high-fidelity":[76,107,118],"models.":[77],"The":[78,142],"benchmarks":[79],"include":[80],"non-polynomial":[81,92],"functions":[84],"various":[86],"input":[87],"dimensions,":[88],"dimensional":[90],"heterogeneous":[91],"functions,":[93],"as":[94,96],"well":[95],"coupled":[98],"spring-mass-system.":[99],"Overall,":[100],"more":[104,155],"ones":[108],"same":[111],"cost,":[112],"especially":[113],"when":[114],"only":[115],"few":[117],"training":[119],"points":[120],"employed.":[122],"Full-order":[123],"PCEs":[124],"tend":[125],"factor":[129],"so":[133],"worse":[134],"SPCES":[136],"in":[137],"terms":[138],"overall":[140],"accuracy.":[141],"leads":[152],"flexible":[158],"method":[159],"overall.":[160]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1}],"updated_date":"2026-02-27T16:54:17.756197","created_date":"2022-04-03T00:00:00"}