Seminar:DeepSPoC:a deep learning based sequential propagation of chaos

Seminar| Institute of Mathematical Sciences

Time:Thursday, May 08th, 2025,10:00-11:00

Abstract:Sequential propagation of chaos (SPoC) is a recently developed tool for solving mean-field stochastic differential equations and their related nonlinear Fokker-Planck equations. Based on the theory of SPoC, we present a new method (DeepSPoC) that combines the interacting particle system of SPoC with deep learning. A recently developed deep generative model called KRnet is used to store the empirical measure of particles in our algorithm. Our method has computational complexity $O(N)$ with respect to particle number and can also significantly reduce the memory used to store particle trajectories. These two features make our method applicable to the computation of complex high-dimensional problems that require simulations of large particle systems. We apply our method to a wide range of different types of mean-field equation and verify its effectiveness and advantages.