{"id":"https://openalex.org/W4410325502","doi":"https://doi.org/10.1007/s00500-025-10624-w","title":"Adaptive hyperparameter selection in kernel-based partition of unity methods by global optimization techniques","display_name":"Adaptive hyperparameter selection in kernel-based partition of unity methods by global optimization techniques","publication_year":2025,"publication_date":"2025-04-01","ids":{"openalex":"https://openalex.org/W4410325502","doi":"https://doi.org/10.1007/s00500-025-10624-w"},"language":"en","primary_location":{"id":"doi:10.1007/s00500-025-10624-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00500-025-10624-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00500-025-10624-w.pdf","source":{"id":"https://openalex.org/S65753830","display_name":"Soft Computing","issn_l":"1432-7643","issn":["1432-7643","1433-7479"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Soft Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00500-025-10624-w.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053041658","display_name":"Roberto Cavoretto","orcid":"https://orcid.org/0000-0001-6076-4115"},"institutions":[{"id":"https://openalex.org/I1330701686","display_name":"Collegio Carlo Alberto","ror":"https://ror.org/0397knh37","country_code":"IT","type":"education","lineage":["https://openalex.org/I1330701686"]},{"id":"https://openalex.org/I2802148964","display_name":"Istituto Nazionale di Alta Matematica Francesco Severi","ror":"https://ror.org/01vx64p53","country_code":"IT","type":"funder","lineage":["https://openalex.org/I2802148964"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Roberto Cavoretto","raw_affiliation_strings":["Department of Mathematics \u201cGiuseppe Peano\u201d, University of Torino, via Carlo Alberto 10, 10123, Torino, Italy","Member of the INdAM Research group GNCS, Rome, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics \u201cGiuseppe Peano\u201d, University of Torino, via Carlo Alberto 10, 10123, Torino, Italy","institution_ids":["https://openalex.org/I1330701686"]},{"raw_affiliation_string":"Member of the INdAM Research group GNCS, Rome, Italy","institution_ids":["https://openalex.org/I2802148964"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001182701","display_name":"Alessandra De Rossi","orcid":"https://orcid.org/0000-0003-1285-3820"},"institutions":[{"id":"https://openalex.org/I1330701686","display_name":"Collegio Carlo Alberto","ror":"https://ror.org/0397knh37","country_code":"IT","type":"education","lineage":["https://openalex.org/I1330701686"]},{"id":"https://openalex.org/I2802148964","display_name":"Istituto Nazionale di Alta Matematica Francesco Severi","ror":"https://ror.org/01vx64p53","country_code":"IT","type":"funder","lineage":["https://openalex.org/I2802148964"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Alessandra De Rossi","raw_affiliation_strings":["Department of Mathematics \u201cGiuseppe Peano\u201d, University of Torino, via Carlo Alberto 10, 10123, Torino, Italy","Member of the INdAM Research group GNCS, Rome, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics \u201cGiuseppe Peano\u201d, University of Torino, via Carlo Alberto 10, 10123, Torino, Italy","institution_ids":["https://openalex.org/I1330701686"]},{"raw_affiliation_string":"Member of the INdAM Research group GNCS, Rome, Italy","institution_ids":["https://openalex.org/I2802148964"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084881904","display_name":"Adeeba Haider","orcid":"https://orcid.org/0009-0001-4198-1808"},"institutions":[{"id":"https://openalex.org/I1330701686","display_name":"Collegio Carlo Alberto","ror":"https://ror.org/0397knh37","country_code":"IT","type":"education","lineage":["https://openalex.org/I1330701686"]},{"id":"https://openalex.org/I2802148964","display_name":"Istituto Nazionale di Alta Matematica Francesco Severi","ror":"https://ror.org/01vx64p53","country_code":"IT","type":"funder","lineage":["https://openalex.org/I2802148964"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Adeeba Haider","raw_affiliation_strings":["Department of Mathematics \u201cGiuseppe Peano\u201d, University of Torino, via Carlo Alberto 10, 10123, Torino, Italy","Member of the INdAM Research group GNCS, Rome, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics \u201cGiuseppe Peano\u201d, University of Torino, via Carlo Alberto 10, 10123, Torino, Italy","institution_ids":["https://openalex.org/I1330701686"]},{"raw_affiliation_string":"Member of the INdAM Research group GNCS, Rome, Italy","institution_ids":["https://openalex.org/I2802148964"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085417391","display_name":"Yaroslav D. Sergeyev","orcid":"https://orcid.org/0000-0002-1429-069X"},"institutions":[{"id":"https://openalex.org/I2802148964","display_name":"Istituto Nazionale di Alta Matematica Francesco Severi","ror":"https://ror.org/01vx64p53","country_code":"IT","type":"funder","lineage":["https://openalex.org/I2802148964"]},{"id":"https://openalex.org/I45204951","display_name":"University of Calabria","ror":"https://ror.org/02rc97e94","country_code":"IT","type":"education","lineage":["https://openalex.org/I45204951"]},{"id":"https://openalex.org/I79563041","display_name":"N. I. Lobachevsky State University of Nizhny Novgorod","ror":"https://ror.org/01bb1zm18","country_code":"RU","type":"education","lineage":["https://openalex.org/I79563041"]}],"countries":["IT","RU"],"is_corresponding":false,"raw_author_name":"Yaroslav D. Sergeyev","raw_affiliation_strings":["DIMES, University of Calabria, via P. Bucci, Cubo 42-C, 87036, Rende, CS, Italy","ITMM, Lobachevsky Nizhni Novgorod State University, Gagarin Avenue 23, Nizhni Novgorod, 603950, Russia","Member of the INdAM Research group GNCS, Rome, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DIMES, University of Calabria, via P. Bucci, Cubo 42-C, 87036, Rende, CS, Italy","institution_ids":["https://openalex.org/I45204951"]},{"raw_affiliation_string":"ITMM, Lobachevsky Nizhni Novgorod State University, Gagarin Avenue 23, Nizhni Novgorod, 603950, Russia","institution_ids":["https://openalex.org/I79563041"]},{"raw_affiliation_string":"Member of the INdAM Research group GNCS, Rome, Italy","institution_ids":["https://openalex.org/I2802148964"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5053041658"],"corresponding_institution_ids":["https://openalex.org/I1330701686","https://openalex.org/I2802148964"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":1.2224,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.7447106,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"29","issue":"7","first_page":"3733","last_page":"3748"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9919000267982483,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hyperparameter","display_name":"Hyperparameter","score":0.7654209136962891},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.622206449508667},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.5517876744270325},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5101447701454163},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4835509955883026},{"id":"https://openalex.org/keywords/selection","display_name":"Selection (genetic algorithm)","score":0.47926995158195496},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3762606978416443},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.35398784279823303}],"concepts":[{"id":"https://openalex.org/C8642999","wikidata":"https://www.wikidata.org/wiki/Q4171168","display_name":"Hyperparameter","level":2,"score":0.7654209136962891},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.622206449508667},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.5517876744270325},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5101447701454163},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4835509955883026},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.47926995158195496},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3762606978416443},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.35398784279823303},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00500-025-10624-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00500-025-10624-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00500-025-10624-w.pdf","source":{"id":"https://openalex.org/S65753830","display_name":"Soft Computing","issn_l":"1432-7643","issn":["1432-7643","1433-7479"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Soft Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00500-025-10624-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00500-025-10624-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00500-025-10624-w.pdf","source":{"id":"https://openalex.org/S65753830","display_name":"Soft Computing","issn_l":"1432-7643","issn":["1432-7643","1433-7479"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Soft Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320309723","display_name":"Fondazione CRT","ror":"https://ror.org/00fgmmg43"},{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320334079","display_name":"Gruppo Nazionale per il Calcolo Scientifico","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4410325502.pdf","grobid_xml":"https://content.openalex.org/works/W4410325502.grobid-xml"},"referenced_works_count":54,"referenced_works":["https://openalex.org/W42253513","https://openalex.org/W60763295","https://openalex.org/W610800591","https://openalex.org/W1535218163","https://openalex.org/W1593317323","https://openalex.org/W1980333922","https://openalex.org/W1988594911","https://openalex.org/W1995124881","https://openalex.org/W2016995064","https://openalex.org/W2018039791","https://openalex.org/W2027655363","https://openalex.org/W2036277535","https://openalex.org/W2044309282","https://openalex.org/W2056083784","https://openalex.org/W2069016826","https://openalex.org/W2087444559","https://openalex.org/W2090843186","https://openalex.org/W2092011174","https://openalex.org/W2122617146","https://openalex.org/W2145090494","https://openalex.org/W2216485242","https://openalex.org/W2341112121","https://openalex.org/W2395641743","https://openalex.org/W2412738729","https://openalex.org/W2481312347","https://openalex.org/W2496298831","https://openalex.org/W2526264695","https://openalex.org/W2532170443","https://openalex.org/W2602861998","https://openalex.org/W2626285949","https://openalex.org/W2750444590","https://openalex.org/W2963670035","https://openalex.org/W2966947530","https://openalex.org/W2976818350","https://openalex.org/W2982751769","https://openalex.org/W2995129051","https://openalex.org/W3003924083","https://openalex.org/W3098972977","https://openalex.org/W3125055604","https://openalex.org/W3138194578","https://openalex.org/W3143295495","https://openalex.org/W3185406869","https://openalex.org/W3204852952","https://openalex.org/W4210748737","https://openalex.org/W4289745762","https://openalex.org/W4290741883","https://openalex.org/W4301180262","https://openalex.org/W4309149523","https://openalex.org/W4380077140","https://openalex.org/W4389166146","https://openalex.org/W4390508765","https://openalex.org/W4393965264","https://openalex.org/W4399588937","https://openalex.org/W4399914180"],"related_works":["https://openalex.org/W4390421286","https://openalex.org/W4280563792","https://openalex.org/W2602382373","https://openalex.org/W3003615511","https://openalex.org/W4285827128","https://openalex.org/W3198113463","https://openalex.org/W2787698406","https://openalex.org/W2963844355","https://openalex.org/W4361251046","https://openalex.org/W98577079"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"article,":[3],"we":[4,47,89],"present":[5],"a":[6,22,52],"new":[7],"numerical":[8],"algorithm":[9,103],"to":[10,82,106,134],"detect":[11],"the":[12,17,42,49,64,108,111,125],"kernel":[13],"shape":[14],"parameter":[15],"and":[16,98,119,131],"subdomain":[18],"radius":[19],"size":[20],"within":[21],"partition":[23],"of":[24,35,45,51,66,110,116,127],"unity":[25],"method":[26],"for":[27],"scattered":[28],"data":[29,136],"interpolation.":[30],"Since":[31],"an":[32,132],"adaptive":[33],"search":[34],"such":[36],"hyperparameters":[37],"is":[38],"quite":[39],"expensive":[40],"from":[41,63,75,124],"computational":[43,83],"point":[44],"view,":[46],"propose":[48],"use":[50],"leave-one-out":[53],"cross-validation":[54],"(LOOCV)":[55],"technique":[56],"combined":[57],"with":[58],"univariate":[59],"global":[60,92],"optimization":[61,93],"tools":[62],"class":[65],"Lipschitz":[67],"derivative-free":[68],"methods.":[69],"Conventional":[70],"LOOCV":[71],"methods":[72],"often":[73],"suffer":[74],"ill-conditioning,":[76],"particularly":[77],"in":[78,114],"high-dimensional":[79],"settings,":[80],"leading":[81],"inefficiencies.":[84],"To":[85],"address":[86],"these":[87],"issues,":[88],"consider":[90],"efficient":[91],"strategies":[94],"characterized":[95],"by":[96],"optimistic":[97],"pessimistic":[99],"improvements.":[100],"The":[101],"resulting":[102],"allows":[104],"us":[105],"improve":[107],"performance":[109],"standard":[112],"approach":[113],"terms":[115],"both":[117],"accuracy":[118],"efficiency.":[120],"Numerical":[121],"results":[122],"deriving":[123],"study":[126],"some":[128],"test":[129],"cases":[130],"application":[133],"real-world":[135],"support":[137],"our":[138],"analysis.":[139]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1}],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2025-10-10T00:00:00"}