Topological Analysis of Ensembles of Hydrodynamic Turbulent Flows An Experimental Study

Nauleau, Florent; Vivodtzev, Fabien; Bridel-Bertomeu, Thibault; Beaugendre, Héloïse; Tierny, Julien

doi:10.1109/ldav57265.2022.9966403

Cited by 12 publications

(2 citation statements)

References 80 publications

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“…Topological data analysis of the O Ba scalar function. Motivated by the success of TDA to describe scalar data through its topological features in numerous applications [9][10][11][12][13][14] including vortex extraction, 15,16 we apply TDA tools to the O Ba scalar field. To our best knowledge, it is the first report on employing TDA in the MICD context.…”

Section: Introductionmentioning

confidence: 99%

Topological data analysis of vortices in the magnetically-induced current density in LiH molecule

Olejniczak

Tierny

2023

Phys. Chem. Chem. Phys.

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Section: Introductionmentioning

confidence: 99%

Topological data analysis of vortices in the magnetically-induced current density in LiH molecule

Olejniczak

Tierny

2023

Phys. Chem. Chem. Phys.

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“…To address this issue, Topological Data Analysis (TDA) [28] has shown over the years its ability to reveal, in a generic, robust and efficient manner, the main structural patterns hidden in complex datasets, in particular for visual data analysis tasks [44]. Successful applications have been documented in multiple fields (turbulent combustion [19], [41], material sciences [43], [81], nuclear energy [57], fluid dynamics [49], [63], bioimaging [3], [14], quantum chemistry [64], [65] or astrophysics [79], [82]). Among the representations studied in TDA, the merge tree [22] (Fig.…”

Section: Introductionmentioning

confidence: 99%

Principal Geodesic Analysis of Merge Trees (and Persistence Diagrams)

Pont¹,

Vidal²,

Tierny³

2023

IEEE Trans. Visual. Comput. Graphics

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This paper presents a computational framework for the Wasserstein auto-encoding of merge trees (MT-WAE), a novel extension of the classical auto-encoder neural network architecture to the Wasserstein metric space of merge trees. In contrast to traditional auto-encoders which operate on vectorized data, our formulation explicitly manipulates merge trees on their associated metric space at each layer of the network, resulting in superior accuracy and interpretability. Our novel neural network approach can be interpreted as a non-linear generalization of previous linear attempts [72] at merge tree encoding. It also trivially extends to persistence diagrams. Extensive experiments on public ensembles demonstrate the efficiency of our algorithms, with MT-WAE computations in the orders of minutes on average. We show the utility of our contributions in two applications adapted from previous work on merge tree encoding [72]. First, we apply MT-WAE to data reduction and reliably compress merge trees by concisely representing them with their coordinates in the final layer of our auto-encoder. Second, we document an application to dimensionality reduction, by exploiting the latent space of our auto-encoder, for the visual analysis of ensemble data. We illustrate the versatility of our framework by introducing two penalty terms, to help preserve in the latent space both the Wasserstein distances between merge trees, as well as their clusters. In both applications, quantitative experiments assess the relevance of our framework. Finally, we provide a C++ implementation that can be used for reproducibility.

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Topological Representations for Data Analysis: Use Cases on Instabilities and Turbulences

Vivodtzev,

Nauleau,

Casner

et al. 2024

EPJ Web Conf.

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Understanding physical phenomena implied in the design of a system or in the guarantee of its performances require to run high fidelity simulation codes and to create experimental campaigns at different scales. Thanks to the use of advanced sensors or imaging capabilities in large facilities such as the Laser Mega Joule and the use of High Performance Computing, very large and complex dataset are generated. The analysis of such data is a real challenge due to the size and the complexity of the data. When dealing with chaotic phenomena, traditional analysis methods often try to average the answer. In this paper, we introduce the use of Topological Data Analysis (TDA) to improve the understanding of the results and avoid costly traditional analysis methods. The key concepts of TDA are presented such as the notion of critical points, persistence and different simplification representations. Then we illustrate the advantages of TDA on successful use cases on the analysis of hydrodynamic instabilities observed during Laser shooting or turbulences computed with a computational fluid dynamic simulation code.

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Topological Analysis of Ensembles of Hydrodynamic Turbulent Flows An Experimental Study

Cited by 12 publications

References 80 publications

Topological data analysis of vortices in the magnetically-induced current density in LiH molecule

Topological data analysis of vortices in the magnetically-induced current density in LiH molecule

Principal Geodesic Analysis of Merge Trees (and Persistence Diagrams)

Topological Representations for Data Analysis: Use Cases on Instabilities and Turbulences

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