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Topological analysis of ensembles of hydrodynamic turbulent flows -- An experimental study

hal.structure.identifierCentre d'études scientifiques et techniques d'Aquitaine [CESTA]
dc.contributor.authorNAULEAU, Florent
hal.structure.identifierCentre d'études scientifiques et techniques d'Aquitaine [CESTA]
dc.contributor.authorVIVODTZEV, Fabien
hal.structure.identifierCentre d'études scientifiques et techniques d'Aquitaine [CESTA]
dc.contributor.authorBRIDEL-BERTOMEU, Thibault
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorBEAUGENDRE, Heloise
hal.structure.identifierAlgorithmes, Programmes et Résolution [APR]
dc.contributor.authorTIERNY, Julien
dc.date.accessioned2024-04-04T02:40:49Z
dc.date.available2024-04-04T02:40:49Z
dc.date.issued2022-07-16
dc.date.conference2022-07-16
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191094
dc.description.abstractEnThis application paper presents a comprehensive experimental evaluation of the suitability of Topological Data Analysis (TDA) for the quantitative comparison of turbulent flows. Specifically, our study documents the usage of the persistence diagram of the maxima of flow enstrophy (an established vorticity indicator), for the topological representation of 180 ensemble members, generated by a coarse sampling of the parameter space of five numerical solvers. We document five main hypotheses reported by domain experts, describing their expectations regarding the variability of the flows generated by the distinct solver configurations. We contribute three evaluation protocols to assess the validation of the above hypotheses by two comparison measures: (i) a standard distance used in scientific imaging (the $L_2$ norm) and (ii) an established topological distance between persistence diagrams (the $L_2$-Wasserstein metric). Extensive experiments on the input ensemble demonstrate the superiority of the topological distance (ii) to report as close to each other flows which are expected to be similar by domain experts, due to the configuration of their vortices. Overall, the insights reported by our study bring an experimental evidence of the suitability of TDA for representing and comparing turbulent flows, thereby providing to the fluid dynamics community confidence for its usage in future work. Also, our flow data and evaluation protocols provide to the TDA community an application-approved benchmark for the evaluation and design of further topological distances.
dc.language.isoen
dc.title.enTopological analysis of ensembles of hydrodynamic turbulent flows -- An experimental study
dc.typeCommunication dans un congrès
dc.subject.halInformatique [cs]/Synthèse d'image et réalité virtuelle [cs.GR]
dc.subject.halInformatique [cs]/Vision par ordinateur et reconnaissance de formes [cs.CV]
dc.subject.halInformatique [cs]/Géométrie algorithmique [cs.CG]
dc.subject.halInformatique [cs]/Logiciel mathématique [cs.MS]
dc.subject.halInformatique [cs]/Mathématique discrète [cs.DM]
dc.subject.halInformatique [cs]/Traitement des images
dc.subject.halInformatique [cs]/Apprentissage [cs.LG]
dc.subject.halPhysique [physics]/Physique [physics]/Dynamique des Fluides [physics.flu-dyn]
dc.identifier.arxiv2207.14080
dc.description.sponsorshipEuropeIn-situ Topological Reduction of Scientific 3D Data - EXCELLENT SCIENCE - European Research Council
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.conference.titleIEEE Symposium on Large Data Analysis and Visualization
bordeaux.countryUS
bordeaux.conference.cityOklahoma City
bordeaux.peerReviewedoui
hal.identifierhal-03740152
hal.version1
hal.invitednon
hal.proceedingsoui
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03740152v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2022-07-16&rft.au=NAULEAU,%20Florent&VIVODTZEV,%20Fabien&BRIDEL-BERTOMEU,%20Thibault&BEAUGENDRE,%20Heloise&TIERNY,%20Julien&rft.genre=unknown


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