{"id":"https://openalex.org/W2024704551","doi":"https://doi.org/10.1109/acc.2012.6315479","title":"On a generalization of the proper orthogonal decomposition and optimal construction of reduced order models","display_name":"On a generalization of the proper orthogonal decomposition and optimal construction of reduced order models","publication_year":2012,"publication_date":"2012-06-01","ids":{"openalex":"https://openalex.org/W2024704551","doi":"https://doi.org/10.1109/acc.2012.6315479","mag":"2024704551"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2012.6315479","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2012.6315479","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 American Control Conference (ACC)","raw_type":"proceedings-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/A5024483587","display_name":"Seddik M. Djouadi","orcid":"https://orcid.org/0000-0002-5211-1939"},"institutions":[{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"S. M. Djouadi","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN, USA","Department of Electrical Engineering and Computer Science at The University of Tennessee, Knoxville, TN 37996"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN, USA","institution_ids":["https://openalex.org/I75027704"]},{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science at The University of Tennessee, Knoxville, TN 37996","institution_ids":["https://openalex.org/I75027704"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076106442","display_name":"Samir Sahyoun","orcid":null},"institutions":[{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"S. Sahyoun","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN, USA","Department of Electrical Engineering and Computer Science at The University of Tennessee, Knoxville, TN 37996"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN, USA","institution_ids":["https://openalex.org/I75027704"]},{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science at The University of Tennessee, Knoxville, TN 37996","institution_ids":["https://openalex.org/I75027704"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5024483587"],"corresponding_institution_ids":["https://openalex.org/I75027704"],"apc_list":null,"apc_paid":null,"fwci":0.7276,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.69818023,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1436","last_page":"1441"},"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/T11254","display_name":"Fluid Dynamics and Vibration Analysis","score":0.9900000095367432,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9891999959945679,"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/mathematics","display_name":"Mathematics","score":0.8075945377349854},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.6577552556991577},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.6263623237609863},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.5770257115364075},{"id":"https://openalex.org/keywords/inner-product-space","display_name":"Inner product space","score":0.536454975605011},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49442076683044434},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4928145706653595},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.49193406105041504},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45727303624153137},{"id":"https://openalex.org/keywords/trace-class","display_name":"Trace class","score":0.41217613220214844},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.23138028383255005}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8075945377349854},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.6577552556991577},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.6263623237609863},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.5770257115364075},{"id":"https://openalex.org/C91855343","wikidata":"https://www.wikidata.org/wiki/Q214159","display_name":"Inner product space","level":2,"score":0.536454975605011},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49442076683044434},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4928145706653595},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.49193406105041504},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45727303624153137},{"id":"https://openalex.org/C131229623","wikidata":"https://www.wikidata.org/wiki/Q977297","display_name":"Trace class","level":3,"score":0.41217613220214844},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.23138028383255005},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2012.6315479","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2012.6315479","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 American Control Conference (ACC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W40130861","https://openalex.org/W1413841356","https://openalex.org/W1609496979","https://openalex.org/W1845740698","https://openalex.org/W1989951672","https://openalex.org/W2011464857","https://openalex.org/W2017745440","https://openalex.org/W2098077093","https://openalex.org/W2120756413","https://openalex.org/W2125225415","https://openalex.org/W2145586686","https://openalex.org/W2147046190","https://openalex.org/W2312584627","https://openalex.org/W2323050068","https://openalex.org/W2330666245","https://openalex.org/W2334158773","https://openalex.org/W2334269637","https://openalex.org/W2506261713","https://openalex.org/W6628037797","https://openalex.org/W6639048148"],"related_works":["https://openalex.org/W1015651293","https://openalex.org/W2164189677","https://openalex.org/W2953883784","https://openalex.org/W2950745223","https://openalex.org/W4299978068","https://openalex.org/W3094256268","https://openalex.org/W4294959669","https://openalex.org/W1934971259","https://openalex.org/W2964340678","https://openalex.org/W3101710363"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"the":[3,10,43,47,57,76,92,105,137,150,161,169],"popular":[4],"proper":[5],"orthogonal":[6],"decomposition":[7],"(POD)":[8],"without":[9],"usual":[11],"integral":[12],"or":[13],"inner":[14],"product":[15,38],"constraints":[16],"is":[17,32,40,71,83,95,145],"extended":[18],"to":[19,62,73,142,149,168],"general":[20],"Hilbert":[21,44],"spaces,":[22,26],"such":[23],"as":[24],"Sobolev":[25],"using":[27,78,124,160],"functional":[28],"analytic":[29],"methods.":[30],"It":[31],"shown":[33,72],"that":[34],"a":[35,87,100],"particular":[36],"tensor":[37],"space":[39,45],"dense":[41],"in":[42,75,104,131],"where":[46,91],"partial":[48],"differential":[49],"equation":[50,140],"(PDE)":[51],"solution":[52,59,94],"lives.":[53],"This":[54,82],"allows":[55],"approximating":[56],"PDE":[58,93],"by":[60,68,85,97,117],"tensors":[61,70],"any":[63],"desired":[64],"accuracy.":[65],"Optimal":[66],"approximation":[67],"these":[69],"result":[74],"POD":[77,111,151],"operator":[79],"theoretic":[80],"arguments.":[81],"achieved":[84],"solving":[86,118],"nonlinear":[88],"optimization":[89],"problem":[90,123],"approximated":[96],"operators":[98],"of":[99],"prescribed":[101],"finite":[102],"rank":[103],"corresponding":[106],"trace":[107],"class":[108],"2":[109],"norm.":[110],"modes":[112],"can":[113],"then":[114,158,166],"be":[115],"computed":[116],"an":[119,128],"infinite":[120],"dimensional":[121],"eigenvalue":[122],"Hilbert-Schmidt":[125],"theory.":[126],"Moreover,":[127],"optimal":[129],"method":[130],"constructing":[132],"reduced":[133,152,162],"order":[134,163,171],"models":[135],"for":[136],"two-dimensional":[138],"Burgers'":[139],"subject":[141],"boundary":[143],"control":[144],"presented":[146],"and":[147,165],"compared":[148],"models.":[153],"A":[154],"closed-loop":[155],"feedback":[156],"controller":[157],"designed":[159],"model":[164],"applied":[167],"full":[170],"model.":[172]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
