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

¹ CEA/CESTA
² Sorbonne Université, CNRS

^* e-mail: fabien.vivodtzev@cea.fr
^** e-mail: florent.nauleau@cea.fr
^*** e-mail: alexis.casner@cea.fr
^**** e-mail: julien.tierny@sorbonne-universite.fr

Published online: 15 October 2024

Abstract

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.