Seminar in Mathematical Modeling and Analysis - Ankush Agarwal

This week's seminar in Mathematical Modeling and Analysis is given by Ankush Agarwal, University of Glasgow

Abstract: The McKean-Vlasov SDEs are a class of SDEs that describe the evolution of particles interacting with a population of other particles, where the dynamics of the system are influenced by the empirical measure of the particles. Typically, the numerical resolution of these equations involves the simulation of interacting particle systems, which can be computationally expensive and computationally challenging, especially in high-dimensional settings. In this paper, we explore an alternative method for the numerical resolution of McKean-Vlasov SDEs that does not rely on the simulation of interacting particle systems. Specifically, we investigate the use of Stochastic Gradient Descent (SGD), which has recently emerged as a powerful tool for high-dimensional optimization problems in machine learning. We propose a novel algorithm that combines a discretization scheme with SGD to efficiently and accurately approximate the solution of McKean-Vlasov SDEs. We present numerical experiments that demonstrate the effectiveness and efficiency of our approach, even in high-dimensional state spaces.