Analysis and Applied Mathematics Seminar
Shi Jin
Shanghai Jiao Tong University
Random Batch Methods for Interacting Particle Systems and its Applications in Consensus-based High Dimensional Global Optimization in Machine Learning
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.
Monday September 9, 2019 at 4:00 PM in 636 SEO