{"id":"https://openalex.org/W3012617434","doi":"https://doi.org/10.1515/jnma-2020-0098","title":"POD-Galerkin model order reduction for parametrized nonlinear time-dependent optimal flow control: an application to shallow water equations","display_name":"POD-Galerkin model order reduction for parametrized nonlinear time-dependent optimal flow control: an application to shallow water equations","publication_year":2021,"publication_date":"2021-11-11","ids":{"openalex":"https://openalex.org/W3012617434","doi":"https://doi.org/10.1515/jnma-2020-0098","mag":"3012617434"},"language":"en","primary_location":{"id":"doi:10.1515/jnma-2020-0098","is_oa":false,"landing_page_url":"https://doi.org/10.1515/jnma-2020-0098","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical Mathematics","raw_type":"journal-article"},"type":"preprint","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2003.09695.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085926069","display_name":"Maria Strazzullo","orcid":"https://orcid.org/0000-0003-1245-271X"},"institutions":[{"id":"https://openalex.org/I138549579","display_name":"Scuola Internazionale Superiore di Studi Avanzati","ror":"https://ror.org/004fze387","country_code":"IT","type":"education","lineage":["https://openalex.org/I138549579"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Maria Strazzullo","raw_affiliation_strings":["mathlab, Mathematics Area, International School for Advanced Studies (SISSA) , Trieste , Italy","International School for Advanced Studies"],"affiliations":[{"raw_affiliation_string":"mathlab, Mathematics Area, International School for Advanced Studies (SISSA) , Trieste , Italy","institution_ids":["https://openalex.org/I138549579"]},{"raw_affiliation_string":"International School for Advanced Studies","institution_ids":["https://openalex.org/I138549579"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049081029","display_name":"Francesco Ballarin","orcid":"https://orcid.org/0000-0001-6460-3538"},"institutions":[{"id":"https://openalex.org/I138549579","display_name":"Scuola Internazionale Superiore di Studi Avanzati","ror":"https://ror.org/004fze387","country_code":"IT","type":"education","lineage":["https://openalex.org/I138549579"]},{"id":"https://openalex.org/I103320735","display_name":"Universit\u00e0 Cattolica del Sacro Cuore","ror":"https://ror.org/03h7r5v07","country_code":"IT","type":"education","lineage":["https://openalex.org/I103320735"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Francesco Ballarin","raw_affiliation_strings":["Department of Mathematics and Physics, Catholic University of the Sacred Heart , Brescia , Italy","mathlab, Mathematics Area, International School for Advanced Studies (SISSA) , Trieste , Italy","International School for Advanced Studies"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Physics, Catholic University of the Sacred Heart , Brescia , Italy","institution_ids":["https://openalex.org/I103320735"]},{"raw_affiliation_string":"mathlab, Mathematics Area, International School for Advanced Studies (SISSA) , Trieste , Italy","institution_ids":["https://openalex.org/I138549579"]},{"raw_affiliation_string":"International School for Advanced Studies","institution_ids":["https://openalex.org/I138549579"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061558433","display_name":"Gianluigi Rozza","orcid":"https://orcid.org/0000-0002-0810-8812"},"institutions":[{"id":"https://openalex.org/I138549579","display_name":"Scuola Internazionale Superiore di Studi Avanzati","ror":"https://ror.org/004fze387","country_code":"IT","type":"education","lineage":["https://openalex.org/I138549579"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Gianluigi Rozza","raw_affiliation_strings":["mathlab, Mathematics Area, International School for Advanced Studies (SISSA) , Trieste , Italy","International School for Advanced Studies"],"affiliations":[{"raw_affiliation_string":"mathlab, Mathematics Area, International School for Advanced Studies (SISSA) , Trieste , Italy","institution_ids":["https://openalex.org/I138549579"]},{"raw_affiliation_string":"International School for Advanced Studies","institution_ids":["https://openalex.org/I138549579"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5061558433"],"corresponding_institution_ids":["https://openalex.org/I138549579"],"apc_list":null,"apc_paid":null,"fwci":0.68015438,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.66071253,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"30","issue":"1","first_page":"63","last_page":"84"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998999834060669,"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":0.9998999834060669,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9986000061035156,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.8045271635055542},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7130914926528931},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.681129515171051},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6674184799194336},{"id":"https://openalex.org/keywords/shallow-water-equations","display_name":"Shallow water equations","score":0.6243771910667419},{"id":"https://openalex.org/keywords/model-order-reduction","display_name":"Model order reduction","score":0.5501132011413574},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5101364254951477},{"id":"https://openalex.org/keywords/tracking","display_name":"Tracking (education)","score":0.4673246443271637},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4664112329483032},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4662700295448303},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.4463464617729187},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.44008103013038635},{"id":"https://openalex.org/keywords/point-of-delivery","display_name":"Point of delivery","score":0.42580318450927734},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41104623675346375},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3854679763317108},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3794410526752472},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.36230552196502686},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.1884261667728424},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14204514026641846},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1087365448474884},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.1012326180934906},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06966981291770935},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06251579523086548}],"concepts":[{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.8045271635055542},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7130914926528931},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.681129515171051},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6674184799194336},{"id":"https://openalex.org/C140295346","wikidata":"https://www.wikidata.org/wiki/Q4008384","display_name":"Shallow water equations","level":2,"score":0.6243771910667419},{"id":"https://openalex.org/C2779277453","wikidata":"https://www.wikidata.org/wiki/Q12202921","display_name":"Model order reduction","level":3,"score":0.5501132011413574},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5101364254951477},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.4673246443271637},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4664112329483032},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4662700295448303},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4463464617729187},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.44008103013038635},{"id":"https://openalex.org/C137776501","wikidata":"https://www.wikidata.org/wiki/Q7208270","display_name":"Point of delivery","level":2,"score":0.42580318450927734},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41104623675346375},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3854679763317108},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3794410526752472},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.36230552196502686},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.1884261667728424},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14204514026641846},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1087365448474884},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.1012326180934906},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06966981291770935},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06251579523086548},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"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/C19417346","wikidata":"https://www.wikidata.org/wiki/Q7922","display_name":"Pedagogy","level":1,"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/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1515/jnma-2020-0098","is_oa":false,"landing_page_url":"https://doi.org/10.1515/jnma-2020-0098","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical Mathematics","raw_type":"journal-article"},{"id":"mag:3012617434","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2003.09695.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2003.09695","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2003.09695","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":"article-journal"}],"best_oa_location":{"id":"mag:3012617434","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2003.09695.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/14","score":0.8700000047683716,"display_name":"Life below water"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":77,"referenced_works":["https://openalex.org/W73123583","https://openalex.org/W178390345","https://openalex.org/W592911714","https://openalex.org/W611772791","https://openalex.org/W1509146450","https://openalex.org/W1523222099","https://openalex.org/W1555557982","https://openalex.org/W1596034966","https://openalex.org/W1596195796","https://openalex.org/W1600371943","https://openalex.org/W1604333309","https://openalex.org/W1708679080","https://openalex.org/W1735823337","https://openalex.org/W1792403156","https://openalex.org/W1820125862","https://openalex.org/W1897434927","https://openalex.org/W1927826268","https://openalex.org/W1964249720","https://openalex.org/W1978399516","https://openalex.org/W1983036154","https://openalex.org/W1995289934","https://openalex.org/W2005586154","https://openalex.org/W2007951274","https://openalex.org/W2010619938","https://openalex.org/W2012386000","https://openalex.org/W2015148405","https://openalex.org/W2038695002","https://openalex.org/W2045627558","https://openalex.org/W2047591100","https://openalex.org/W2052690618","https://openalex.org/W2070576468","https://openalex.org/W2075064535","https://openalex.org/W2088638050","https://openalex.org/W2093049475","https://openalex.org/W2096345667","https://openalex.org/W2097150043","https://openalex.org/W2097652335","https://openalex.org/W2098343517","https://openalex.org/W2102753028","https://openalex.org/W2103226631","https://openalex.org/W2114235273","https://openalex.org/W2115291951","https://openalex.org/W2122166233","https://openalex.org/W2128702576","https://openalex.org/W2130499633","https://openalex.org/W2131341924","https://openalex.org/W2131595610","https://openalex.org/W2133041109","https://openalex.org/W2140820418","https://openalex.org/W2141870784","https://openalex.org/W2143724684","https://openalex.org/W2145280251","https://openalex.org/W2148094730","https://openalex.org/W2148759576","https://openalex.org/W2152609732","https://openalex.org/W2159840341","https://openalex.org/W2160413789","https://openalex.org/W2244435620","https://openalex.org/W2254664843","https://openalex.org/W2333109051","https://openalex.org/W2333801887","https://openalex.org/W2340065481","https://openalex.org/W2488897645","https://openalex.org/W2494836731","https://openalex.org/W2561770886","https://openalex.org/W2752626032","https://openalex.org/W2963340469","https://openalex.org/W2996420704","https://openalex.org/W3004113558","https://openalex.org/W3029273935","https://openalex.org/W3033721662","https://openalex.org/W3093747345","https://openalex.org/W3165126898","https://openalex.org/W3209174574","https://openalex.org/W4245654886","https://openalex.org/W4246432471","https://openalex.org/W6601103585"],"related_works":["https://openalex.org/W3211378307","https://openalex.org/W3210728045","https://openalex.org/W2974791629","https://openalex.org/W3000293971","https://openalex.org/W2287455428","https://openalex.org/W2996420704","https://openalex.org/W2133041109","https://openalex.org/W2010334931","https://openalex.org/W3027732438","https://openalex.org/W108355476","https://openalex.org/W2996964001","https://openalex.org/W2245418780","https://openalex.org/W2486801753","https://openalex.org/W2016276456","https://openalex.org/W3038064391","https://openalex.org/W1558506802","https://openalex.org/W2754720210","https://openalex.org/W2949257877","https://openalex.org/W2129670964","https://openalex.org/W1516829775"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"the":[2,85,98,133,144,152],"present":[3],"paper":[4],"we":[5,35,88],"propose":[6],"reduced":[7,68,106,134],"order":[8,69,95],"methods":[9],"as":[10],"a":[11,27,56,80,91,103,130],"reliable":[12],"strategy":[13],"to":[14,45,65,96,115],"efficiently":[15],"solve":[16,97],"parametrized":[17,33],"optimal":[18,99,120,135],"control":[19,100,121,136],"problems":[20],"governed":[21,138],"by":[22,139],"shallow":[23,140],"waters":[24,141],"equations":[25,142],"in":[26,55,73,79,94,102],"solution":[28],"tracking":[29],"setting.":[30],"The":[31,108,123],"physical":[32],"model":[34],"deal":[36],"with":[37,129],"is":[38,64,112,126],"nonlinear":[39,117],"and":[40,77,147],"time":[41,47,118],"dependent:":[42],"this":[43],"leads":[44],"very":[46],"consuming":[48],"simulations":[49],"which":[50],"can":[51],"be":[52],"unbearable,":[53],"e.g.,":[54],"marine":[57],"environmental":[58],"monitoring":[59],"plan":[60],"application.":[61],"Our":[62],"aim":[63],"show":[66],"how":[67],"modelling":[70],"could":[71],"help":[72],"studying":[74],"different":[75],"configurations":[76],"phenomena":[78],"fast":[81],"way.":[82],"After":[83],"building":[84],"optimality":[86],"system,":[87],"rely":[89],"on":[90],"POD-Galerkin":[92],"reduction":[93],"problem":[101,137],"low":[104],"dimensional":[105],"space.":[107],"presented":[109],"theoretical":[110],"framework":[111],"actually":[113],"suited":[114],"general":[116],"dependent":[119],"problems.":[122],"proposed":[124],"methodology":[125],"finally":[127],"tested":[128],"numerical":[131],"experiment:":[132],"reproduces":[143],"desired":[145],"velocity":[146],"height":[148],"profiles":[149],"faster":[150],"than":[151],"standard":[153],"model,":[154],"still":[155],"remaining":[156],"accurate.":[157]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
