{"id":"https://openalex.org/W2973162955","doi":"https://doi.org/10.3390/s19184002","title":"A Novel Recurrent Neural Network-Based Ultra-Fast, Robust, and Scalable Solver for Inverting a \u201cTime-Varying Matrix\u201d","display_name":"A Novel Recurrent Neural Network-Based Ultra-Fast, Robust, and Scalable Solver for Inverting a \u201cTime-Varying Matrix\u201d","publication_year":2019,"publication_date":"2019-09-16","ids":{"openalex":"https://openalex.org/W2973162955","doi":"https://doi.org/10.3390/s19184002","mag":"2973162955","pmid":"https://pubmed.ncbi.nlm.nih.gov/31527511"},"language":"en","primary_location":{"id":"doi:10.3390/s19184002","is_oa":true,"landing_page_url":"https://doi.org/10.3390/s19184002","pdf_url":"https://www.mdpi.com/1424-8220/19/18/4002/pdf?version=1568641016","source":{"id":"https://openalex.org/S101949793","display_name":"Sensors","issn_l":"1424-8220","issn":["1424-8220"],"is_oa":true,"is_in_doaj":true,"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":"Sensors","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1424-8220/19/18/4002/pdf?version=1568641016","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035234540","display_name":"Vahid Tavakkoli","orcid":null},"institutions":[{"id":"https://openalex.org/I4210166741","display_name":"University of Klagenfurt","ror":"https://ror.org/05q9m0937","country_code":"AT","type":"education","lineage":["https://openalex.org/I4210166741"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Vahid Tavakkoli","raw_affiliation_strings":["Institute for Smart Systems Technologies, University Klagenfurt, A9020 Klagenfurt, Austria"],"affiliations":[{"raw_affiliation_string":"Institute for Smart Systems Technologies, University Klagenfurt, A9020 Klagenfurt, Austria","institution_ids":["https://openalex.org/I4210166741"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016318683","display_name":"Jean Chamberlain Chedjou","orcid":"https://orcid.org/0000-0002-5675-4747"},"institutions":[{"id":"https://openalex.org/I4210166741","display_name":"University of Klagenfurt","ror":"https://ror.org/05q9m0937","country_code":"AT","type":"education","lineage":["https://openalex.org/I4210166741"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Jean Chamberlain Chedjou","raw_affiliation_strings":["Institute for Smart Systems Technologies, University Klagenfurt, A9020 Klagenfurt, Austria"],"affiliations":[{"raw_affiliation_string":"Institute for Smart Systems Technologies, University Klagenfurt, A9020 Klagenfurt, Austria","institution_ids":["https://openalex.org/I4210166741"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061137052","display_name":"Kyandoghere Kyamakya","orcid":"https://orcid.org/0000-0003-0773-9476"},"institutions":[{"id":"https://openalex.org/I4210166741","display_name":"University of Klagenfurt","ror":"https://ror.org/05q9m0937","country_code":"AT","type":"education","lineage":["https://openalex.org/I4210166741"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Kyandoghere Kyamakya","raw_affiliation_strings":["Institute for Smart Systems Technologies, University Klagenfurt, A9020 Klagenfurt, Austria"],"affiliations":[{"raw_affiliation_string":"Institute for Smart Systems Technologies, University Klagenfurt, A9020 Klagenfurt, Austria","institution_ids":["https://openalex.org/I4210166741"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5035234540"],"corresponding_institution_ids":["https://openalex.org/I4210166741"],"apc_list":{"value":2400,"currency":"CHF","value_usd":2598},"apc_paid":{"value":2400,"currency":"CHF","value_usd":2598},"fwci":0.7233,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.78937695,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"19","issue":"18","first_page":"4002","last_page":"4002"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9959999918937683,"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/T11222","display_name":"Magnetic Properties and Applications","score":0.9850000143051147,"subfield":{"id":"https://openalex.org/subfields/2504","display_name":"Electronic, Optical and Magnetic Materials"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5795135498046875},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.575709342956543},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.557939887046814},{"id":"https://openalex.org/keywords/inversion","display_name":"Inversion (geology)","score":0.5563133955001831},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5002396106719971},{"id":"https://openalex.org/keywords/recurrent-neural-network","display_name":"Recurrent neural network","score":0.4894920587539673},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.44894126057624817},{"id":"https://openalex.org/keywords/state-transition-matrix","display_name":"State-transition matrix","score":0.43319427967071533},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3669168949127197},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31168338656425476},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.21401062607765198},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.18842431902885437},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.17721757292747498}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5795135498046875},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.575709342956543},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.557939887046814},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.5563133955001831},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5002396106719971},{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.4894920587539673},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44894126057624817},{"id":"https://openalex.org/C22629506","wikidata":"https://www.wikidata.org/wiki/Q7602993","display_name":"State-transition matrix","level":4,"score":0.43319427967071533},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3669168949127197},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31168338656425476},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.21401062607765198},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.18842431902885437},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.17721757292747498},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C109007969","wikidata":"https://www.wikidata.org/wiki/Q749565","display_name":"Structural basin","level":2,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/s19184002","is_oa":true,"landing_page_url":"https://doi.org/10.3390/s19184002","pdf_url":"https://www.mdpi.com/1424-8220/19/18/4002/pdf?version=1568641016","source":{"id":"https://openalex.org/S101949793","display_name":"Sensors","issn_l":"1424-8220","issn":["1424-8220"],"is_oa":true,"is_in_doaj":true,"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":"Sensors","raw_type":"journal-article"},{"id":"pmid:31527511","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/31527511","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sensors (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:6fd6b19e604f498ba3c0333a59409ba9","is_oa":true,"landing_page_url":"https://doaj.org/article/6fd6b19e604f498ba3c0333a59409ba9","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Sensors, Vol 19, Iss 18, p 4002 (2019)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1424-8220/19/18/4002/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/s19184002","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":"Sensors","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:6767331","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/6767331","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Sensors (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/s19184002","is_oa":true,"landing_page_url":"https://doi.org/10.3390/s19184002","pdf_url":"https://www.mdpi.com/1424-8220/19/18/4002/pdf?version=1568641016","source":{"id":"https://openalex.org/S101949793","display_name":"Sensors","issn_l":"1424-8220","issn":["1424-8220"],"is_oa":true,"is_in_doaj":true,"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":"Sensors","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2973162955.pdf","grobid_xml":"https://content.openalex.org/works/W2973162955.grobid-xml"},"referenced_works_count":56,"referenced_works":["https://openalex.org/W77658930","https://openalex.org/W1597286183","https://openalex.org/W1964693520","https://openalex.org/W1980081495","https://openalex.org/W1982436049","https://openalex.org/W1986576881","https://openalex.org/W1990180092","https://openalex.org/W1992468081","https://openalex.org/W2004771101","https://openalex.org/W2005754028","https://openalex.org/W2007178709","https://openalex.org/W2010411578","https://openalex.org/W2011703186","https://openalex.org/W2013635942","https://openalex.org/W2018385545","https://openalex.org/W2031390440","https://openalex.org/W2034514780","https://openalex.org/W2041364558","https://openalex.org/W2057255661","https://openalex.org/W2063978165","https://openalex.org/W2068123024","https://openalex.org/W2073454980","https://openalex.org/W2074739448","https://openalex.org/W2093131444","https://openalex.org/W2096347908","https://openalex.org/W2097113878","https://openalex.org/W2098316308","https://openalex.org/W2099636542","https://openalex.org/W2105363862","https://openalex.org/W2114377423","https://openalex.org/W2120565705","https://openalex.org/W2128332575","https://openalex.org/W2128970593","https://openalex.org/W2130317597","https://openalex.org/W2130416988","https://openalex.org/W2138244240","https://openalex.org/W2138430352","https://openalex.org/W2138594241","https://openalex.org/W2145856765","https://openalex.org/W2159308419","https://openalex.org/W2160121923","https://openalex.org/W2172501111","https://openalex.org/W2257439149","https://openalex.org/W2396721583","https://openalex.org/W2508436209","https://openalex.org/W2511885285","https://openalex.org/W2731903941","https://openalex.org/W2752379147","https://openalex.org/W2783335378","https://openalex.org/W2801203341","https://openalex.org/W2963600917","https://openalex.org/W3140285855","https://openalex.org/W6635603907","https://openalex.org/W6641593339","https://openalex.org/W6669493263","https://openalex.org/W6674851045"],"related_works":["https://openalex.org/W2169060258","https://openalex.org/W2155184776","https://openalex.org/W4390870012","https://openalex.org/W1972612702","https://openalex.org/W2055579779","https://openalex.org/W2061454923","https://openalex.org/W2551884148","https://openalex.org/W2404563124","https://openalex.org/W2051818031","https://openalex.org/W2162460987"],"abstract_inverted_index":{"The":[0,39,57,185],"concept":[1],"presented":[2],"in":[3,87,122,313],"this":[4,171],"paper":[5],"is":[6,19,55,69,105,129,138,167,181,188,275,299,303],"based":[7],"on":[8],"previous":[9,223],"dynamical":[10],"methods":[11,80,225],"to":[12,62,74,82,144,214,220,289],"realize":[13],"a":[14,21,33,43,49,84,112,130,145,158,173,241,282,304],"time-varying":[15,102,178],"matrix":[16,50,54,65,68,85,103,118,179,310],"inversion.":[17],"It":[18,274],"essentially":[20],"set":[22],"of":[23,90,95,107,147,151,296,308,316],"coupled":[24,40],"ordinary":[25],"differential":[26],"equations":[27],"(ODEs)":[28],"which":[29],"does":[30,60],"indeed":[31],"constitute":[32,42],"recurrent":[34],"neural":[35,193,199,230,235],"network":[36,194,200,236],"(RNN)":[37],"model.":[38],"ODEs":[41],"universal":[44],"modeling":[45],"framework":[46],"for":[47,157,177],"realizing":[48],"inversion":[51,86,104,119,180],"provided":[52],"the":[53,63,67,101,117,123,125,135,148,152,155,191,197,221,256,278,290,294,309,314],"invertible.":[56],"proposed":[58,182,186],"model":[59,205],"converge":[61],"inverted":[64],"if":[66],"invertible,":[70],"otherwise":[71],"it":[72,209,239,298],"converges":[73],"an":[75],"approximated":[76],"inverse.":[77],"Although":[78],"various":[79,88],"exist":[81],"solve":[83],"areas":[89],"science":[91],"and":[92,141,183,196,232,264,269],"engineering,":[93],"most":[94],"them":[96],"do":[97],"assume":[98],"that":[99,208,277,301],"either":[100],"free":[106],"noise":[108,126],"or":[109,237],"they":[110],"involve":[111],"denoising":[113,136],"module":[114],"before":[115],"starting":[116],"computation.":[120],"However,":[121],"practice,":[124],"presence":[127,315],"issue":[128],"very":[131,305],"serious":[132],"problem.":[133],"Also,":[134],"process":[137],"computationally":[139],"expensive":[140],"can":[142],"lead":[143],"violation":[146],"real-time":[149],"property":[150],"system.":[153],"Hence,":[154],"search":[156],"new":[159,174,204,253],"'matrix":[160],"inversion'":[161],"solving":[162],"method":[163,176,187,280],"inherently":[164],"integrating":[165],"noise-cancelling":[166],"highly":[168],"demanded.":[169],"In":[170],"paper,":[172],"combined/extended":[175],"investigated.":[184],"extending":[189],"both":[190,265],"gradient":[192],"(GNN)":[195],"Zhang":[198,234],"(ZNN)":[201],"concepts.":[202],"Our":[203],"has":[206,210,240,281],"proven":[207,300],"exponential":[211],"stability":[212],"according":[213],"Lyapunov":[215],"theory.":[216],"Furthermore,":[217],"when":[218,287],"compared":[219,260,288],"other":[222,291],"related":[224],"(namely":[226],"GNN,":[227],"ZNN,":[228],"Chen":[229],"network,":[231],"integration-enhanced":[233],"IEZNN)":[238],"much":[242],"better":[243,283],"theoretical":[244],"convergence":[245,268,285],"speed.":[246],"To":[247],"finish,":[248],"all":[249],"named":[250],"models":[251],"(the":[252],"one":[254],"versus":[255],"old":[257],"ones)":[258],"are":[259,272],"through":[261],"practical":[262,284],"examples":[263],"their":[266],"respective":[267],"error":[270],"rates":[271],"measured.":[273],"shown/observed":[276],"novel/proposed":[279],"rate":[286],"models.":[292],"Regarding":[293],"amount":[295],"noise,":[297],"there":[302],"good":[306],"approximation":[307],"inverse":[311],"even":[312],"noise.":[317]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
