{"id":"https://openalex.org/W3092417881","doi":"https://doi.org/10.1137/20m1372500","title":"Approximative Policy Iteration for Exit Time Feedback Control Problems Driven by Stochastic Differential Equations using Tensor Train Format","display_name":"Approximative Policy Iteration for Exit Time Feedback Control Problems Driven by Stochastic Differential Equations using Tensor Train Format","publication_year":2022,"publication_date":"2022-03-01","ids":{"openalex":"https://openalex.org/W3092417881","doi":"https://doi.org/10.1137/20m1372500","mag":"3092417881"},"language":"en","primary_location":{"id":"doi:10.1137/20m1372500","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1372500","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling & Simulation","raw_type":"journal-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/A5040304386","display_name":"Konstantin Fackeldey","orcid":"https://orcid.org/0000-0002-4373-3672"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Konstantin Fackeldey","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-4373-3672","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070098945","display_name":"Mathias Oster","orcid":"https://orcid.org/0000-0001-6603-7883"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mathias Oster","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014942878","display_name":"Leon Sallandt","orcid":"https://orcid.org/0000-0002-7102-7767"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Leon Sallandt","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-7102-7767","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5102878006","display_name":"Reinhold Schneider","orcid":"https://orcid.org/0000-0003-0529-7467"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Reinhold Schneider","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-0529-7467","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8304,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.846791,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":98},"biblio":{"volume":"20","issue":"1","first_page":"379","last_page":"403"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9988999962806702,"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":0.9988999962806702,"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/T12303","display_name":"Tensor decomposition and applications","score":0.9980000257492065,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ansatz","display_name":"Ansatz","score":0.9015039205551147},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.658613920211792},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.586718738079071},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.5523098111152649},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5342895984649658},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.46807894110679626},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.4613485634326935},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.44402486085891724},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4417303800582886},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.44019123911857605},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23086947202682495}],"concepts":[{"id":"https://openalex.org/C130979935","wikidata":"https://www.wikidata.org/wiki/Q568954","display_name":"Ansatz","level":2,"score":0.9015039205551147},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.658613920211792},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.586718738079071},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5523098111152649},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5342895984649658},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.46807894110679626},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.4613485634326935},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.44402486085891724},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4417303800582886},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.44019123911857605},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23086947202682495},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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:10.1137/20m1372500","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1372500","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling & Simulation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":94,"referenced_works":["https://openalex.org/W50417968","https://openalex.org/W79554687","https://openalex.org/W194482449","https://openalex.org/W234899517","https://openalex.org/W587977125","https://openalex.org/W1487586009","https://openalex.org/W1542004730","https://openalex.org/W1560724230","https://openalex.org/W1575104486","https://openalex.org/W1690544311","https://openalex.org/W1698155719","https://openalex.org/W1802196594","https://openalex.org/W1974854353","https://openalex.org/W1980822517","https://openalex.org/W1984414107","https://openalex.org/W1989786408","https://openalex.org/W1993482030","https://openalex.org/W1995406764","https://openalex.org/W1997054581","https://openalex.org/W1997312835","https://openalex.org/W2005448420","https://openalex.org/W2006690173","https://openalex.org/W2007734734","https://openalex.org/W2021092589","https://openalex.org/W2022794769","https://openalex.org/W2022829242","https://openalex.org/W2026787390","https://openalex.org/W2028145673","https://openalex.org/W2031216664","https://openalex.org/W2036133196","https://openalex.org/W2046290306","https://openalex.org/W2047278710","https://openalex.org/W2066083439","https://openalex.org/W2068168851","https://openalex.org/W2074185358","https://openalex.org/W2074388175","https://openalex.org/W2098432798","https://openalex.org/W2100571430","https://openalex.org/W2109416652","https://openalex.org/W2124477018","https://openalex.org/W2127061658","https://openalex.org/W2128089417","https://openalex.org/W2135512293","https://openalex.org/W2137522587","https://openalex.org/W2146292423","https://openalex.org/W2168071446","https://openalex.org/W2170316986","https://openalex.org/W2187194588","https://openalex.org/W2228567937","https://openalex.org/W2264072961","https://openalex.org/W2323824333","https://openalex.org/W2328013571","https://openalex.org/W2341171179","https://openalex.org/W2343408237","https://openalex.org/W2489279134","https://openalex.org/W2498807917","https://openalex.org/W2515829451","https://openalex.org/W2519527018","https://openalex.org/W2551937961","https://openalex.org/W2557283755","https://openalex.org/W2595442784","https://openalex.org/W2612326543","https://openalex.org/W2613664588","https://openalex.org/W2749408143","https://openalex.org/W2766347619","https://openalex.org/W2767333586","https://openalex.org/W2767784613","https://openalex.org/W2771020255","https://openalex.org/W2793097553","https://openalex.org/W2803629276","https://openalex.org/W2805915852","https://openalex.org/W2895471748","https://openalex.org/W2899283552","https://openalex.org/W2904727539","https://openalex.org/W2913860142","https://openalex.org/W2953807250","https://openalex.org/W2962782763","https://openalex.org/W2965381950","https://openalex.org/W2980125990","https://openalex.org/W2986878057","https://openalex.org/W3025010137","https://openalex.org/W3038118776","https://openalex.org/W3098898877","https://openalex.org/W3099267538","https://openalex.org/W3103239355","https://openalex.org/W3103737926","https://openalex.org/W3104914132","https://openalex.org/W3105822863","https://openalex.org/W3105898488","https://openalex.org/W3125896160","https://openalex.org/W3132715927","https://openalex.org/W4255975175","https://openalex.org/W4300004105","https://openalex.org/W4301018487"],"related_works":["https://openalex.org/W2089909466","https://openalex.org/W2986094430","https://openalex.org/W3208000705","https://openalex.org/W2089799198","https://openalex.org/W2126034343","https://openalex.org/W3193597985","https://openalex.org/W2460950183","https://openalex.org/W3114815494","https://openalex.org/W4287549300","https://openalex.org/W2308319479"],"abstract_inverted_index":{"We":[0,51],"consider":[1],"a":[2,22,27,70,90,94],"stochastic":[3,96],"optimal":[4],"exit":[5],"time":[6],"feedback":[7],"control":[8],"problem.":[9,59],"The":[10,60],"Bellman":[11],"equation":[12],"is":[13,67,76],"solved":[14],"approximatively":[15],"via":[16,69,78],"the":[17,38,43,64,74,86],"Policy":[18,65],"Iteration":[19,66],"algorithm":[20],"on":[21],"polynomial":[23],"ansatz":[24,72],"space":[25],"by":[26],"sequence":[28],"of":[29,45],"linear":[30],"equations.":[31],"As":[32],"high":[33],"degree":[34],"multipolynomials":[35],"are":[36,83],"needed,":[37],"corresponding":[39],"equations":[40],"suffer":[41],"from":[42],"curse":[44],"dimensionality":[46],"even":[47],"in":[48],"moderate":[49],"dimensions.":[50],"employ":[52],"Tensor-Train":[53],"methods":[54],"to":[55],"account":[56],"for":[57,85],"this":[58],"approximation":[61],"process":[62],"within":[63],"done":[68,77],"Least-Squares":[71],"and":[73,93],"integration":[75],"Monte-Carlo":[79],"methods.":[80],"Numerical":[81],"evidences":[82],"given":[84],"(multidimensional)":[87],"double-well":[88],"potential,":[89,92],"three-hole":[91],"40-dimensional":[95],"Van":[97],"der":[98],"Pol":[99],"oscillator.":[100]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}