{"id":"https://openalex.org/W2049753327","doi":"https://doi.org/10.1137/090766498","title":"Nonlinear Model Reduction via Discrete Empirical Interpolation","display_name":"Nonlinear Model Reduction via Discrete Empirical Interpolation","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2049753327","doi":"https://doi.org/10.1137/090766498","mag":"2049753327"},"language":"en","primary_location":{"id":"doi:10.1137/090766498","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090766498","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/A5072662735","display_name":"Saifon Chaturantabut","orcid":"https://orcid.org/0000-0001-5824-5519"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Saifon Chaturantabut","raw_affiliation_strings":["[email\u00a0protected] and [email\u00a0protected]#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[email\u00a0protected] and [email\u00a0protected]#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109874470","display_name":"Danny C. Sorensen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Danny C. Sorensen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":25.624,"has_fulltext":false,"cited_by_count":1940,"citation_normalized_percentile":{"value":0.99802817,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"32","issue":"5","first_page":"2737","last_page":"2764"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":1.0,"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":1.0,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9961000084877014,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9761000275611877,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8205111622810364},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.6745592355728149},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6638879776000977},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6257157325744629},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6133937239646912},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6043991446495056},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6034033894538879},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.5796388387680054},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5338109135627747},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4849946200847626},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4443662762641907},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.4315090775489807},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34975481033325195},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3472350835800171},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.27333927154541016},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10010027885437012},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07090377807617188}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8205111622810364},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6745592355728149},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6638879776000977},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6257157325744629},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6133937239646912},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6043991446495056},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6034033894538879},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.5796388387680054},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5338109135627747},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4849946200847626},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4443662762641907},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.4315090775489807},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34975481033325195},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3472350835800171},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.27333927154541016},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10010027885437012},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07090377807617188},{"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/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"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/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/090766498","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090766498","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:repository.rice.edu:1911/102182","is_oa":false,"landing_page_url":"https://hdl.handle.net/1911/102182&quot;&gt;https://hdl.handle.net/1911/102182&lt;/a&gt;.","pdf_url":null,"source":{"id":"https://openalex.org/S4306401268","display_name":"Rice Research Repository (Rice University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I74775410","host_organization_name":"Rice University","host_organization_lineage":["https://openalex.org/I74775410"],"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":"Technical report"},{"id":"pmh:oai:repository.rice.edu:1911/70218","is_oa":false,"landing_page_url":"https://hdl.handle.net/1911/70218&quot;&gt;https://hdl.handle.net/1911/70218&lt;/a&gt;.","pdf_url":null,"source":{"id":"https://openalex.org/S4306401268","display_name":"Rice Research Repository (Rice University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I74775410","host_organization_name":"Rice University","host_organization_lineage":["https://openalex.org/I74775410"],"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":"Thesis"},{"id":"pmh:oai:scholarship.rice.edu:1911/102182","is_oa":false,"landing_page_url":"http://hdl.handle.net/1911/102182","pdf_url":null,"source":{"id":"https://openalex.org/S4306401268","display_name":"Rice Research Repository (Rice University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I74775410","host_organization_name":"Rice University","host_organization_lineage":["https://openalex.org/I74775410"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Technical report"},{"id":"pmh:oai:scholarship.rice.edu:1911/70218","is_oa":false,"landing_page_url":"http://hdl.handle.net/1911/70218","pdf_url":null,"source":{"id":"https://openalex.org/S4306401268","display_name":"Rice Research Repository (Rice University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I74775410","host_organization_name":"Rice University","host_organization_lineage":["https://openalex.org/I74775410"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Thesis"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":84,"referenced_works":["https://openalex.org/W84177944","https://openalex.org/W105602876","https://openalex.org/W571068634","https://openalex.org/W1261010427","https://openalex.org/W1506690472","https://openalex.org/W1507402195","https://openalex.org/W1570007728","https://openalex.org/W1590943005","https://openalex.org/W1966450732","https://openalex.org/W1970250678","https://openalex.org/W1970592681","https://openalex.org/W1974533022","https://openalex.org/W1977681898","https://openalex.org/W1981119767","https://openalex.org/W1982290494","https://openalex.org/W1985365411","https://openalex.org/W1987307696","https://openalex.org/W1989951672","https://openalex.org/W1998233602","https://openalex.org/W1999800849","https://openalex.org/W2006029468","https://openalex.org/W2007259720","https://openalex.org/W2008939121","https://openalex.org/W2009380226","https://openalex.org/W2009926327","https://openalex.org/W2014071022","https://openalex.org/W2017745440","https://openalex.org/W2023844638","https://openalex.org/W2033666012","https://openalex.org/W2036360532","https://openalex.org/W2036852510","https://openalex.org/W2040309011","https://openalex.org/W2042816208","https://openalex.org/W2045627558","https://openalex.org/W2047591100","https://openalex.org/W2055391622","https://openalex.org/W2056328108","https://openalex.org/W2059316647","https://openalex.org/W2059821792","https://openalex.org/W2060898145","https://openalex.org/W2060996269","https://openalex.org/W2067145579","https://openalex.org/W2072136228","https://openalex.org/W2077763222","https://openalex.org/W2080556931","https://openalex.org/W2086496856","https://openalex.org/W2092440000","https://openalex.org/W2095222360","https://openalex.org/W2098077093","https://openalex.org/W2098653095","https://openalex.org/W2098980185","https://openalex.org/W2102273815","https://openalex.org/W2102753028","https://openalex.org/W2102831657","https://openalex.org/W2104225554","https://openalex.org/W2108311308","https://openalex.org/W2109628201","https://openalex.org/W2110649199","https://openalex.org/W2114211305","https://openalex.org/W2117590489","https://openalex.org/W2120101088","https://openalex.org/W2124500362","https://openalex.org/W2124916960","https://openalex.org/W2125032211","https://openalex.org/W2126903321","https://openalex.org/W2133642820","https://openalex.org/W2138291458","https://openalex.org/W2140006076","https://openalex.org/W2140820418","https://openalex.org/W2146900442","https://openalex.org/W2147414751","https://openalex.org/W2147836374","https://openalex.org/W2154062528","https://openalex.org/W2156368851","https://openalex.org/W2159651350","https://openalex.org/W2161024376","https://openalex.org/W2168970443","https://openalex.org/W2259411569","https://openalex.org/W2317926736","https://openalex.org/W2480471205","https://openalex.org/W2924040522","https://openalex.org/W3037995832","https://openalex.org/W3117475098","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W3082668976","https://openalex.org/W2517973022","https://openalex.org/W1543121148","https://openalex.org/W1580703421","https://openalex.org/W2618518959","https://openalex.org/W2231364979","https://openalex.org/W4295745414","https://openalex.org/W4382202915","https://openalex.org/W2489516236","https://openalex.org/W4297273858"],"abstract_inverted_index":{"A":[0],"dimension":[1,52,129,220,253],"reduction":[2,254],"method":[3,25,80,119],"called":[4],"discrete":[5,116],"empirical":[6,78,117],"interpolation":[7,79,118],"is":[8,82,124,145,179,215],"proposed":[9],"and":[10,255],"shown":[11,216],"to":[12,100,104,147,168,205,217,223],"dramatically":[13],"reduce":[14,218],"the":[15,19,41,47,54,63,67,73,89,93,97,105,128,165,185,197,211,219],"computational":[16],"complexity":[17,64,90],"of":[18,43,65,72,85,91,96,107,130,132,137,154,171,184,199,203,210],"popular":[20],"proper":[21],"orthogonal":[22],"decomposition":[23],"(POD)":[24],"for":[26,30,126],"constructing":[27],"reduced-order":[28],"models":[29],"time":[31,155],"dependent":[32,156,160],"and/or":[33,158],"parametrized":[34],"nonlinear":[35,68,94,172,237],"partial":[36],"differential":[37,134],"equations":[38,135,214],"(PDEs).":[39],"In":[40],"presence":[42],"a":[44,83,101,115,121,138,180,188,206,231],"general":[45],"nonlinearity,":[46],"standard":[48],"POD-Galerkin":[49],"technique":[50],"reduces":[51,88],"in":[53,187,245],"sense":[55],"that":[56,71,87,123,191,234],"far":[57],"fewer":[58],"variables":[59,109,226],"are":[60],"present,":[61],"but":[62],"evaluating":[66,92],"term":[69,95],"remains":[70],"original":[74,77],"problem.":[75],"The":[76],"(EIM)":[81],"modification":[84],"POD":[86],"reduced":[98,108],"model":[99],"cost":[102],"proportional":[103],"number":[106],"obtained":[110],"by":[111],"POD.":[112],"We":[113,241],"propose":[114],"(DEIM),":[120],"variant":[122],"suitable":[125],"reducing":[127],"systems":[131,170],"ordinary":[133],"(ODEs)":[136],"certain":[139],"type.":[140],"As":[141],"presented":[142],"here,":[143],"it":[144],"applicable":[146],"ODEs":[148,173],"arising":[149],"from":[150,221],"finite":[151,207],"difference":[152,208],"discretization":[153,209],"PDEs":[157],"parametrically":[159],"steady":[161],"state":[162,251],"problems.":[163],"However,":[164],"approach":[166],"extends":[167],"arbitrary":[169],"with":[174,227,249],"minor":[175],"modification.":[176],"Our":[177],"contribution":[178],"greatly":[181],"simplified":[182],"description":[183],"EIM":[186],"finite-dimensional":[189],"setting":[190],"possesses":[192],"an":[193],"error":[194,229],"bound":[195],"on":[196],"quality":[198],"approximation.":[200],"An":[201],"application":[202],"DEIM":[204],"one-dimensional":[212],"FitzHugh\u2013Nagumo":[213],"1024":[222],"order":[224],"5":[225],"negligible":[228],"over":[230],"long-time":[232],"integration":[233],"fully":[235],"captures":[236],"limit":[238],"cycle":[239],"behavior.":[240],"also":[242],"demonstrate":[243],"applicability":[244],"higher":[246],"spatial":[247],"dimensions":[248],"similar":[250],"space":[252],"accuracy":[256],"results.":[257]},"counts_by_year":[{"year":2026,"cited_by_count":109},{"year":2025,"cited_by_count":145},{"year":2024,"cited_by_count":156},{"year":2023,"cited_by_count":192},{"year":2022,"cited_by_count":174},{"year":2021,"cited_by_count":171},{"year":2020,"cited_by_count":196},{"year":2019,"cited_by_count":164},{"year":2018,"cited_by_count":118},{"year":2017,"cited_by_count":132},{"year":2016,"cited_by_count":101},{"year":2015,"cited_by_count":97},{"year":2014,"cited_by_count":74},{"year":2013,"cited_by_count":60},{"year":2012,"cited_by_count":40}],"updated_date":"2026-09-05T08:02:43.246662","created_date":"2025-10-10T00:00:00"}
