{"id":"https://openalex.org/W2029538494","doi":"https://doi.org/10.1137/050639983","title":"Hierarchical Nonlinear Approximation for Experimental Design and Statistical Data Fitting","display_name":"Hierarchical Nonlinear Approximation for Experimental Design and Statistical Data Fitting","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2029538494","doi":"https://doi.org/10.1137/050639983","mag":"2029538494"},"language":"en","primary_location":{"id":"doi:10.1137/050639983","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050639983","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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":"SIAM Journal on Scientific Computing","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/A5043422201","display_name":"Daniel Busby","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Daniel Busby","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009838698","display_name":"Chris L. Farmer","orcid":"https://orcid.org/0000-0003-3783-495X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chris L. Farmer","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5028418165","display_name":"Armin Iske","orcid":"https://orcid.org/0000-0003-1743-5484"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Armin Iske","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.4828,"has_fulltext":false,"cited_by_count":73,"citation_normalized_percentile":{"value":0.97443718,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"29","issue":"1","first_page":"49","last_page":"69"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9987000226974487,"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/T11798","display_name":"Optimal Experimental Design Methods","score":0.9958000183105469,"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/computer-science","display_name":"Computer science","score":0.6062291860580444},{"id":"https://openalex.org/keywords/kriging","display_name":"Kriging","score":0.591556191444397},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5180142521858215},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5080516338348389},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.45904654264450073},{"id":"https://openalex.org/keywords/computer-experiment","display_name":"Computer experiment","score":0.45689699053764343},{"id":"https://openalex.org/keywords/design-of-experiments","display_name":"Design of experiments","score":0.4384183883666992},{"id":"https://openalex.org/keywords/software","display_name":"Software","score":0.42039045691490173},{"id":"https://openalex.org/keywords/data-point","display_name":"Data point","score":0.4163625240325928},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.37727826833724976},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.28749990463256836},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.2167031168937683},{"id":"https://openalex.org/keywords/simulation","display_name":"Simulation","score":0.196161150932312},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11792540550231934}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6062291860580444},{"id":"https://openalex.org/C81692654","wikidata":"https://www.wikidata.org/wiki/Q225926","display_name":"Kriging","level":2,"score":0.591556191444397},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5180142521858215},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5080516338348389},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45904654264450073},{"id":"https://openalex.org/C87466663","wikidata":"https://www.wikidata.org/wiki/Q5157537","display_name":"Computer experiment","level":2,"score":0.45689699053764343},{"id":"https://openalex.org/C34559072","wikidata":"https://www.wikidata.org/wiki/Q2334061","display_name":"Design of experiments","level":2,"score":0.4384183883666992},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.42039045691490173},{"id":"https://openalex.org/C21080849","wikidata":"https://www.wikidata.org/wiki/Q13611879","display_name":"Data point","level":2,"score":0.4163625240325928},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.37727826833724976},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28749990463256836},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.2167031168937683},{"id":"https://openalex.org/C44154836","wikidata":"https://www.wikidata.org/wiki/Q45045","display_name":"Simulation","level":1,"score":0.196161150932312},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11792540550231934},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/050639983","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050639983","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.94.8378","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.94.8378","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uni-hamburg.de/home/iske/papers/madace.pdf","raw_type":"text"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:bbb3182d-7df8-4ea0-8a0c-51185093cb6b","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:bbb3182d-7df8-4ea0-8a0c-51185093cb6b","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symplectic Elements at Oxford","raw_type":"Journal article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure","score":0.46000000834465027}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W80942810","https://openalex.org/W167612029","https://openalex.org/W189411257","https://openalex.org/W1486164486","https://openalex.org/W1571883544","https://openalex.org/W1589534817","https://openalex.org/W1669854886","https://openalex.org/W1973333099","https://openalex.org/W1995875735","https://openalex.org/W2000359198","https://openalex.org/W2018044188","https://openalex.org/W2019257888","https://openalex.org/W2023711160","https://openalex.org/W2024697317","https://openalex.org/W2026170388","https://openalex.org/W2031503901","https://openalex.org/W2038669746","https://openalex.org/W2044771513","https://openalex.org/W2076580309","https://openalex.org/W2084835095","https://openalex.org/W2092262344","https://openalex.org/W2097441841","https://openalex.org/W2098043077","https://openalex.org/W2107699930","https://openalex.org/W2151084831","https://openalex.org/W2163247537","https://openalex.org/W2164602066","https://openalex.org/W2204394100"],"related_works":["https://openalex.org/W1779837200","https://openalex.org/W83509125","https://openalex.org/W3175443657","https://openalex.org/W2072337188","https://openalex.org/W1969131648","https://openalex.org/W1990178414","https://openalex.org/W2162424869","https://openalex.org/W2630312803","https://openalex.org/W3151859097","https://openalex.org/W2158196689"],"abstract_inverted_index":{"This":[0,190],"paper":[1,175],"proposes":[2],"a":[3,48,82,113,122,127,139,156],"hierarchical":[4,99,170,200],"nonlinear":[5],"approximation":[6,21],"scheme":[7],"for":[8,51,165,177],"scalar\u2010valued":[9],"multivariate":[10],"functions,":[11],"where":[12,88,107],"the":[13,40,64,108,143,149,166,224],"main":[14],"objective":[15],"is":[16,86,92,101,110,136,191],"to":[17,78,103,208],"obtain":[18],"an":[19,134],"accurate":[20,130,212],"with":[22,46,94],"using":[23,155],"only":[24],"very":[25,114,157],"few":[26],"function":[27],"evaluations.":[28],"To":[29],"this":[30,74,125,174],"end,":[31],"our":[32,199],"iterative":[33],"method":[34,50,85,100,171,201],"combines":[35],"at":[36,70,203],"any":[37],"refinement":[38,91],"step":[39],"selection":[41],"of":[42,66,142,148,160],"suitable":[43],"evaluation":[44,68],"points":[45,69],"kriging,":[47],"standard":[49,188],"statistical":[52,104,131],"data":[53,105,109],"analysis.":[54],"Particular":[55],"improvements":[56],"over":[57],"previous":[58],"nonhierarchical":[59,215],"methods":[60],"are":[61],"mainly":[62],"concerning":[63],"construction":[65,75,147],"new":[67],"run":[71],"time.":[72],"In":[73,124],"process,":[76],"referred":[77],"as":[79,138,217],"experimental":[80,96],"design,":[81],"flexible":[83],"two\u2010stage":[84],"employed,":[87],"adaptive":[89],"domain":[90],"combined":[93],"sequential":[95],"design.":[97],"The":[98,146,169],"applied":[102],"analysis,":[106],"generated":[111],"by":[112,193],"complex":[115],"and":[116,129],"computationally":[117],"expensive":[118,144],"computer":[119,153],"model,":[120],"called":[121,133],"simulator.":[123,145],"application,":[126],"fast":[128],"approximation,":[132],"emulator,":[135],"required":[137],"cheap":[140],"surrogate":[141],"emulator":[150],"relies":[151],"on":[152,223],"experiments":[154],"small":[158],"set":[159],"carefully":[161],"selected":[162],"input":[163],"configurations":[164],"simulator":[167],"runs.":[168],"proposed":[172],"in":[173,219],"is,":[176,202],"various":[178],"analyzed":[179],"models":[180],"from":[181],"reservoir":[182],"forecasting,":[183],"more":[184,211],"efficient":[185],"than":[186,213],"existing":[187],"methods.":[189],"supported":[192],"numerical":[194],"results,":[195],"which":[196],"show":[197],"that":[198],"comparable":[204],"computational":[205],"costs,":[206],"up":[207],"ten":[209],"times":[210],"traditional":[214],"methods,":[216],"utilized":[218],"commercial":[220],"software":[221],"relying":[222],"response":[225],"surface":[226],"methodology":[227],"(RSM).":[228]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":6}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}