{"id":"https://openalex.org/W2127135659","doi":"https://doi.org/10.1109/tcad.2011.2142184","title":"QLMOR: A Projection-Based Nonlinear Model Order Reduction Approach Using Quadratic-Linear Representation of Nonlinear Systems","display_name":"QLMOR: A Projection-Based Nonlinear Model Order Reduction Approach Using Quadratic-Linear Representation of Nonlinear Systems","publication_year":2011,"publication_date":"2011-08-25","ids":{"openalex":"https://openalex.org/W2127135659","doi":"https://doi.org/10.1109/tcad.2011.2142184","mag":"2127135659"},"language":"en","primary_location":{"id":"doi:10.1109/tcad.2011.2142184","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcad.2011.2142184","pdf_url":null,"source":{"id":"https://openalex.org/S100835903","display_name":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems","issn_l":"0278-0070","issn":["0278-0070","1937-4151"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems","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/A5088326953","display_name":"Chenjie Gu","orcid":"https://orcid.org/0000-0002-1339-4534"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Chenjie Gu","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University of California Berkeley, Berkeley, CA, USA","Dept. of Electr. Eng. & Comput. Sci., Univ. of California at Berkeley, Berkeley, CA, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of California Berkeley, Berkeley, CA, USA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"Dept. of Electr. Eng. & Comput. Sci., Univ. of California at Berkeley, Berkeley, CA, USA#TAB#","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5088326953"],"corresponding_institution_ids":["https://openalex.org/I95457486"],"apc_list":null,"apc_paid":null,"fwci":4.5761,"has_fulltext":false,"cited_by_count":189,"citation_normalized_percentile":{"value":0.95405286,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"30","issue":"9","first_page":"1307","last_page":"1320"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9925000071525574,"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/T10305","display_name":"Power System Optimization and Stability","score":0.9836000204086304,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/nonlinear-system","display_name":"Nonlinear system","score":0.7162870168685913},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.5943742394447327},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.512127161026001},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.504776120185852},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4925556778907776},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.47796961665153503},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42791748046875},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40799111127853394},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37814420461654663},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.09643742442131042},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07871520519256592}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7162870168685913},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.5943742394447327},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.512127161026001},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.504776120185852},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4925556778907776},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.47796961665153503},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42791748046875},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40799111127853394},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37814420461654663},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.09643742442131042},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07871520519256592},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcad.2011.2142184","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcad.2011.2142184","pdf_url":null,"source":{"id":"https://openalex.org/S100835903","display_name":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems","issn_l":"0278-0070","issn":["0278-0070","1937-4151"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W6323944","https://openalex.org/W110690611","https://openalex.org/W1561445488","https://openalex.org/W1597839575","https://openalex.org/W1876456565","https://openalex.org/W2002936353","https://openalex.org/W2022997559","https://openalex.org/W2023285936","https://openalex.org/W2029030701","https://openalex.org/W2037579718","https://openalex.org/W2060707164","https://openalex.org/W2079063703","https://openalex.org/W2108311308","https://openalex.org/W2112369634","https://openalex.org/W2119695238","https://openalex.org/W2123947147","https://openalex.org/W2126903321","https://openalex.org/W2128919817","https://openalex.org/W2133642820","https://openalex.org/W2133825750","https://openalex.org/W2134067926","https://openalex.org/W2136202185","https://openalex.org/W2150930321","https://openalex.org/W2154725907","https://openalex.org/W2156158690","https://openalex.org/W2159651350","https://openalex.org/W2163626738","https://openalex.org/W2167848581","https://openalex.org/W2605543710","https://openalex.org/W3142232850","https://openalex.org/W3142948162","https://openalex.org/W3150176780","https://openalex.org/W4235775569","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2532234348","https://openalex.org/W108084911","https://openalex.org/W2154204858","https://openalex.org/W2393440248","https://openalex.org/W2351452215","https://openalex.org/W3209622820","https://openalex.org/W2617963432","https://openalex.org/W2673314300","https://openalex.org/W1854082044","https://openalex.org/W3169007055"],"abstract_inverted_index":{"We":[0,170],"present":[1],"a":[2,47,59,184,187,199],"projection-based":[3],"nonlinear":[4,26,40,75,221],"model":[5,10,76,135],"order":[6,11,77,245],"reduction":[7,12,72,78],"method,":[8],"named":[9],"via":[13],"quadratic-linear":[14,50],"systems":[15],"(QLMOR).":[16],"QLMOR":[17,103,172],"employs":[18],"two":[19],"novel":[20],"ideas:":[21],"1)":[22],"we":[23,57,68],"show":[24],"that":[25,146,193,219],"ordinary":[27],"differential":[28,51],"equations,":[29],"and":[30,55,67,186,191,253],"more":[31],"generally":[32],"differential-algebraic":[33],"equations":[34,53],"(DAEs)":[35],"with":[36,237],"many":[37],"commonly":[38],"encountered":[39],"kernels":[41],"can":[42,224],"be":[43],"re-written":[44],"equivalently":[45],"in":[46,124,225],"special":[48],"representation,":[49,102],"algebraic":[52],"(QLDAEs),":[54],"2)":[56],"perform":[58],"Volterra":[60,65],"analysis":[61],"to":[62,85,130],"derive":[63],"the":[64,70,97,100,125,133],"kernels,":[66],"adapt":[69],"moment-matching":[71],"technique":[73],"of":[74,91,96,99,147,203],"method":[79],"(NORM)":[80],"<citerefgrp":[81,111,176,208,247,258],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[82,112,177,209,248,259],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><citeref":[83,113,178,210,260],"refid=\"ref1\"/></citerefgrp>":[84],"reduce":[86],"these":[87],"QLDAEs":[88,90],"into":[89],"much":[92],"smaller":[93],"size.":[94],"Because":[95,132],"generality":[98],"QLDAE":[101],"has":[104,136,163],"significantly":[105,200],"broader":[106,229],"applicability":[107,230],"than":[108,145,205,231],"Taylor-expansion-based":[109,206],"methods":[110,175,207,239,255],"refid=\"ref1\"/>":[114],"<citeref":[115,181,213,250],"refid=\"ref2\"/><citeref":[116],"refid=\"ref3\"/></citerefgrp>":[117,182,214],"since":[118],"there":[119],"is":[120,143],"no":[121],"approximation":[122],"involved":[123],"transformation":[126],"from":[127],"original":[128],"DAEs":[129],"QLDAEs.":[131],"reduced":[134,244],"only":[137],"quadratic":[138],"nonlinearities,":[139],"its":[140],"computational":[141],"complexity":[142],"less":[144],"similar":[148],"prior":[149,174],"methods.":[150],"In":[151],"addition,":[152],"QLMOR,":[153,216],"unlike":[154],"NORM,":[155],"totally":[156],"avoids":[157],"explicit":[158],"moment":[159],"calculations,":[160],"hence":[161],"it":[162],"improved":[164],"numerical":[165],"stability":[166],"properties":[167],"as":[168],"well.":[169],"compare":[171],"against":[173],"refid=\"ref1\"/><citeref":[179,211],"refid=\"ref2\"/>":[180,212],"on":[183],"circuit":[185],"biochemical":[188],"reaction-like":[189],"system,":[190],"demonstrate":[192],"QLMOR-reduced":[194],"models":[195],"retain":[196],"accuracy":[197],"over":[198],"wider":[201],"range":[202],"excitation":[204],".":[215],"therefore,":[217],"demonstrates":[218],"Volterra-kernel-based":[220],"MOR":[222],"techniques":[223],"fact":[226],"have":[227],"far":[228],"previously":[232],"suspected,":[233],"possibly":[234],"being":[235],"competitive":[236],"trajectory-based":[238],"(e.g.,":[240,256],"trajectory":[241],"piece-wise":[242],"linear":[243],"modeling":[246],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[249],"refid=\"ref4\"/></citerefgrp>":[251],")":[252],"nonlinear-projection-based":[254],"maniMOR":[257],"refid=\"ref5\"/></citerefgrp>":[261],").":[262]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":13},{"year":2024,"cited_by_count":25},{"year":2023,"cited_by_count":15},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":30},{"year":2020,"cited_by_count":19},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":12},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":14},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-07T14:57:38.498316","created_date":"2025-10-10T00:00:00"}