{"id":"https://openalex.org/W4416063068","doi":"https://doi.org/10.1007/s10444-026-10323-6","title":"Kernel-based greedy approximation of parametric elliptic boundary value problems","display_name":"Kernel-based greedy approximation of parametric elliptic boundary value problems","publication_year":2026,"publication_date":"2026-07-03","ids":{"openalex":"https://openalex.org/W4416063068","doi":"https://doi.org/10.1007/s10444-026-10323-6"},"language":"en","primary_location":{"id":"doi:10.1007/s10444-026-10323-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10444-026-10323-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10444-026-10323-6.pdf","source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"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":"Advances in Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10444-026-10323-6.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073837806","display_name":"Bernard Haasdonk","orcid":null},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Bernard Haasdonk","raw_affiliation_strings":["Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Stuttgart, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Stuttgart, Germany","institution_ids":["https://openalex.org/I100066346"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047250646","display_name":"Tizian Wenzel","orcid":null},"institutions":[{"id":"https://openalex.org/I3018771216","display_name":"LMU Klinikum","ror":"https://ror.org/02jet3w32","country_code":"DE","type":"healthcare","lineage":["https://openalex.org/I3018771216","https://openalex.org/I8204097"]},{"id":"https://openalex.org/I4403386549","display_name":"Munich Center for Machine Learning","ror":"https://ror.org/02nfy3535","country_code":null,"type":"education","lineage":["https://openalex.org/I4403386549","https://openalex.org/I62916508","https://openalex.org/I8204097"]},{"id":"https://openalex.org/I8204097","display_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/05591te55","country_code":"DE","type":"education","lineage":["https://openalex.org/I8204097"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Tizian Wenzel","raw_affiliation_strings":["Department of Mathematics, LMU Munich, Munich, Germany","Munich Center for Machine Learning, Munich, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, LMU Munich, Munich, Germany","institution_ids":["https://openalex.org/I3018771216","https://openalex.org/I8204097"]},{"raw_affiliation_string":"Munich Center for Machine Learning, Munich, Germany","institution_ids":["https://openalex.org/I4403386549"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087671511","display_name":"Gabriele Santin","orcid":"https://orcid.org/0000-0001-6959-1070"},"institutions":[{"id":"https://openalex.org/I149461666","display_name":"Ca' Foscari University of Venice","ror":"https://ror.org/04yzxz566","country_code":"IT","type":"education","lineage":["https://openalex.org/I149461666"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Gabriele Santin","raw_affiliation_strings":["Department of Environmental Sciences, Informatics and Statistics, Ca\u2019 Foscari University of Venice, Venice, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Environmental Sciences, Informatics and Statistics, Ca\u2019 Foscari University of Venice, Venice, Italy","institution_ids":["https://openalex.org/I149461666"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5073837806"],"corresponding_institution_ids":["https://openalex.org/I100066346"],"apc_list":{"value":3190,"currency":"USD","value_usd":3190},"apc_paid":{"value":3190,"currency":"USD","value_usd":3190},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02215999,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"52","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.795799970626831,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.795799970626831,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.14640000462532043,"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"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.012799999676644802,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.5922999978065491},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5476999878883362},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4390999972820282},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4350000023841858},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.43470001220703125},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.4311000108718872},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4099000096321106},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.3555999994277954},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.3490000069141388}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7972000241279602},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5922999978065491},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5476999878883362},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5354999899864197},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4390999972820282},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4350000023841858},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.43470001220703125},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.4311000108718872},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4099000096321106},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3628000020980835},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.3555999994277954},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.3490000069141388},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3452000021934509},{"id":"https://openalex.org/C51823790","wikidata":"https://www.wikidata.org/wiki/Q504353","display_name":"Greedy algorithm","level":2,"score":0.3393999934196472},{"id":"https://openalex.org/C2775918384","wikidata":"https://www.wikidata.org/wiki/Q4660961","display_name":"A priori estimate","level":2,"score":0.3278000056743622},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3273000121116638},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.303600013256073},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.28610000014305115},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.28040000796318054},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.28029999136924744},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.2784000039100647},{"id":"https://openalex.org/C70610323","wikidata":"https://www.wikidata.org/wiki/Q427625","display_name":"Elliptic operator","level":2,"score":0.2775000035762787},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.275299996137619},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.27129998803138733},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.26010000705718994}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s10444-026-10323-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10444-026-10323-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10444-026-10323-6.pdf","source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"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":"Advances in Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:elib.uni-stuttgart.de:11682/18960","is_oa":true,"landing_page_url":"http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-ds-189600","pdf_url":null,"source":{"id":"https://openalex.org/S4306401556","display_name":"OPUS Publication Server of the University of Stuttgart (University of Stuttgart)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I100066346","host_organization_name":"University of Stuttgart","host_organization_lineage":["https://openalex.org/I100066346"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:arXiv.org:2507.06731","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2507.06731","pdf_url":"https://arxiv.org/pdf/2507.06731","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"doi:10.48550/arxiv.2507.06731","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2507.06731","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.18419/opus-18941","is_oa":true,"landing_page_url":"https://doi.org/10.18419/opus-18941","pdf_url":null,"source":{"id":"https://openalex.org/S7407052998","display_name":"Universit\u00e4tsbibliothek Stuttgart","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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Other"}],"best_oa_location":{"id":"doi:10.1007/s10444-026-10323-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10444-026-10323-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10444-026-10323-6.pdf","source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"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":"Advances in Computational Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1486546336","display_name":null,"funder_award_id":"EXC2075390740016","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G4783225636","display_name":null,"funder_award_id":"540080351","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7249683039","display_name":null,"funder_award_id":"EXC 2075","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8784604414","display_name":"EXC 2075: Datenintegrierte Simulationswissenschaft (SimTech)","funder_award_id":"390740016","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4416063068.pdf","grobid_xml":"https://content.openalex.org/works/W4416063068.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"We":[1,80,101],"recently":[2],"introduced":[3],"a":[4,24,55,83,135],"scale":[5],"of":[6,14,63,77,85,92,110,118,153],"kernel-based":[7],"greedy":[8,56],"schemes":[9],"for":[10,72,89,157,163],"approximating":[11],"the":[12,43,61,90,104,108,116,123,127,151,154],"solutions":[13,76],"elliptic":[15],"boundary":[16],"value":[17],"problems.":[18],"The":[19],"procedure":[20,156],"is":[21,52],"based":[22],"on":[23],"generalized":[25],"interpolation":[26],"framework":[27],"in":[28,54],"reproducing":[29],"kernel":[30,96],"Hilbert":[31],"spaces":[32],"and":[33,59,75,97],"was":[34],"coined":[35],"PDE-":[36],"$$\\beta":[37,45],"$$":[38,48],"\u03b2":[39,49],"-greedy":[40],"procedure,":[41],"where":[42],"parameter":[44],"\\ge":[46],"0":[47,51],"\u2265":[50],"used":[53],"selection":[57],"criterion":[58],"steers":[60],"degree":[62],"function":[64],"adaptivity.":[65],"Algebraic":[66],"convergence":[67,87],"rates":[68,88],"have":[69],"been":[70],"obtained":[71],"Sobolev-space":[73],"kernels":[74],"finite":[78],"smoothness.":[79],"now":[81],"report":[82],"result":[84],"exponential":[86],"case":[91,109],"an":[93,134],"infinitely":[94,98],"smooth":[95,99],"solutions.":[100],"furthermore":[102],"extend":[103],"approximation":[105,155],"scheme":[106],"to":[107,145],"parametric":[111,165],"partial":[112],"differential":[113],"equations":[114],"by":[115],"use":[117],"position-parameter":[119],"product":[120],"kernels.":[121],"In":[122],"surrogate":[124],"modelling":[125],"context,":[126],"resulting":[128],"approach":[129],"can":[130],"be":[131,146],"interpreted":[132],"as":[133,140,161],"priori":[136],"model":[137,166],"reduction":[138,168],"approach,":[139],"no":[141],"solution":[142],"snapshots":[143],"need":[144],"precomputed.":[147],"Numerical":[148],"results":[149],"show":[150],"efficiency":[152],"problems":[158],"which":[159],"occur":[160],"challenges":[162],"other":[164],"order":[167],"procedures:":[169],"non-affine":[170],"geometry":[171],"parametrizations,":[172],"moving":[173],"sources,":[174],"or":[175],"high-dimensional":[176],"domains.":[177]},"counts_by_year":[],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}