{"id":"https://openalex.org/W2341535875","doi":"https://doi.org/10.1137/16m1071493","title":"Dynamical Model Reduction Method for Solving Parameter-Dependent Dynamical Systems","display_name":"Dynamical Model Reduction Method for Solving Parameter-Dependent Dynamical Systems","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2341535875","doi":"https://doi.org/10.1137/16m1071493","mag":"2341535875"},"language":"en","primary_location":{"id":"doi:10.1137/16m1071493","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1071493","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1604.05706","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Marie Billaud-Friess","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marie Billaud-Friess","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Anthony Nouy","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Anthony Nouy","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":1.0041,"has_fulltext":true,"cited_by_count":27,"citation_normalized_percentile":{"value":0.73470381,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"39","issue":"4","first_page":"A1766","last_page":"A1792"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9976999759674072,"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":0.9976999759674072,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6888999938964844},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.629800021648407},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5623000264167786},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.5595999956130981},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5475000143051147},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.5389000177383423},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.5347999930381775},{"id":"https://openalex.org/keywords/model-order-reduction","display_name":"Model order reduction","score":0.531499981880188},{"id":"https://openalex.org/keywords/linear-dynamical-system","display_name":"Linear dynamical system","score":0.47920000553131104}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7493000030517578},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6888999938964844},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.629800021648407},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5623000264167786},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.5595999956130981},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5475000143051147},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5460000038146973},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.5389000177383423},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.5347999930381775},{"id":"https://openalex.org/C2779277453","wikidata":"https://www.wikidata.org/wiki/Q12202921","display_name":"Model order reduction","level":3,"score":0.531499981880188},{"id":"https://openalex.org/C114275822","wikidata":"https://www.wikidata.org/wiki/Q621512","display_name":"Linear dynamical system","level":3,"score":0.47920000553131104},{"id":"https://openalex.org/C93812963","wikidata":"https://www.wikidata.org/wiki/Q7249433","display_name":"Projected dynamical system","level":5,"score":0.391400009393692},{"id":"https://openalex.org/C193817511","wikidata":"https://www.wikidata.org/wiki/Q7291964","display_name":"Random dynamical system","level":4,"score":0.3718999922275543},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.3686999976634979},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3490999937057495},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3310000002384186},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.32670000195503235},{"id":"https://openalex.org/C51823790","wikidata":"https://www.wikidata.org/wiki/Q504353","display_name":"Greedy algorithm","level":2,"score":0.2955999970436096},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.290800005197525},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2806999981403351},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.2784000039100647},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.27300000190734863},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.2651999890804291},{"id":"https://openalex.org/C119247159","wikidata":"https://www.wikidata.org/wiki/Q1366192","display_name":"System identification","level":3,"score":0.2630999982357025},{"id":"https://openalex.org/C2776003309","wikidata":"https://www.wikidata.org/wiki/Q1988072","display_name":"Adaptive algorithm","level":2,"score":0.2596000134944916},{"id":"https://openalex.org/C2775918384","wikidata":"https://www.wikidata.org/wiki/Q4660961","display_name":"A priori estimate","level":2,"score":0.25780001282691956},{"id":"https://openalex.org/C19768560","wikidata":"https://www.wikidata.org/wiki/Q320727","display_name":"Dependency (UML)","level":2,"score":0.2558000087738037},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2547000050544739},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.25130000710487366}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/16m1071493","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1071493","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1604.05706","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1604.05706","pdf_url":"https://arxiv.org/pdf/1604.05706","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-01387231v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01387231","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"ISSN: 1064-8275","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1604.05706","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1604.05706","pdf_url":"https://arxiv.org/pdf/1604.05706","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322892","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1973359087","https://openalex.org/W1977681898","https://openalex.org/W2011121645","https://openalex.org/W2022264564","https://openalex.org/W2034840616","https://openalex.org/W2039055345","https://openalex.org/W2047591100","https://openalex.org/W2049753327","https://openalex.org/W2060200773","https://openalex.org/W2085335060","https://openalex.org/W2087257783","https://openalex.org/W2093049475","https://openalex.org/W2104225554","https://openalex.org/W2110917150","https://openalex.org/W2114235273","https://openalex.org/W2119334003","https://openalex.org/W2120433265","https://openalex.org/W2122080931","https://openalex.org/W2131771606","https://openalex.org/W2152279941","https://openalex.org/W2155257515","https://openalex.org/W2157928602","https://openalex.org/W2161797061"],"related_works":[],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2,51,56,71,78,101,107,113],"projection-based":[3],"model":[4,35],"order":[5],"reduction":[6],"method":[7,17,96,105],"for":[8,87],"the":[9,20,30,33,48,63,67,88,117,120],"solution":[10,31,49],"of":[11,22,29,32,50,66,91,110,116],"parameter-dependent":[12],"dynamical":[13,53,102],"systems.":[14],"The":[15,41,94],"proposed":[16,86],"relies":[18],"on":[19],"construction":[21],"time-dependent":[23],"reduced":[24,52,68],"spaces":[25],"generated":[26],"from":[27],"evaluations":[28],"full-order":[34],"at":[36],"some":[37],"selected":[38],"parameter":[39,92,121],"values.":[40,93],"approximation":[42,104],"obtained":[43],"by":[44],"Galerkin":[45],"projection":[46],"is":[47,75,85],"system":[54],"with":[55,106],"modified":[57],"flux":[58],"that":[59],"takes":[60],"into":[61],"account":[62],"time":[64],"dependency":[65],"spaces.":[69],"An":[70],"posteriori":[72],"error":[73,83,118],"estimate":[74,84],"derived,":[76],"and":[77,112],"greedy":[79],"algorithm":[80],"using":[81],"this":[82],"adaptive":[89],"selection":[90],"resulting":[95],"can":[97],"be":[98],"interpreted":[99],"as":[100],"low-rank":[103],"subspace":[108],"point":[109],"view":[111],"uniform":[114],"control":[115],"over":[119],"set.":[122]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2016-06-24T00:00:00"}
