{"id":"https://openalex.org/W7131347832","doi":"https://doi.org/10.1007/s10915-026-03215-w","title":"Barycentric Rational Approximation for Learning the Index of a Dynamical System from Limited Data","display_name":"Barycentric Rational Approximation for Learning the Index of a Dynamical System from Limited Data","publication_year":2026,"publication_date":"2026-02-25","ids":{"openalex":"https://openalex.org/W7131347832","doi":"https://doi.org/10.1007/s10915-026-03215-w"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-026-03215-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-026-03215-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-026-03215-w.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10915-026-03215-w.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018807402","display_name":"Davide Pradovera","orcid":"https://orcid.org/0000-0003-0398-1580"},"institutions":[{"id":"https://openalex.org/I4210135511","display_name":"AlbaNova","ror":"https://ror.org/044kkfr75","country_code":"SE","type":"facility","lineage":["https://openalex.org/I4210135511"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Davide Pradovera","raw_affiliation_strings":["Stockholm University, Albanov\u00e4gen 28, 11419, Stockholm, Sweden"],"raw_orcid":"https://orcid.org/0000-0003-0398-1580","affiliations":[{"raw_affiliation_string":"Stockholm University, Albanov\u00e4gen 28, 11419, Stockholm, Sweden","institution_ids":["https://openalex.org/I4210135511"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Ion Victor Gosea","orcid":null},"institutions":[{"id":"https://openalex.org/I4210127568","display_name":"Max Planck Institute for Dynamics of Complex Technical Systems","ror":"https://ror.org/030h7k016","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210127568"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ion Victor Gosea","raw_affiliation_strings":["Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr.\u00a01, 39106, Magdeburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr.\u00a01, 39106, Magdeburg, Germany","institution_ids":["https://openalex.org/I4210127568"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042908408","display_name":"Jan Heiland","orcid":"https://orcid.org/0000-0003-0228-8522"},"institutions":[{"id":"https://openalex.org/I119449181","display_name":"Technische Universit\u00e4t Ilmenau","ror":"https://ror.org/01weqhp73","country_code":"DE","type":"education","lineage":["https://openalex.org/I119449181"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Jan Heiland","raw_affiliation_strings":["Ilmenau University of Technology, Weimarer Str.\u00a025, 98693, Ilmenau, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ilmenau University of Technology, Weimarer Str.\u00a025, 98693, Ilmenau, Germany","institution_ids":["https://openalex.org/I119449181"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5018807402"],"corresponding_institution_ids":["https://openalex.org/I4210135511"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.3972751,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"107","issue":"1","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":0.7901999950408936,"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":0.7901999950408936,"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/T11236","display_name":"Control Systems and Identification","score":0.1282999962568283,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10534","display_name":"Structural Health Monitoring Techniques","score":0.012600000016391277,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/barycentric-coordinate-system","display_name":"Barycentric coordinate system","score":0.8216000199317932},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.6103000044822693},{"id":"https://openalex.org/keywords/mirroring","display_name":"Mirroring","score":0.5877000093460083},{"id":"https://openalex.org/keywords/extrapolation","display_name":"Extrapolation","score":0.5791000127792358},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.5475999712944031},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5253000259399414},{"id":"https://openalex.org/keywords/system-identification","display_name":"System identification","score":0.4984999895095825},{"id":"https://openalex.org/keywords/linear-dynamical-system","display_name":"Linear dynamical system","score":0.4124999940395355},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.3993000090122223}],"concepts":[{"id":"https://openalex.org/C128356825","wikidata":"https://www.wikidata.org/wiki/Q738422","display_name":"Barycentric coordinate system","level":2,"score":0.8216000199317932},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6103000044822693},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6003000140190125},{"id":"https://openalex.org/C189645446","wikidata":"https://www.wikidata.org/wiki/Q350865","display_name":"Mirroring","level":2,"score":0.5877000093460083},{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.5791000127792358},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.5475999712944031},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5253000259399414},{"id":"https://openalex.org/C119247159","wikidata":"https://www.wikidata.org/wiki/Q1366192","display_name":"System identification","level":3,"score":0.4984999895095825},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4706000089645386},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46950000524520874},{"id":"https://openalex.org/C114275822","wikidata":"https://www.wikidata.org/wiki/Q621512","display_name":"Linear dynamical system","level":3,"score":0.4124999940395355},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.3993000090122223},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.39899998903274536},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.39890000224113464},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37310001254081726},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.36719998717308044},{"id":"https://openalex.org/C81299745","wikidata":"https://www.wikidata.org/wiki/Q334269","display_name":"Transfer function","level":2,"score":0.35920000076293945},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3465999960899353},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.33480000495910645},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.3334999978542328},{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.3172000050544739},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.31369999051094055},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30469998717308044},{"id":"https://openalex.org/C131675550","wikidata":"https://www.wikidata.org/wiki/Q7646884","display_name":"Surrogate model","level":2,"score":0.30469998717308044},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.2799000144004822},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.27639999985694885},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.2759000062942505},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.26750001311302185},{"id":"https://openalex.org/C77405623","wikidata":"https://www.wikidata.org/wiki/Q598451","display_name":"System dynamics","level":2,"score":0.2667999863624573},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.2565000057220459},{"id":"https://openalex.org/C205979905","wikidata":"https://www.wikidata.org/wiki/Q215084","display_name":"Analytic function","level":2,"score":0.2524999976158142}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10915-026-03215-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-026-03215-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-026-03215-w.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10915-026-03215-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-026-03215-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-026-03215-w.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320325669","display_name":"Stockholms Universitet","ror":"https://ror.org/05f0yaq80"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7131347832.pdf","grobid_xml":"https://content.openalex.org/works/W7131347832.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W1499219562","https://openalex.org/W1551480811","https://openalex.org/W1981115560","https://openalex.org/W2003368653","https://openalex.org/W2050409837","https://openalex.org/W2164302731","https://openalex.org/W2171353752","https://openalex.org/W2552352299","https://openalex.org/W2560261741","https://openalex.org/W2591843631","https://openalex.org/W2886166777","https://openalex.org/W2947840872","https://openalex.org/W2962990378","https://openalex.org/W2981871387","https://openalex.org/W3003803858","https://openalex.org/W3010890826","https://openalex.org/W3092403430","https://openalex.org/W3128378954","https://openalex.org/W3131496751","https://openalex.org/W3134935986","https://openalex.org/W3157689902","https://openalex.org/W3179955115","https://openalex.org/W3187382410","https://openalex.org/W3201413149","https://openalex.org/W4254671851","https://openalex.org/W4289704156","https://openalex.org/W4360879534","https://openalex.org/W4385065129","https://openalex.org/W4386779630","https://openalex.org/W4388865084","https://openalex.org/W4400946990","https://openalex.org/W4402794138"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"We":[1,45,190],"consider":[2],"the":[3,29,96,100,104,128,132,145,157,160,164,177,192,197],"task":[4],"of":[5,8,28,37,98,103,127,149,159,196,204],"data-driven":[6],"identification":[7],"dynamical":[9],"systems,":[10],"specifically":[11],"for":[12],"systems":[13,69],"whose":[14],"behavior":[15,102],"at":[16],"large":[17],"frequencies":[18],"is":[19,76,114],"non-standard,":[20],"as":[21,41],"encoded":[22],"by":[23],"a":[24,34,38,42,83,137,150,169,202],"non-trivial":[25,35,71],"relative":[26,72,92,147],"degree":[27,93,113,148,158],"transfer":[30],"function":[31],"or,":[32],"alternatively,":[33],"index":[36],"corresponding":[39],"realization":[40],"descriptor":[43],"system.":[44],"develop":[46],"novel":[47],"surrogate":[48,88,110,170],"modeling":[49],"strategies":[50],"that":[51,140,162],"allow":[52],"state-of-the-art":[53],"rational":[54,87,129],"approximation":[55],"algorithms":[56],"(e.g.,":[57],"AAA":[58],"and":[59,194],"vector":[60],"fitting)":[61],"to":[62,85,143,175],"better":[63],"handle":[64],"data":[65,178],"coming":[66],"from":[67,152],"such":[68],"with":[70,90,95],"degree.":[73],"Our":[74],"contribution":[75],"twofold.":[77],"On":[78,131],"one":[79,142],"hand,":[80,134],"we":[81,135,166],"describe":[82],"strategy":[84],"build":[86,168],"models":[89],"prescribed":[91],",":[94],"objective":[97],"mirroring":[99],"high-frequency":[101],"high-fidelity":[105],"problem,":[106],"when":[107],"known.":[108],"The":[109],"model\u2019s":[111],"desired":[112],"achieved":[115],"through":[116,124,201],"constraints":[117],"on":[118],"its":[119],"barycentric":[120],"coefficients,":[121],"rather":[122],"than":[123],"ad-hoc":[125],"modifications":[126],"form.":[130],"other":[133],"present":[136],"degree-identification":[138],"routine":[139],"allows":[141],"estimate":[144],"unknown":[146],"system":[151,161],"low-frequency":[153],"data.":[154],"By":[155],"identifying":[156],"generated":[163],"data,":[165],"can":[167],"model":[171],"that,":[172],"in":[173],"addition":[174],"matching":[176],"well":[179],"(at":[180,187],"low":[181],"frequencies),":[182],"has":[183],"enhanced":[184],"extrapolation":[185],"capabilities":[186],"high":[188],"frequencies).":[189],"showcase":[191],"effectiveness":[193],"robustness":[195],"newly":[198],"proposed":[199],"method":[200],"suite":[203],"numerical":[205],"tests.":[206]},"counts_by_year":[],"updated_date":"2026-05-05T08:41:31.759640","created_date":"2026-02-25T00:00:00"}
