{"id":"https://openalex.org/W1985692767","doi":"https://doi.org/10.1109/acc.2014.6859175","title":"A tensor decomposition approach to high dimensional stationary Fokker-Planck equations","display_name":"A tensor decomposition approach to high dimensional stationary Fokker-Planck equations","publication_year":2014,"publication_date":"2014-06-01","ids":{"openalex":"https://openalex.org/W1985692767","doi":"https://doi.org/10.1109/acc.2014.6859175","mag":"1985692767"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2014.6859175","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2014.6859175","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2014 American Control Conference","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101937400","display_name":"Yifei Sun","orcid":"https://orcid.org/0000-0003-4154-7910"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yifei Sun","raw_affiliation_strings":["University of Florida, Gainesville, FL, US","[Dept. of Mech. & Aerosp. Eng., Univ. of Florida, Gainesville, FL, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Florida, Gainesville, FL, US","institution_ids":["https://openalex.org/I33213144"]},{"raw_affiliation_string":"[Dept. of Mech. & Aerosp. Eng., Univ. of Florida, Gainesville, FL, USA]","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073597636","display_name":"Mrinal Kumar","orcid":"https://orcid.org/0000-0001-9747-9449"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mrinal Kumar","raw_affiliation_strings":["University of Florida, Gainesville, FL, US","[Dept. of Mech. & Aerosp. Eng., Univ. of Florida, Gainesville, FL, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Florida, Gainesville, FL, US","institution_ids":["https://openalex.org/I33213144"]},{"raw_affiliation_string":"[Dept. of Mech. & Aerosp. Eng., Univ. of Florida, Gainesville, FL, USA]","institution_ids":["https://openalex.org/I33213144"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9374,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.71855011,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"4500","last_page":"4505"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/T12303","display_name":"Tensor decomposition and applications","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":0.9653000235557556,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9380999803543091,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.6400780081748962},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.597206711769104},{"id":"https://openalex.org/keywords/planck","display_name":"Planck","score":0.5619802474975586},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.5389905571937561},{"id":"https://openalex.org/keywords/degrees-of-freedom","display_name":"Degrees of freedom (physics and chemistry)","score":0.5328721404075623},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5324963331222534},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5251455307006836},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4892539978027344},{"id":"https://openalex.org/keywords/fokker\u2013planck-equation","display_name":"Fokker\u2013Planck equation","score":0.4884747564792633},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.4327845573425293},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3517608940601349},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33660784363746643},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3342553377151489},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.2826215624809265},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27018433809280396},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.12676721811294556},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11685776710510254}],"concepts":[{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.6400780081748962},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.597206711769104},{"id":"https://openalex.org/C166126730","wikidata":"https://www.wikidata.org/wiki/Q725309","display_name":"Planck","level":2,"score":0.5619802474975586},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5389905571937561},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.5328721404075623},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5324963331222534},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5251455307006836},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4892539978027344},{"id":"https://openalex.org/C69123182","wikidata":"https://www.wikidata.org/wiki/Q891766","display_name":"Fokker\u2013Planck equation","level":3,"score":0.4884747564792633},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.4327845573425293},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3517608940601349},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33660784363746643},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3342553377151489},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2826215624809265},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27018433809280396},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.12676721811294556},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11685776710510254},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2014.6859175","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2014.6859175","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2014 American Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.8299999833106995}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1490180844","https://openalex.org/W1504748373","https://openalex.org/W1805381866","https://openalex.org/W1964200011","https://openalex.org/W1967077133","https://openalex.org/W1989786408","https://openalex.org/W2000168014","https://openalex.org/W2000215628","https://openalex.org/W2010868646","https://openalex.org/W2024165284","https://openalex.org/W2024200924","https://openalex.org/W2025603201","https://openalex.org/W2044777402","https://openalex.org/W2057577185","https://openalex.org/W2060662954","https://openalex.org/W2063997360","https://openalex.org/W2073469810","https://openalex.org/W2079407403","https://openalex.org/W2080467174","https://openalex.org/W2121739212","https://openalex.org/W2125246840","https://openalex.org/W2154998879","https://openalex.org/W2341171179","https://openalex.org/W2597279391","https://openalex.org/W6656109976","https://openalex.org/W6735173822"],"related_works":["https://openalex.org/W1995622179","https://openalex.org/W1484111231","https://openalex.org/W1552543208","https://openalex.org/W1977095816","https://openalex.org/W2074396517","https://openalex.org/W2166963679","https://openalex.org/W2187269125","https://openalex.org/W1641615907","https://openalex.org/W3089231081","https://openalex.org/W2093956241"],"abstract_inverted_index":{"This":[0],"paper":[1],"addresses":[2],"the":[3,8,20,25,30,39,52,60,65,66,70,98,101],"curse":[4],"of":[5,11,27,29,51,64,69,81,83,100],"dimensionality":[6,90],"in":[7,33],"numerical":[9],"solution":[10],"stationary":[12],"Fokker-Planck":[13,72],"equations.":[14],"Combined":[15],"with":[16],"Chebyshev":[17],"spectral":[18],"differentiation,":[19],"tensor":[21],"approach":[22],"significantly":[23],"reduces":[24],"degrees":[26,82],"freedom":[28,84],"approximation":[31],"essentially":[32],"exchange":[34],"for":[35,62],"nonlinearity,":[36],"such":[37],"that":[38],"resulting":[40],"discretized":[41,71],"nonlinear":[42],"system":[43],"is":[44],"solved":[45],"by":[46],"alternating":[47],"least":[48],"squares.":[49],"Enforcement":[50],"normality":[53],"condition":[54],"via":[55],"a":[56,78],"penalty":[57],"method":[58,76],"avoids":[59],"need":[61],"exploration":[63],"null":[67],"space":[68],"operator.":[73],"The":[74],"proposed":[75,102],"enables":[77],"drastic":[79],"reduction":[80],"required":[85],"to":[86,96],"maintain":[87],"accuracy":[88],"as":[89],"increases.":[91],"Numerical":[92],"results":[93],"are":[94],"presented":[95],"illustrate":[97],"effectiveness":[99],"method.":[103]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}