Gaussian interacting particles via Wasserstein gradient flow

"Estimating general multimodal distributions is challenging, but a powerful approach is to view this distribution as the asymptotic limit of a Fokker–Planck equation (FPE). While many traditional methods rely on MCMC to sample on this limiting distribution, an alternative is to directly approximate the solution of the FPE. Since Otto’s seminal work, the solution of the Fokker–Planck equation can be interpreted as the minimization of a relative entropy functional in Wasserstein space, leading to the Wasserstein gradient flow. Following the projected gradient flow framework, we approximate this flow by projecting its gradient onto the tangent space of a finite-dimensional parametric manifold. In particular, choosing the Bures manifold leads to the Bures–Wasserstein gradient flow, which exhibits fast convergence properties for log-concave distribution. Finally, this framework can be lifted to a Gaussian-particle representation, enabling efficient approximation of complex multimodal distributions using multiple particles."

The presentation will be based on the following articles https://arxiv.org/abs/2205.15902 and https://arxiv.org/abs/2506.13613.