{"id":"https://openalex.org/W2958519735","doi":"https://doi.org/10.1137/20m1313106","title":"A Reduced Order Modeling Technique to Study Bifurcating Phenomena: Application to the Gross--Pitaevskii Equation","display_name":"A Reduced Order Modeling Technique to Study Bifurcating Phenomena: Application to the Gross--Pitaevskii Equation","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2958519735","doi":"https://doi.org/10.1137/20m1313106","mag":"2958519735"},"language":"en","primary_location":{"id":"doi:10.1137/20m1313106","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1313106","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","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1907.07082","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067097015","display_name":"Federico Pichi","orcid":"https://orcid.org/0000-0002-1163-3386"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Federico Pichi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000102598","display_name":"Annalisa Quaini","orcid":"https://orcid.org/0000-0001-9686-9058"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Annalisa Quaini","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-9686-9058","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5061558433","display_name":"Gianluigi Rozza","orcid":"https://orcid.org/0000-0002-0810-8812"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gianluigi Rozza","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-0810-8812","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2737,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.42995295,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"42","issue":"5","first_page":"B1115","last_page":"B1135"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9894999861717224,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9894999861717224,"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"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9887999892234802,"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/T11575","display_name":"Nonlinear Photonic Systems","score":0.986299991607666,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/continuation","display_name":"Continuation","score":0.750650942325592},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.6855605840682983},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6839967370033264},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.6653986573219299},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6485941410064697},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6162942051887512},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.5757051706314087},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.5526149272918701},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.529074490070343},{"id":"https://openalex.org/keywords/diagram","display_name":"Diagram","score":0.4481639862060547},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.4332959055900574},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4235967993736267},{"id":"https://openalex.org/keywords/gross\u2013pitaevskii-equation","display_name":"Gross\u2013Pitaevskii equation","score":0.4166290760040283},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3861549496650696},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23751702904701233},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12556588649749756},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11014792323112488}],"concepts":[{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.750650942325592},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6855605840682983},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6839967370033264},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.6653986573219299},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6485941410064697},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6162942051887512},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.5757051706314087},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.5526149272918701},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.529074490070343},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.4481639862060547},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.4332959055900574},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4235967993736267},{"id":"https://openalex.org/C2776902821","wikidata":"https://www.wikidata.org/wiki/Q910667","display_name":"Gross\u2013Pitaevskii equation","level":3,"score":0.4166290760040283},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3861549496650696},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23751702904701233},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12556588649749756},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11014792323112488},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/20m1313106","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1313106","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:1907.07082","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1907.07082","pdf_url":"https://arxiv.org/pdf/1907.07082","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"mag:2958519735","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1907.07082.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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.1907.07082","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1907.07082","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"pmh:oai:arXiv.org:1907.07082","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1907.07082","pdf_url":"https://arxiv.org/pdf/1907.07082","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":[{"id":"https://openalex.org/G3440810358","display_name":null,"funder_award_id":"DMS-1620384","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3672363659","display_name":"Advanced Reduced Order Methods with Applications in Computational Fluid Dynamics","funder_award_id":"681447","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"},{"id":"https://openalex.org/G450780426","display_name":null,"funder_award_id":"DMS-1953535","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320332999","display_name":"Horizon 2020 Framework Programme","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2958519735.pdf","grobid_xml":"https://content.openalex.org/works/W2958519735.grobid-xml"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W73123583","https://openalex.org/W333643410","https://openalex.org/W825718113","https://openalex.org/W1554696454","https://openalex.org/W1607862333","https://openalex.org/W1975041367","https://openalex.org/W1997425251","https://openalex.org/W2004510429","https://openalex.org/W2012143101","https://openalex.org/W2025040617","https://openalex.org/W2027551883","https://openalex.org/W2041321164","https://openalex.org/W2043097539","https://openalex.org/W2047591100","https://openalex.org/W2049753327","https://openalex.org/W2050651297","https://openalex.org/W2050785320","https://openalex.org/W2052690618","https://openalex.org/W2052938973","https://openalex.org/W2093525403","https://openalex.org/W2097808322","https://openalex.org/W2122674116","https://openalex.org/W2133041109","https://openalex.org/W2164505969","https://openalex.org/W2212370034","https://openalex.org/W2291876840","https://openalex.org/W2295099209","https://openalex.org/W2563402977","https://openalex.org/W2605025295","https://openalex.org/W2612569362","https://openalex.org/W2884367278","https://openalex.org/W2909966777","https://openalex.org/W2963232429","https://openalex.org/W2963307204","https://openalex.org/W2963713697","https://openalex.org/W3011524864","https://openalex.org/W3102272456","https://openalex.org/W3103065173","https://openalex.org/W3103442356","https://openalex.org/W3114610601"],"related_works":["https://openalex.org/W3103832480","https://openalex.org/W2981885498","https://openalex.org/W3087439622","https://openalex.org/W2582528562","https://openalex.org/W3137036857","https://openalex.org/W2263246755","https://openalex.org/W3035680717","https://openalex.org/W2061648414","https://openalex.org/W2189622796","https://openalex.org/W3205470423","https://openalex.org/W3124001662","https://openalex.org/W3184099360","https://openalex.org/W1590465541","https://openalex.org/W1650427170","https://openalex.org/W2163451285","https://openalex.org/W2963006454","https://openalex.org/W2060235470","https://openalex.org/W2744720674","https://openalex.org/W2059515224","https://openalex.org/W2625059883"],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2,31,39,64,71,80,98,129,133],"computationally":[3],"efficient":[4],"framework":[5],"to":[6,55],"treat":[7],"nonlinear":[8,41,99],"partial":[9],"differential":[10],"equations":[11],"having":[12],"bifurcating":[13],"solutions":[14,37],"as":[15,106],"one":[16,107],"or":[17,108],"more":[18],"physical":[19,110],"control":[20],"parameters":[21,111],"are":[22,112],"varied.":[23,113],"Our":[24],"focus":[25],"is":[26,123],"on":[27],"steady":[28,94],"bifurcations.":[29],"Plotting":[30],"bifurcation":[32,130],"diagram":[33,131],"entails":[34],"computing":[35],"multiple":[36],"of":[38,50,87,97],"parametrized,":[40],"problem,":[42],"which":[43],"can":[44],"be":[45],"extremely":[46],"expensive":[47],"in":[48,127],"terms":[49],"computational":[51,59],"time.":[52],"In":[53,114],"order":[54,73,136],"reduce":[56],"these":[57],"demanding":[58],"costs,":[60],"our":[61,88,121],"approach":[62,122],"combines":[63],"continuation":[65],"technique":[66],"and":[67],"Newton's":[68],"method":[69],"with":[70,79],"reduced":[72],"modeling":[74],"(ROM)":[75],"technique,":[76],"suitably":[77],"supplemented":[78],"hyperreduction":[81],"method.":[82,137],"To":[83],"demonstrate":[84],"the":[85,93,103,115],"effectiveness":[86],"ROM":[89],"approach,":[90],"we":[91,118],"trace":[92],"solution":[95],"branches":[96],"Schr\u00f6dinger":[100],"equation,":[101,105],"called":[102],"Gross--Pitaevskii":[104],"two":[109],"two-parameter":[116],"study,":[117],"show":[119],"that":[120],"60":[124],"times":[125],"faster":[126],"constructing":[128],"than":[132],"standard":[134],"full":[135]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}
