{"id":"https://openalex.org/W4220878700","doi":"https://doi.org/10.3390/sym14030556","title":"A Stochastic Discrete Empirical Interpolation Approach for Parameterized Systems","display_name":"A Stochastic Discrete Empirical Interpolation Approach for Parameterized Systems","publication_year":2022,"publication_date":"2022-03-10","ids":{"openalex":"https://openalex.org/W4220878700","doi":"https://doi.org/10.3390/sym14030556"},"language":"en","primary_location":{"id":"doi:10.3390/sym14030556","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14030556","pdf_url":"https://www.mdpi.com/2073-8994/14/3/556/pdf?version=1646971740","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/3/556/pdf?version=1646971740","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091436686","display_name":"Daheng Cai","orcid":"https://orcid.org/0000-0003-0756-1866"},"institutions":[{"id":"https://openalex.org/I30809798","display_name":"ShanghaiTech University","ror":"https://ror.org/030bhh786","country_code":"CN","type":"education","lineage":["https://openalex.org/I30809798"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Daheng Cai","raw_affiliation_strings":["School of Information Science and Technology, ShanghaiTech University, Shanghai 201210, China"],"raw_orcid":"https://orcid.org/0000-0003-0756-1866","affiliations":[{"raw_affiliation_string":"School of Information Science and Technology, ShanghaiTech University, Shanghai 201210, China","institution_ids":["https://openalex.org/I30809798"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038926450","display_name":"Chengbin Yao","orcid":null},"institutions":[{"id":"https://openalex.org/I4210132539","display_name":"Northwest Institute of Mechanical and Electrical Engineering","ror":"https://ror.org/03pz37k82","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210132539"]},{"id":"https://openalex.org/I89652312","display_name":"Northwest A&F University","ror":"https://ror.org/0051rme32","country_code":"CN","type":"education","lineage":["https://openalex.org/I89652312"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chengbin Yao","raw_affiliation_strings":["College of Natural Resources and Environment, Northwest A&F University, Xianyang 712100, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Natural Resources and Environment, Northwest A&F University, Xianyang 712100, China","institution_ids":["https://openalex.org/I4210132539","https://openalex.org/I89652312"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014407690","display_name":"Qifeng Liao","orcid":"https://orcid.org/0000-0003-2033-6356"},"institutions":[{"id":"https://openalex.org/I30809798","display_name":"ShanghaiTech University","ror":"https://ror.org/030bhh786","country_code":"CN","type":"education","lineage":["https://openalex.org/I30809798"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qifeng Liao","raw_affiliation_strings":["School of Information Science and Technology, ShanghaiTech University, Shanghai 201210, China"],"raw_orcid":"https://orcid.org/0000-0003-2033-6356","affiliations":[{"raw_affiliation_string":"School of Information Science and Technology, ShanghaiTech University, Shanghai 201210, China","institution_ids":["https://openalex.org/I30809798"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5014407690"],"corresponding_institution_ids":["https://openalex.org/I30809798"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.1251,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.39415343,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"14","issue":"3","first_page":"556","last_page":"556"},"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":0.9994000196456909,"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/T11254","display_name":"Fluid Dynamics and Vibration Analysis","score":0.9883000254631042,"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/parameterized-complexity","display_name":"Parameterized complexity","score":0.7293019890785217},{"id":"https://openalex.org/keywords/variance-reduction","display_name":"Variance reduction","score":0.6810163855552673},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.678676426410675},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6236680746078491},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6090932488441467},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.543685793876648},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5218828320503235},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.4411763846874237},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4165138602256775},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4122040867805481},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.386009156703949},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24588394165039062},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22865602374076843},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1868632733821869},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1256970465183258},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.12142270803451538}],"concepts":[{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.7293019890785217},{"id":"https://openalex.org/C62644790","wikidata":"https://www.wikidata.org/wiki/Q3454689","display_name":"Variance reduction","level":3,"score":0.6810163855552673},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.678676426410675},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6236680746078491},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6090932488441467},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.543685793876648},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5218828320503235},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.4411763846874237},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4165138602256775},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4122040867805481},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.386009156703949},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24588394165039062},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22865602374076843},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1868632733821869},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1256970465183258},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.12142270803451538},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"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/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","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/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14030556","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14030556","pdf_url":"https://www.mdpi.com/2073-8994/14/3/556/pdf?version=1646971740","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:2e4b787e429f4fbd97241ee3adb9ced4","is_oa":true,"landing_page_url":"https://doaj.org/article/2e4b787e429f4fbd97241ee3adb9ced4","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 14, Iss 3, p 556 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/3/556/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14030556","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14030556","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14030556","pdf_url":"https://www.mdpi.com/2073-8994/14/3/556/pdf?version=1646971740","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4220878700.pdf","grobid_xml":"https://content.openalex.org/works/W4220878700.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W106225695","https://openalex.org/W595079961","https://openalex.org/W1657134403","https://openalex.org/W1969080915","https://openalex.org/W2010916308","https://openalex.org/W2047591100","https://openalex.org/W2049753327","https://openalex.org/W2062987778","https://openalex.org/W2067145579","https://openalex.org/W2075783780","https://openalex.org/W2082406229","https://openalex.org/W2103012681","https://openalex.org/W2131049189","https://openalex.org/W2133074406","https://openalex.org/W2152896489","https://openalex.org/W2168970443","https://openalex.org/W2345313423","https://openalex.org/W2397849264","https://openalex.org/W2562390720","https://openalex.org/W2775056138","https://openalex.org/W2999070312","https://openalex.org/W6603720152"],"related_works":["https://openalex.org/W2051058708","https://openalex.org/W1494268238","https://openalex.org/W154868527","https://openalex.org/W1983207144","https://openalex.org/W2490706771","https://openalex.org/W2480116122","https://openalex.org/W4255576661","https://openalex.org/W1516574938","https://openalex.org/W2625725254","https://openalex.org/W2563912921"],"abstract_inverted_index":{"As":[0],"efficient":[1],"separation":[2,97],"of":[3,46,80,93,98,107],"variables":[4,99],"plays":[5],"a":[6,20,39,54],"central":[7],"role":[8],"in":[9],"model":[10],"reduction":[11],"for":[12,27,66,100,118],"nonlinear":[13,102],"and":[14,43,69,113],"nonaffine":[15],"parameterized":[16],"systems,":[17],"we":[18],"propose":[19],"stochastic":[21],"discrete":[22],"empirical":[23],"interpolation":[24],"method":[25],"(SDEIM)":[26],"this":[28],"purpose.":[29],"In":[30],"our":[31],"SDEIM,":[32,94],"candidate":[33,63],"basis":[34],"functions":[35,106],"are":[36,86],"generated":[37],"through":[38],"random":[40,58],"sampling":[41,59],"procedure,":[42],"the":[44,47,70,78,81,90,108],"dimension":[45,79],"approximation":[48,82],"space":[49],"is":[50,126],"systematically":[51],"determined":[52],"by":[53,129],"probability":[55,71],"threshold.":[56],"This":[57],"procedure":[60],"avoids":[61],"large":[62],"sample":[64],"sets":[65],"high-dimensional":[67],"parameters,":[68],"based":[72],"stopping":[73],"criterion":[74],"can":[75],"efficiently":[76],"control":[77],"space.":[83],"Numerical":[84],"experiments":[85],"conducted":[87],"to":[88],"demonstrate":[89],"computational":[91],"efficiency":[92],"which":[95],"include":[96],"general":[101],"functions,":[103],"e.g.,":[104],"exponential":[105],"Karhu":[109],"nen\u2013Lo\u00e8ve":[110],"(KL)":[111],"expansion,":[112],"constructing":[114],"reduced":[115],"order":[116],"models":[117],"FitzHugh\u2013Nagumo":[119],"equations,":[120],"where":[121],"symmetry":[122],"among":[123],"limit":[124],"cycles":[125],"well":[127],"captured":[128],"SDEIM.":[130]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
