{"id":"https://openalex.org/W3093179871","doi":"https://doi.org/10.23919/acc50511.2021.9483404","title":"Approximate Stochastic Reachability for High Dimensional Systems","display_name":"Approximate Stochastic Reachability for High Dimensional Systems","publication_year":2021,"publication_date":"2021-05-25","ids":{"openalex":"https://openalex.org/W3093179871","doi":"https://doi.org/10.23919/acc50511.2021.9483404","mag":"3093179871"},"language":"en","primary_location":{"id":"doi:10.23919/acc50511.2021.9483404","is_oa":false,"landing_page_url":"https://doi.org/10.23919/acc50511.2021.9483404","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 American Control Conference (ACC)","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1910.10818","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032775298","display_name":"Adam J. Thorpe","orcid":"https://orcid.org/0000-0001-7120-0913"},"institutions":[{"id":"https://openalex.org/I169521973","display_name":"University of New Mexico","ror":"https://ror.org/05fs6jp91","country_code":"US","type":"education","lineage":["https://openalex.org/I169521973"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Adam J. Thorpe","raw_affiliation_strings":["University of New Mexico, Albuquerque, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of New Mexico, Albuquerque, United States","institution_ids":["https://openalex.org/I169521973"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082314299","display_name":"Vignesh Sivaramakrishnan","orcid":"https://orcid.org/0000-0003-1127-9628"},"institutions":[{"id":"https://openalex.org/I169521973","display_name":"University of New Mexico","ror":"https://ror.org/05fs6jp91","country_code":"US","type":"education","lineage":["https://openalex.org/I169521973"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vignesh Sivaramakrishnan","raw_affiliation_strings":["University of New Mexico, Albuquerque, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of New Mexico, Albuquerque, United States","institution_ids":["https://openalex.org/I169521973"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070060161","display_name":"Meeko Oishi","orcid":"https://orcid.org/0000-0003-3722-8837"},"institutions":[{"id":"https://openalex.org/I169521973","display_name":"University of New Mexico","ror":"https://ror.org/05fs6jp91","country_code":"US","type":"education","lineage":["https://openalex.org/I169521973"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Meeko M. K. Oishi","raw_affiliation_strings":["University of New Mexico, Albuquerque, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of New Mexico, Albuquerque, United States","institution_ids":["https://openalex.org/I169521973"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1399,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.51485093,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"1287","last_page":"1293"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9977999925613403,"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"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9977999925613403,"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/reachability","display_name":"Reachability","score":0.6650212407112122},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.5915758013725281},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5625027418136597},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.551748514175415},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4843979477882385},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.4744761288166046},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.452546089887619},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4463728666305542},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.43272578716278076},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.416951060295105},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4112168550491333},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3894025385379791},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3591894209384918},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13679596781730652},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.11799359321594238}],"concepts":[{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.6650212407112122},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.5915758013725281},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5625027418136597},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.551748514175415},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4843979477882385},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.4744761288166046},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.452546089887619},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4463728666305542},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.43272578716278076},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.416951060295105},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4112168550491333},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3894025385379791},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3591894209384918},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13679596781730652},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.11799359321594238},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.23919/acc50511.2021.9483404","is_oa":false,"landing_page_url":"https://doi.org/10.23919/acc50511.2021.9483404","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 American Control Conference (ACC)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1910.10818","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1910.10818","pdf_url":"https://arxiv.org/pdf/1910.10818","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":"","raw_type":"text"},{"id":"mag:3093179871","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1910.10818v3","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.1910.10818","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1910.10818","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1910.10818","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1910.10818","pdf_url":"https://arxiv.org/pdf/1910.10818","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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2834232345","display_name":null,"funder_award_id":"CMMI-1254990,CNS-1836900","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4497378093","display_name":"NRI: Planning, Collaborative Guidance and Navigation in Uncertain Dynamic Environments","funder_award_id":"1528047","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5398608241","display_name":null,"funder_award_id":"CNS-1836900","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6012051226","display_name":null,"funder_award_id":"DE-NA-0003525","funder_id":"https://openalex.org/F4320337547","funder_display_name":"Laboratory Directed Research and Development"},{"id":"https://openalex.org/G6020313407","display_name":null,"funder_award_id":"CMMI-1254990","funder_id":"https://openalex.org/F4320337391","funder_display_name":"Division of Civil, Mechanical and Manufacturing Innovation"},{"id":"https://openalex.org/G6068018176","display_name":null,"funder_award_id":"IIS-1528047","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7166948679","display_name":null,"funder_award_id":"DE-NA-0003525","funder_id":"https://openalex.org/F4320332369","funder_display_name":"National Nuclear Security Administration"},{"id":"https://openalex.org/G7310172615","display_name":null,"funder_award_id":"1836900","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7410743818","display_name":null,"funder_award_id":"DE-NA-0003525","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G7462044558","display_name":"CAREER: Formal Tools For Analysis and Design of Collaborative Hybrid Systems","funder_award_id":"1254990","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7642757584","display_name":null,"funder_award_id":"DE-NA-0003525","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G805931733","display_name":null,"funder_award_id":"DE-NA-0003525","funder_id":"https://openalex.org/F4320338291","funder_display_name":"Sandia National Laboratories"},{"id":"https://openalex.org/G912397303","display_name":null,"funder_award_id":"CMMI-1254990","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/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320332369","display_name":"National Nuclear Security Administration","ror":"https://ror.org/03sk1we31"},{"id":"https://openalex.org/F4320337391","display_name":"Division of Civil, Mechanical and Manufacturing Innovation","ror":"https://ror.org/028yd4c30"},{"id":"https://openalex.org/F4320337547","display_name":"Laboratory Directed Research and Development","ror":"https://ror.org/01e41cf67"},{"id":"https://openalex.org/F4320338291","display_name":"Sandia National Laboratories","ror":"https://ror.org/01apwpt12"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3093179871.pdf","grobid_xml":"https://content.openalex.org/works/W3093179871.grobid-xml"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W1494154421","https://openalex.org/W1512937499","https://openalex.org/W1529558080","https://openalex.org/W1560724230","https://openalex.org/W1565176583","https://openalex.org/W1698155719","https://openalex.org/W1746819321","https://openalex.org/W1898511152","https://openalex.org/W1946137962","https://openalex.org/W1986280275","https://openalex.org/W1992244412","https://openalex.org/W2012811607","https://openalex.org/W2077933344","https://openalex.org/W2084772009","https://openalex.org/W2115003579","https://openalex.org/W2118563516","https://openalex.org/W2123395972","https://openalex.org/W2144902422","https://openalex.org/W2146641075","https://openalex.org/W2160536246","https://openalex.org/W2365516273","https://openalex.org/W2400318990","https://openalex.org/W2593166942","https://openalex.org/W2606133973","https://openalex.org/W2796084235","https://openalex.org/W2887363327","https://openalex.org/W2911421980","https://openalex.org/W2913029553","https://openalex.org/W2939750219","https://openalex.org/W2940589930","https://openalex.org/W2949361666","https://openalex.org/W2953256123","https://openalex.org/W2963013450","https://openalex.org/W2972315120","https://openalex.org/W2972858943","https://openalex.org/W3098617035","https://openalex.org/W3098919244","https://openalex.org/W6640697403","https://openalex.org/W6678945949","https://openalex.org/W6681302627","https://openalex.org/W6694266080","https://openalex.org/W6756182987","https://openalex.org/W6759227737","https://openalex.org/W6763645266","https://openalex.org/W6785516799"],"related_works":["https://openalex.org/W3185186402","https://openalex.org/W2981945633","https://openalex.org/W3092670197","https://openalex.org/W3098617035","https://openalex.org/W2535870504","https://openalex.org/W1494154421","https://openalex.org/W3135991946","https://openalex.org/W2033966800","https://openalex.org/W2063718256","https://openalex.org/W3203238008","https://openalex.org/W2790728601","https://openalex.org/W3196340102","https://openalex.org/W2113715225","https://openalex.org/W3112385784","https://openalex.org/W1606433297","https://openalex.org/W2085975572","https://openalex.org/W3119401774","https://openalex.org/W2114383819","https://openalex.org/W2108008892","https://openalex.org/W2159942104"],"abstract_inverted_index":{"We":[0,70,118],"present":[1],"a":[2,21,36,46,72,123,132],"method":[3],"to":[4,30,54,81],"compute":[5,55],"the":[6,32,41,56,83,93,99,111,114],"stochastic":[7,13,33,60],"reachability":[8,61],"safety":[9,57,102],"probabilities":[10,58,103],"for":[11,59,87,104],"high-dimensional":[12,88,105],"dynamical":[14],"systems.":[15,89],"Our":[16],"approach":[17,121],"takes":[18],"advantage":[19],"of":[20,95,101,110,113],"nonparametric":[22],"learning":[23],"technique":[24,91],"known":[25],"as":[26,63],"conditional":[27],"distribution":[28],"embeddings":[29],"model":[31],"kernel":[34,48],"using":[35],"data-driven":[37],"approach.":[38],"By":[39],"embedding":[40],"dynamics":[42,115],"and":[43,67,97,127],"uncertainty":[44],"within":[45],"reproducing":[47],"Hilbert":[49],"space,":[50],"it":[51],"becomes":[52],"possible":[53],"problems":[62],"simple":[64],"matrix":[65],"operations":[66],"inner":[68],"products.":[69],"employ":[71],"convergent":[73],"approximation":[74],"technique,":[75],"random":[76],"Fourier":[77],"features,":[78],"in":[79],"order":[80],"alleviate":[82],"increased":[84],"computational":[85],"requirements":[86],"This":[90],"avoids":[92],"curse":[94],"dimensionality,":[96],"enables":[98],"computation":[100],"systems":[106],"without":[107],"prior":[108],"knowledge":[109],"structure":[112],"or":[116],"uncertainty.":[117],"validate":[119],"this":[120],"on":[122,131],"double":[124],"integrator":[125],"system,":[126],"demonstrate":[128],"its":[129],"capabilities":[130],"million-dimensional,":[133],"nonlinear,":[134],"non-Gaussian,":[135],"repeated":[136],"planar":[137],"quadrotor":[138],"system.":[139]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}