Data Assimilation and Reduced Modeling for High Dimensional Problems

CIRM, Luminy, France
July 19-August 27, 2021

Computation of the auto-diffusion coefficient of a cross-diffusion system with tensor methods

Supervisors: V. Ehrlacher, O. Mula (Ecole des Ponts ParisTech, Dauphine, Inria)
Students: Open to 1 student

Project Description: The aim of this project is to investigate a new iterative method in order to solve high-dimensional PDEs with neural networks: the main idea is to explore the combination of greedy algorithms together with adaptive sampling methods so as to optimize the sampling procedure needed to define the training data set of the neural network. This method will first be tested on simple test cases, before being extended to higher-dimensional problems arising either from kinetic theory or mean-field games.