{"id":"https://openalex.org/W2135944183","doi":"https://doi.org/10.4304/jnw.9.6.1518-1525","title":"New Basis Functions for Model Reduction of Nonlinear PDEs","display_name":"New Basis Functions for Model Reduction of Nonlinear PDEs","publication_year":2014,"publication_date":"2014-06-09","ids":{"openalex":"https://openalex.org/W2135944183","doi":"https://doi.org/10.4304/jnw.9.6.1518-1525","mag":"2135944183"},"language":"en","primary_location":{"id":"doi:10.4304/jnw.9.6.1518-1525","is_oa":false,"landing_page_url":"https://doi.org/10.4304/jnw.9.6.1518-1525","pdf_url":null,"source":{"id":"https://openalex.org/S189188848","display_name":"Journal of Networks","issn_l":"1796-2056","issn":["1796-2056"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318660","host_organization_name":"Academy Publisher","host_organization_lineage":["https://openalex.org/P4310318660"],"host_organization_lineage_names":["Academy Publisher"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Networks","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/A5080372566","display_name":"Jun Shuai","orcid":"https://orcid.org/0000-0001-8379-3402"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jun Shuai","raw_affiliation_strings":["Central South University/ School of Mathematics and Statistics, Changsha"],"affiliations":[{"raw_affiliation_string":"Central South University/ School of Mathematics and Statistics, Changsha","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053082670","display_name":"Xuli Han","orcid":"https://orcid.org/0000-0001-7708-6971"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuli Han","raw_affiliation_strings":["Central South University/ School of Mathematics and Statistics, Changsha"],"affiliations":[{"raw_affiliation_string":"Central South University/ School of Mathematics and Statistics, Changsha","institution_ids":["https://openalex.org/I139660479"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5080372566"],"corresponding_institution_ids":["https://openalex.org/I139660479"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14742949,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"9","issue":"6","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":0.9983999729156494,"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":0.9983999729156494,"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":0.9296000003814697,"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/computer-science","display_name":"Computer science","score":0.8504760265350342},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.7381706237792969},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.734343409538269},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6591860055923462},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.5733499526977539},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3690721094608307},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3272724151611328},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.12942257523536682},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07132682204246521},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.052540719509124756}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8504760265350342},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.7381706237792969},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.734343409538269},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6591860055923462},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.5733499526977539},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3690721094608307},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3272724151611328},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.12942257523536682},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07132682204246521},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.052540719509124756},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.4304/jnw.9.6.1518-1525","is_oa":false,"landing_page_url":"https://doi.org/10.4304/jnw.9.6.1518-1525","pdf_url":null,"source":{"id":"https://openalex.org/S189188848","display_name":"Journal of Networks","issn_l":"1796-2056","issn":["1796-2056"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318660","host_organization_name":"Academy Publisher","host_organization_lineage":["https://openalex.org/P4310318660"],"host_organization_lineage_names":["Academy Publisher"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Networks","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":15,"referenced_works":["https://openalex.org/W40130861","https://openalex.org/W1980375450","https://openalex.org/W1993240642","https://openalex.org/W1997878934","https://openalex.org/W2005050892","https://openalex.org/W2040522090","https://openalex.org/W2048955329","https://openalex.org/W2048973123","https://openalex.org/W2078746189","https://openalex.org/W2083592448","https://openalex.org/W2091872644","https://openalex.org/W2104124666","https://openalex.org/W2152195021","https://openalex.org/W2177384389","https://openalex.org/W2334947040"],"related_works":["https://openalex.org/W2006953814","https://openalex.org/W2542637001","https://openalex.org/W1972782945","https://openalex.org/W3028700241","https://openalex.org/W3212981098","https://openalex.org/W4221090543","https://openalex.org/W2130622405","https://openalex.org/W2109887391","https://openalex.org/W2296657975","https://openalex.org/W1748978355"],"abstract_inverted_index":{"The":[0,84,109,136,181],"selection":[1],"of":[2,13,32,72,95,104,138,147,150,177,200,209],"the":[3,14,28,33,36,42,45,56,59,67,70,73,92,113,129,132,139,145,148,151,155,175,178,187,193,196,201],"spatial":[4,37,106],"basis":[5,38,61,89,107,157,204],"functions":[6,39,62,90,142,158,205],"is":[7,116],"very":[8],"important":[9],"for":[10,91,112,122,206],"model":[11,93,207],"reduction":[12,94,208],"nonlinear":[15,96,179,210],"partial":[16],"differential":[17,48],"equations":[18],"(PDEs)":[19],"under":[20],"time/space":[21],"separation":[22],"framework,":[23],"which":[24,98],"will":[25],"significantly":[26],"affect":[27],"accuracy":[29],"and":[30,41,131,160,169,192,198],"efficiency":[31],"modeling.":[34],"Using":[35,154],"expansions":[40,159],"Galerkin":[43,161],"method,":[44,162],"finite-dimensional":[46],"ordinary":[47],"equation":[49],"(ODE)":[50],"systems":[51],"can":[52,164],"be":[53],"obtained":[54,100],"from":[55,118],"PDEs.":[57,180,211],"However,":[58],"general":[60,105],"are":[63,76,99,184],"not":[64,77],"optimal":[65],"in":[66,190],"sense":[68],"that":[69],"dimensions":[71],"ODE":[74,172],"system":[75],"lowest":[78],"at":[79],"a":[80,166],"given":[81],"modeling":[82,182],"accuracy.":[83],"current":[85],"study":[86],"proposes":[87],"new":[88,156,203],"PDEs,":[97],"by":[101],"linear":[102],"combinations":[103],"functions.":[108],"transformation":[110],"matrix":[111],"combination":[114],"coefficients":[115],"derived":[117],"straightforward":[119],"optimization":[120],"techniques":[121],"an":[123],"improved":[124,140],"spatio-temporal":[125],"error":[126,141],"function":[127],"between":[128],"approximation":[130],"measured":[133],"spatial-temporal":[134,152],"output.":[135],"derivation":[137],"also":[143],"considers":[144],"influence":[146],"variance":[149],"error.":[153],"it":[163],"provide":[165],"lower":[167],"dimensional":[168],"more":[170],"precise":[171],"to":[173],"approximate":[174],"dynamics":[176],"performance":[183],"compared":[185],"with":[186],"method":[188],"proposed":[189,202],"reference,":[191],"simulations":[194],"shows":[195],"feasibility":[197],"effectiveness":[199]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
