{"id":"https://openalex.org/W3015052221","doi":"https://doi.org/10.1137/20m1329354","title":"A Convergent Discretization Method for Transition Path Theory for Diffusion Processes","display_name":"A Convergent Discretization Method for Transition Path Theory for Diffusion Processes","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3015052221","doi":"https://doi.org/10.1137/20m1329354","mag":"3015052221"},"language":"en","primary_location":{"id":"doi:10.1137/20m1329354","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1329354","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1907.05799","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055078612","display_name":"Nada Cvetkovi\u0107","orcid":"https://orcid.org/0000-0002-7640-7347"},"institutions":[{"id":"https://openalex.org/I176453806","display_name":"University of Potsdam","ror":"https://ror.org/03bnmw459","country_code":"DE","type":"education","lineage":["https://openalex.org/I176453806"]},{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Nada Cvetkovi\u0107","raw_affiliation_strings":["Department of Mathematics and Computer Science, Freie Universit\u00e4t Berlin, Arnimallee 6, 14195 Berlin, Germany","Universit\u00e4t Potsdam, Institut f\u00fcr Mathematik, Karl-Liebknecht Str. 24/25, D-14476 Potsdam OT Golm, Germany"],"raw_orcid":"https://orcid.org/0000-0002-7640-7347","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Freie Universit\u00e4t Berlin, Arnimallee 6, 14195 Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]},{"raw_affiliation_string":"Universit\u00e4t Potsdam, Institut f\u00fcr Mathematik, Karl-Liebknecht Str. 24/25, D-14476 Potsdam OT Golm, Germany","institution_ids":["https://openalex.org/I176453806"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012229905","display_name":"Tim Conrad","orcid":"https://orcid.org/0000-0002-5590-5726"},"institutions":[{"id":"https://openalex.org/I176453806","display_name":"University of Potsdam","ror":"https://ror.org/03bnmw459","country_code":"DE","type":"education","lineage":["https://openalex.org/I176453806"]},{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Tim Conrad","raw_affiliation_strings":["Department of Mathematics and Computer Science, Freie Universit\u00e4t Berlin, Arnimallee 6, 14195 Berlin, Germany","Universit\u00e4t Potsdam, Institut f\u00fcr Mathematik, Karl-Liebknecht Str. 24/25, D-14476 Potsdam OT Golm, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Freie Universit\u00e4t Berlin, Arnimallee 6, 14195 Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]},{"raw_affiliation_string":"Universit\u00e4t Potsdam, Institut f\u00fcr Mathematik, Karl-Liebknecht Str. 24/25, D-14476 Potsdam OT Golm, Germany","institution_ids":["https://openalex.org/I176453806"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052637565","display_name":"Han Cheng Lie","orcid":"https://orcid.org/0000-0002-6905-9903"},"institutions":[{"id":"https://openalex.org/I176453806","display_name":"University of Potsdam","ror":"https://ror.org/03bnmw459","country_code":"DE","type":"education","lineage":["https://openalex.org/I176453806"]},{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Han Cheng Lie","raw_affiliation_strings":["Universit\u00e4t Potsdam, Institut f\u00fcr Mathematik, Karl-Liebknecht Str. 24/25, D-14476 Potsdam OT Golm, Germany","Department of Mathematics and Computer Science, Freie Universit\u00e4t Berlin, Arnimallee 6, 14195 Berlin, Germany"],"raw_orcid":"https://orcid.org/0000-0002-6905-9903","affiliations":[{"raw_affiliation_string":"Universit\u00e4t Potsdam, Institut f\u00fcr Mathematik, Karl-Liebknecht Str. 24/25, D-14476 Potsdam OT Golm, Germany","institution_ids":["https://openalex.org/I176453806"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science, Freie Universit\u00e4t Berlin, Arnimallee 6, 14195 Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5055078612"],"corresponding_institution_ids":["https://openalex.org/I176453806","https://openalex.org/I75951250"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00559868,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"1","first_page":"242","last_page":"266"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9988999962806702,"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"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9988999962806702,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T13187","display_name":"Diffusion and Search Dynamics","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7244621515274048},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5807584524154663},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5410266518592834},{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.5214806795120239},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5132558345794678},{"id":"https://openalex.org/keywords/diffusion-process","display_name":"Diffusion process","score":0.4734572768211365},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.46662724018096924},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.45914387702941895},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.4573180079460144},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4414253830909729},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.43253475427627563},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.42477312684059143},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.41196727752685547},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3225853741168976},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2681170105934143},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2229364812374115},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11031657457351685}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7244621515274048},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5807584524154663},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5410266518592834},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.5214806795120239},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5132558345794678},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.4734572768211365},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.46662724018096924},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.45914387702941895},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.4573180079460144},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4414253830909729},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.43253475427627563},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.42477312684059143},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.41196727752685547},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3225853741168976},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2681170105934143},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2229364812374115},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11031657457351685},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C3017618536","wikidata":"https://www.wikidata.org/wiki/Q304994","display_name":"Innovation diffusion","level":2,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C56739046","wikidata":"https://www.wikidata.org/wiki/Q192060","display_name":"Knowledge management","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/20m1329354","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1329354","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"},{"id":"pmh:oai:arXiv.org:1907.05799","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1907.05799","pdf_url":"https://arxiv.org/pdf/1907.05799","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":null,"raw_type":"text"},{"id":"pmh:oai:kobv.de-opus4-uni-potsdam:62778","is_oa":false,"landing_page_url":"https://publishup.uni-potsdam.de/frontdoor/index/index/docId/62778","pdf_url":null,"source":{"id":"https://openalex.org/S4306400594","display_name":"publish.UP (University of Potsdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I176453806","host_organization_name":"University of Potsdam","host_organization_lineage":["https://openalex.org/I176453806"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1907.05799","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1907.05799","pdf_url":"https://arxiv.org/pdf/1907.05799","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5374426315","display_name":null,"funder_award_id":"3FO18501","funder_id":"https://openalex.org/F4320321114","funder_display_name":"Bundesministerium f\u00fcr Bildung und Forschung"},{"id":"https://openalex.org/G5626449879","display_name":null,"funder_award_id":"SFB1294/1 - 318763901","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321114","display_name":"Bundesministerium f\u00fcr Bildung und Forschung","ror":"https://ror.org/04pz7b180"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W1498636830","https://openalex.org/W1531327550","https://openalex.org/W1583452899","https://openalex.org/W1956046463","https://openalex.org/W1967005434","https://openalex.org/W1967722756","https://openalex.org/W1971008678","https://openalex.org/W1978607920","https://openalex.org/W1979070806","https://openalex.org/W1984414107","https://openalex.org/W1986117336","https://openalex.org/W1988220126","https://openalex.org/W2024257794","https://openalex.org/W2027743806","https://openalex.org/W2031843459","https://openalex.org/W2051752778","https://openalex.org/W2055484248","https://openalex.org/W2068741469","https://openalex.org/W2070359441","https://openalex.org/W2080454718","https://openalex.org/W2083544350","https://openalex.org/W2085213650","https://openalex.org/W2093915651","https://openalex.org/W2103607079","https://openalex.org/W2133858770","https://openalex.org/W2151822821","https://openalex.org/W2155816874","https://openalex.org/W2161241898","https://openalex.org/W2211106937","https://openalex.org/W2265661434","https://openalex.org/W2574675855","https://openalex.org/W2888484855","https://openalex.org/W2896498657","https://openalex.org/W2956903327","https://openalex.org/W3103584642","https://openalex.org/W3104017145","https://openalex.org/W4213311833"],"related_works":["https://openalex.org/W50969306","https://openalex.org/W2390585021","https://openalex.org/W412641959","https://openalex.org/W4292101436","https://openalex.org/W2341040961","https://openalex.org/W4287207389","https://openalex.org/W4287662864","https://openalex.org/W3088324674","https://openalex.org/W2057373567","https://openalex.org/W1965170265"],"abstract_inverted_index":{"Transition":[0],"path":[1],"theory":[2],"(TPT)":[3],"for":[4,10,28,74,83,94,129],"diffusion":[5,17,49,95],"processes":[6,18],"is":[7,56],"a":[8,35,40,79,120,162,170],"framework":[9],"analyzing":[11],"the":[12,32,47,52,85,117,130,146,166],"transitions":[13],"of":[14,23,34,42,54,106,119,148,156],"multiscale":[15],"ergodic":[16],"between":[19],"disjoint":[20],"metastable":[21],"subsets":[22],"state":[24,37,43,107],"space.":[25],"Most":[26],"methods":[27],"applying":[29],"TPT":[30,93,132],"involve":[31],"construction":[33,118],"Markov":[36],"model":[38],"on":[39,110,169],"discretization":[41],"space":[44,108],"that":[45,164],"approximates":[46],"underlying":[48],"process.":[50,123],"However,":[51],"assumption":[53],"Markovianity":[55],"difficult":[57],"to":[58,65,138,141,161],"verify":[59],"in":[60,145],"practice,":[61],"and":[62,90,104,134],"there":[63],"are":[64],"date":[66],"no":[67],"known":[68],"error":[69,127],"bounds":[70,128,137],"or":[71],"convergence":[72,140],"results":[73],"these":[75,136],"methods.":[76],"We":[77,124,152],"propose":[78],"Monte":[80],"Carlo":[81],"method":[82,98,158],"approximating":[84,122],"forward":[86],"committor,":[87],"probability":[88],"current,":[89],"streamlines":[91],"from":[92],"processes.":[96],"Our":[97],"uses":[99],"only":[100],"sample":[101],"trajectory":[102],"data":[103],"partitions":[105],"based":[109],"Voronoi":[111],"tessellations.":[112],"It":[113],"does":[114],"not":[115],"require":[116],"Markovian":[121],"rigorously":[125],"prove":[126],"approximate":[131],"objects":[133],"use":[135],"show":[139],"their":[142],"exact":[143],"counterparts":[144],"limit":[147],"arbitrarily":[149],"fine":[150],"discretization.":[151],"illustrate":[153],"some":[154],"features":[155],"our":[157],"by":[159],"application":[160],"process":[163],"solves":[165],"Smoluchowski":[167],"equation":[168],"triple-well":[171],"potential.":[172]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2020-04-10T00:00:00"}