Thesis subject:
The aim of this PhD thesis is to develop new approaches to analyze, represent and store high-precision simulation data obtained on fine meshes (mainly volume meshes, but also surface meshes). To do this, the proposed approach aims at decomposing the result of the simulation on representative bases resulting from a so-called non-local joint analysis. However, the data generated on meshes do not benefit from regular prior structure and the thesis will focus on the obstacles posed by this restriction. This thesis will include numerical aspects to analyze the data independently of its supporting mesh but also algorithmic aspects to take into account the specificity and size of the meshes. It will also be possible to benefit from the optimization power of lightweight neural networks for dimensional reduction of the various problems.

Skills required:
Skills in applied mathematics and computer science (Algorithmic, C++ programming and Python) are required for this thesis, as well as knowledge of numerical optimization tools such as PyTorch and/or PyAnsys tools.

Working conditions:
· The doctoral student will divide his or her time between LIRIS (Nautibus building, La Doua campus, Lyon 1 University) and ANSYS (Le Patio building, rue Louis Guérin, Villeurbanne). Both locations are less than a 15minutes walk apart. Villeurbanne is a city right next to Lyon, a dynamic multicultural city of France.
· Expected beginning of the thesis: September or October 2025