Shi Jin : Random Batch Methods for Interacting Particle Systems and its Applications in Consensus-based High Dimensional Global Optimization in Machine Learning

Posted by Ian Tobasco , part of the Analysis and Applied Mathematics Seminar.

At

Sept. 9, 2019, 4 p.m.

In

636 SEO

Abstract

We develop random batch methods for interacting particle systems with large number of particles. These methods use small but random batches for particle interactions, thus the computational cost is reduced from O(N^2) per time step to O(N), for a system with N particles with binary interactions. For one of the methods, we give a particle number independent error estimate under some special interactions. Then, we apply these methods to some representative problems in mathematics, physics, social and data sciences, including the Dyson Brownian motion from random matrix theory, Thomson's problem, distribution of wealth, opinion dynamics and clustering. Numerical results show that the methods can capture both the transient solutions and the global equilibrium in these problems.