{"id":"https://openalex.org/W1979404050","doi":"https://doi.org/10.1109/ecc.2014.6862414","title":"Parametric model order reduction by sparse-grid-based interpolation on matrix manifolds for multidimensional parameter spaces","display_name":"Parametric model order reduction by sparse-grid-based interpolation on matrix manifolds for multidimensional parameter spaces","publication_year":2014,"publication_date":"2014-06-01","ids":{"openalex":"https://openalex.org/W1979404050","doi":"https://doi.org/10.1109/ecc.2014.6862414","mag":"1979404050"},"language":"en","primary_location":{"id":"doi:10.1109/ecc.2014.6862414","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ecc.2014.6862414","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2014 European Control Conference (ECC)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5067476399","display_name":"Matthias Geu\u00df","orcid":null},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Matthias Geuss","raw_affiliation_strings":["Department of Mechanical Engineering, Institute of Automatic Control, Technische Universit\u00e4t M\u00fcnchen, Garching, Germany","Technical University of Munich"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Institute of Automatic Control, Technische Universit\u00e4t M\u00fcnchen, Garching, Germany","institution_ids":["https://openalex.org/I62916508"]},{"raw_affiliation_string":"Technical University of Munich","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020720458","display_name":"Daniel Butnaru","orcid":null},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Daniel Butnaru","raw_affiliation_strings":["Department of Informatics, Scientific Computing Group, Technische Universit\u00e4t M\u00fcnchen, Garching, Germany","Technical University of Munich"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Informatics, Scientific Computing Group, Technische Universit\u00e4t M\u00fcnchen, Garching, Germany","institution_ids":["https://openalex.org/I62916508"]},{"raw_affiliation_string":"Technical University of Munich","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027402421","display_name":"Benjamin Peherstorfer","orcid":"https://orcid.org/0000-0002-1558-6775"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Benjamin Peherstorfer","raw_affiliation_strings":["Department of Informatics, Scientific Computing Group, Technische Universit\u00e4t M\u00fcnchen, Garching, Germany","Dept. of Inf., Sci. Comput. Group, Tech. Univ. Munchen, Garching, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Informatics, Scientific Computing Group, Technische Universit\u00e4t M\u00fcnchen, Garching, Germany","institution_ids":["https://openalex.org/I62916508"]},{"raw_affiliation_string":"Dept. of Inf., Sci. Comput. Group, Tech. Univ. Munchen, Garching, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068403289","display_name":"Hans\u2010Joachim Bungartz","orcid":"https://orcid.org/0000-0002-0171-0712"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Hans-Joachim Bungartz","raw_affiliation_strings":["Department of Informatics, Scientific Computing Group, Technische Universit\u00e4t M\u00fcnchen, Garching, Germany","Technical University of Munich"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Informatics, Scientific Computing Group, Technische Universit\u00e4t M\u00fcnchen, Garching, Germany","institution_ids":["https://openalex.org/I62916508"]},{"raw_affiliation_string":"Technical University of Munich","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006081522","display_name":"Boris Lohmann","orcid":"https://orcid.org/0000-0002-7881-8385"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Boris Lohmann","raw_affiliation_strings":["Department of Mechanical Engineering, Institute of Automatic Control, Technische Universit\u00e4t M\u00fcnchen, Garching, Germany","Technical University of Munich"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Institute of Automatic Control, Technische Universit\u00e4t M\u00fcnchen, Garching, Germany","institution_ids":["https://openalex.org/I62916508"]},{"raw_affiliation_string":"Technical University of Munich","institution_ids":["https://openalex.org/I62916508"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I62916508"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"2727","last_page":"2732"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998999834060669,"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":0.9998999834060669,"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/T12810","display_name":"Real-time simulation and control systems","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9883000254631042,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.7229182124137878},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.5953314900398254},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5747891664505005},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.550900399684906},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.547006368637085},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.5347620248794556},{"id":"https://openalex.org/keywords/sparse-grid","display_name":"Sparse grid","score":0.5322240591049194},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.5232117176055908},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5226980447769165},{"id":"https://openalex.org/keywords/weighting","display_name":"Weighting","score":0.520733118057251},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.5046018362045288},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.49497145414352417},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48780325055122375},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4770745038986206},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46333467960357666},{"id":"https://openalex.org/keywords/parametric-equation","display_name":"Parametric equation","score":0.4521997272968292},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.41098111867904663},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12495666742324829},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11665111780166626}],"concepts":[{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.7229182124137878},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5953314900398254},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5747891664505005},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.550900399684906},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.547006368637085},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.5347620248794556},{"id":"https://openalex.org/C156439662","wikidata":"https://www.wikidata.org/wiki/Q7573793","display_name":"Sparse grid","level":2,"score":0.5322240591049194},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.5232117176055908},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5226980447769165},{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.520733118057251},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.5046018362045288},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.49497145414352417},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48780325055122375},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4770745038986206},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46333467960357666},{"id":"https://openalex.org/C99636146","wikidata":"https://www.wikidata.org/wiki/Q35889","display_name":"Parametric equation","level":2,"score":0.4521997272968292},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.41098111867904663},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12495666742324829},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11665111780166626},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"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/C126838900","wikidata":"https://www.wikidata.org/wiki/Q77604","display_name":"Radiology","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ecc.2014.6862414","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ecc.2014.6862414","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2014 European Control Conference (ECC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W162332476","https://openalex.org/W1551480811","https://openalex.org/W1582373441","https://openalex.org/W1976406204","https://openalex.org/W1985365411","https://openalex.org/W1992066335","https://openalex.org/W2054836895","https://openalex.org/W2080556931","https://openalex.org/W2116251284","https://openalex.org/W2152985666","https://openalex.org/W2312884521","https://openalex.org/W2760683735","https://openalex.org/W4255975175","https://openalex.org/W6606581618","https://openalex.org/W6634511323","https://openalex.org/W6744817607"],"related_works":["https://openalex.org/W1995622179","https://openalex.org/W1484111231","https://openalex.org/W1552543208","https://openalex.org/W2074396517","https://openalex.org/W2166963679","https://openalex.org/W2187269125","https://openalex.org/W1641615907","https://openalex.org/W3089231081","https://openalex.org/W2093956241","https://openalex.org/W2354420595"],"abstract_inverted_index":{"Current":[0],"methods":[1],"of":[2,11,34,38,81,99,115],"parametric":[3],"model":[4],"order":[5,29],"reduction":[6],"based":[7],"on":[8],"the":[9,32,36,57,60,64,84,100,106,111,116],"interpolation":[10],"system":[12,102],"matrices":[13,62],"are":[14,68],"extended":[15],"in":[16],"this":[17],"paper":[18],"to":[19,23,30,63,72],"an":[20,51],"efficient":[21],"method":[22,118],"tackle":[24],"multidimensional":[25],"parameter":[26],"spaces.":[27],"In":[28,56],"overcome":[31],"curse":[33],"dimensionality":[35],"technique":[37],"sparse":[39,85],"grids":[40],"with":[41,70],"multiple":[42],"outputs":[43],"is":[44,48,119],"applied.":[45],"The":[46,79,97,113],"procedure":[47],"divided":[49],"into":[50],"offline":[52,58],"and":[53,75],"online":[54,107],"phase.":[55],"phase":[59,108],"weighting":[61],"corresponding":[65],"basis":[66],"functions":[67],"computed":[69],"respect":[71],"generalized":[73],"coordinates":[74],"appropriate":[76],"matrix":[77],"manifolds.":[78],"number":[80],"levels":[82],"for":[83],"grid":[86],"can":[87],"be":[88],"set":[89],"manually":[90],"or":[91],"determined":[92],"by":[93,109,121],"a":[94],"tolerance":[95],"criterion.":[96],"calculation":[98],"interpolated":[101],"takes":[103],"place":[104],"during":[105],"evaluating":[110],"interpolant.":[112],"performance":[114],"proposed":[117],"demonstrated":[120],"two":[122],"numerical":[123],"examples.":[124]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}