The fuel cells are energy conversion systems. Their efficiency is linked to the geometry of the microstructures of which they are composed. Several very different models have been developed in the laboratory, in collaboration with teams of the CEA-Liten in Grenoble. In particular, random fields simulate ensembles whose geometry is close to that of real-life real observations. However, this technique does not allow to adapt to spatial or temporal variations in microstructures, and the manipulation of random fields fields remains relatively simple.

The Minkowski functionals are elementary functionals that describe the geometry of mathematical objects (in 2D of 3D in our case). They give interesting criteria that can be used to compare microstructures together.

The aim of this PhD thesis is to study the evolution of the Minkowski functionals according to the time and the three dimensions (in case of non stationary materials) in order to better simulate the microstructures. Generative 3D models, like diffusion models or GANs, in three dimensions, in conjunction to the Minkowski functions, will be used. The physics principles will be described and compared to real data.

A PhD grant of 3 years is secured. Location is campus of Saint-Etienne, France.