{"id":"https://openalex.org/W7165662432","doi":"https://doi.org/10.48550/arxiv.2606.23077","title":"Non-intrusive nonlinear reduced-order modeling with variable projection","display_name":"Non-intrusive nonlinear reduced-order modeling with variable projection","publication_year":2026,"publication_date":"2026-06-22","ids":{"openalex":"https://openalex.org/W7165662432","doi":"https://doi.org/10.48550/arxiv.2606.23077"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.23077","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.23077","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.23077","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5116425078","display_name":"Dimitrios Xylogiannis","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xylogiannis, Dimitrios","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087553375","display_name":"Charles Poussot-Vassal","orcid":"https://orcid.org/0000-0001-9106-1893"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Poussot-Vassal, Charles","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5111424010","display_name":"Claire Sarrat","orcid":"https://orcid.org/0000-0002-3318-805X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sarrat, Claire","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.5939000248908997,"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":0.5939000248908997,"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":0.3370000123977661,"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":0.022099999710917473,"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/nonlinear-system","display_name":"Nonlinear system","score":0.7235999703407288},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.7067999839782715},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5681999921798706},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.5623999834060669},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5148000121116638},{"id":"https://openalex.org/keywords/state-variable","display_name":"State variable","score":0.4311999976634979},{"id":"https://openalex.org/keywords/projection-method","display_name":"Projection method","score":0.4068000018596649},{"id":"https://openalex.org/keywords/system-identification","display_name":"System identification","score":0.37220001220703125},{"id":"https://openalex.org/keywords/identification","display_name":"Identification (biology)","score":0.3508000075817108}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7235999703407288},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.7067999839782715},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5702999830245972},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5681999921798706},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.5623999834060669},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5148000121116638},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4438000023365021},{"id":"https://openalex.org/C129537906","wikidata":"https://www.wikidata.org/wiki/Q7603913","display_name":"State variable","level":2,"score":0.4311999976634979},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42329999804496765},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4131999909877777},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.4068000018596649},{"id":"https://openalex.org/C119247159","wikidata":"https://www.wikidata.org/wiki/Q1366192","display_name":"System identification","level":3,"score":0.37220001220703125},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.3508000075817108},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.3422999978065491},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3327000141143799},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.3215000033378601},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3197999894618988},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.3197000026702881},{"id":"https://openalex.org/C22157029","wikidata":"https://www.wikidata.org/wiki/Q17080460","display_name":"Nonlinear system identification","level":4,"score":0.3190000057220459},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.31619998812675476},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.31130000948905945},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.3091000020503998},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.3010999858379364},{"id":"https://openalex.org/C169272836","wikidata":"https://www.wikidata.org/wiki/Q5668307","display_name":"Variable elimination","level":3,"score":0.28999999165534973},{"id":"https://openalex.org/C162144332","wikidata":"https://www.wikidata.org/wiki/Q1665305","display_name":"Instrumental variable","level":2,"score":0.2784000039100647},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.2720000147819519},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.2639000117778778},{"id":"https://openalex.org/C202426404","wikidata":"https://www.wikidata.org/wiki/Q5318686","display_name":"Dykstra's projection algorithm","level":2,"score":0.25999999046325684},{"id":"https://openalex.org/C55660270","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization","level":2,"score":0.2551000118255615}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.23077","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.23077","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.23077","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.23077","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"work":[1,179],"presents":[2],"a":[3,72,96,128],"method":[4,87,123],"for":[5,90,175],"constructing":[6],"nonlinear":[7,33,81,155],"reduced-order":[8],"models":[9,35],"from":[10,153],"input-output":[11],"time-domain":[12],"data.":[13],"The":[14,122],"proposed":[15,171],"approach,":[16],"termed":[17],"Mixed":[18],"Interpolatory":[19],"Inference":[20],"with":[21,92,146],"Variable":[22,46],"Projection":[23,47],"(MIIvp),":[24],"exploits":[25],"the":[26,29,39,45,50,55,61,74,80,86,115,139,154,164,167,170],"fact":[27],"that":[28,111],"considered":[30],"class":[31],"of":[32,169],"state-space":[34],"is":[36,52,109,124,143],"linear":[37,68],"in":[38],"output":[40,62,75],"equation":[41,57,63],"parameters.":[42],"By":[43],"applying":[44],"(VarPro)":[48],"algorithm,":[49],"optimization":[51,82],"restricted":[53],"to":[54,120],"state":[56],"parameters":[58,64,118],"alone,":[59],"while":[60],"are":[65,180],"recovered":[66],"via":[67],"least":[69],"squares.":[70],"As":[71],"consequence,":[73],"dimension":[76],"does":[77],"not":[78],"enter":[79],"parameter":[83],"vector,":[84],"making":[85],"well":[88],"suited":[89],"systems":[91],"very":[93],"high-dimensional":[94],"outputs,":[95],"setting":[97],"where":[98,132],"many":[99],"other":[100],"approaches":[101],"become":[102],"computationally":[103],"prohibitive.":[104],"Under":[105],"mild":[106],"assumptions,":[107],"it":[108,133],"shown":[110],"MIIvp":[112,142],"can":[113],"recover":[114],"true":[116,140],"model":[117],"up":[119],"similarity.":[121],"first":[125],"validated":[126],"on":[127,149],"synthetic":[129],"bilinear":[130],"system,":[131],"achieves":[134],"machine-precision":[135],"accuracy":[136],"and":[137,166,177],"recovers":[138],"eigenvalues.":[141],"then":[144],"compared":[145],"existing":[147],"methods":[148],"two":[150],"experimental":[151],"benchmarks":[152],"system":[156],"identification":[157],"literature.":[158],"These":[159],"numerical":[160],"experiments":[161],"showcase":[162],"both":[163],"validity":[165],"limitations":[168],"approach.":[172],"Finally,":[173],"directions":[174],"improvements":[176],"future":[178],"outlined.":[181]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-24T00:00:00"}
