{"id":"https://openalex.org/W7225655348","doi":"https://doi.org/10.5281/zenodo.24084197","title":"FLOW MATCHING AND OPTIMAL TRANSPORT: AN ILLUSTRATED INTRODUCTION TO WASSERSTEIN\u2013OTTO GEOMETRY","display_name":"FLOW MATCHING AND OPTIMAL TRANSPORT: AN ILLUSTRATED INTRODUCTION TO WASSERSTEIN\u2013OTTO GEOMETRY","publication_year":2026,"publication_date":"2026-11-09","ids":{"openalex":"https://openalex.org/W7225655348","doi":"https://doi.org/10.5281/zenodo.24084197"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24084197","doi":"https://doi.org/10.5281/zenodo.24084197","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24084197","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24084197","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083980531","display_name":"Pierre Guilbert","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Guilbert, Pierre","raw_affiliation_strings":["Independent Researcher"],"raw_orcid":"https://orcid.org/0009-0002-1582-4435","affiliations":[{"raw_affiliation_string":"Independent Researcher","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5083980531"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied 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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied 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/T12536","display_name":"Topological and Geometric Data Analysis","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11564","display_name":"Mathematical Inequalities and Applications","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/flow-matching","display_name":"flow matching","score":0.9739999771118164},{"id":"https://openalex.org/keywords/optimal-transport","display_name":"optimal transport","score":0.9649999737739563},{"id":"https://openalex.org/keywords/geodesics","display_name":"geodesics","score":0.7850000262260437},{"id":"https://openalex.org/keywords/continuity-equation","display_name":"continuity equation","score":0.8939999938011169}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7103999853134155},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.6743000149726868},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5306000113487244},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.527899980545044},{"id":"https://openalex.org/C86941820","wikidata":"https://www.wikidata.org/wiki/Q6865391","display_name":"Minimisation (clinical trials)","level":2,"score":0.5026999711990356},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.4810999929904938},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.47929999232292175},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.45649999380111694},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.40369999408721924},{"id":"https://openalex.org/C136005978","wikidata":"https://www.wikidata.org/wiki/Q1362077","display_name":"First variation","level":2,"score":0.38580000400543213},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.38530001044273376},{"id":"https://openalex.org/C167879884","wikidata":"https://www.wikidata.org/wiki/Q727568","display_name":"Balanced flow","level":2,"score":0.374099999666214},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3334999978542328},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.3237999975681305},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.320499986410141},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.3197000026702881},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.31360000371932983},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3098999857902527},{"id":"https://openalex.org/C130402806","wikidata":"https://www.wikidata.org/wiki/Q5361768","display_name":"Random field","level":2,"score":0.30309998989105225},{"id":"https://openalex.org/C142259097","wikidata":"https://www.wikidata.org/wiki/Q5891314","display_name":"Homogeneity (statistics)","level":2,"score":0.30300000309944153},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.28850001096725464},{"id":"https://openalex.org/C51267290","wikidata":"https://www.wikidata.org/wiki/Q5527848","display_name":"Gaussian random field","level":4,"score":0.2856999933719635},{"id":"https://openalex.org/C14961307","wikidata":"https://www.wikidata.org/wiki/Q5377176","display_name":"Energy minimization","level":2,"score":0.27239999175071716},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.2567000091075897},{"id":"https://openalex.org/C2983502797","wikidata":"https://www.wikidata.org/wiki/Q828402","display_name":"Energy density","level":2,"score":0.2563999891281128},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.2556000053882599},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2502000033855438}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24084197","doi":"https://doi.org/10.5281/zenodo.24084197","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24084197","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.24084198","doi":"https://doi.org/10.5281/zenodo.24084198","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24084198","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.24084197","doi":"https://doi.org/10.5281/zenodo.24084197","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24084197","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7165767198","https://openalex.org/W7122600326","https://openalex.org/W4413061805","https://openalex.org/W7204621531","https://openalex.org/W7161560916","https://openalex.org/W7134551648","https://openalex.org/W7169839954","https://openalex.org/W7201886458","https://openalex.org/W6983668601","https://openalex.org/W7220962620"],"abstract_inverted_index":{"We":[0,36,55,100],"recall":[1],"and":[2,23,44,109,123],"derive":[3],"the":[4,12,17,27,33,39,46,64,70,75,84,89,97,102,110,113],"equations":[5],"underlying":[6],"Flow":[7,65],"Match-":[8],"ing,":[9],"making":[10],"explicit":[11,121],"probability":[13],"density":[14,41,76],"function":[15],"of":[16,74,112],"linearly":[18],"in-":[19],"terpolated":[20],"random":[21],"variable":[22],"relating":[24],"it":[25],"to":[26],"transporting":[28],"veloc-":[29],"ity":[30],"field":[31,68],"through":[32],"continuity":[34,85],"equation.":[35],"visualise":[37],"how":[38],"initial":[40,62],"is":[42,69,91],"transported":[43],"compare":[45],"resulting":[47],"path":[48,90],"with":[49,117],"a":[50,94],"geodesic":[51,95],"in":[52],"Wasserstein\u2013Otto":[53,98],"geometry.":[54],"demonstrate":[56],"that,":[57],"for":[58],"an":[59],"isotropic":[60],"Gaussian":[61],"law,":[63],"Matching":[66],"velocity":[67],"minimum-":[71],"energy":[72],"representative":[73],"variation":[77],"at":[78],"each":[79],"time,":[80],"among":[81],"fields":[82],"satisfying":[83],"equation,":[86],"even":[87],"though":[88],"generally":[92],"not":[93],"under":[96],"metric.":[99],"explain":[101],"dis-":[103],"tinction":[104],"between":[105],"this":[106],"local":[107],"minimisation":[108,111],"action":[114],"over":[115],"paths":[116],"fixed":[118],"endpoints":[119],"using":[120],"calculations":[122],"illustrations.":[124]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-10T00:00:00"}
