Speaker:  Katy Craig (University of California, Santa Barbara)

Title: Nonlocal approximation of optimal transport and diffusion

Abstract: Particle methods are a fundamental tool for computing flows in the space of probability measures, whether the flow describes the evolution of fluid in a porous medium, agents in a robotic swarm, or samples transported to a desired target distribution. As a counterpoint to classical stochastic particle methods, such as Langevin dynamics, in today’s talk, I will present recent progress on deterministic particle methods, including (1) a nonlocal approximation of dynamic optimal transport, with state and control constraints, and (2) a nonlocal approximation of general nonlinear diffusion equations.