Speaker
Description
In this talk, I will present an approach to particle-based discretizations of Wasserstein gradient flows based on the Moreau-Yosida regularization of the underlying energies. This approach allows to approximate some evolution PDEs (such as Fokker-Planck, porous media or crowd motion models) with interacting particle systems, the interaction being through a mesh which is canonically associated to each point cloud by the regularized energy. These schemes are numerically appealing, but their numerical analysis seems difficult. One of the reason is that the driving ODEs have spurious stationary points, which do not correspond to Wasserstein critical points of the energy of the continuous gradient flow. I will nonetheless mention some convergence results, and explain proof techniques.
