Talk
Interacting Particle Systems：Fast Algorithms and High Dimensional Non-convex Global Optimization
Talk by Prof. Dr. Shi Jin
Date: 04.03.20 Time: 16.15 - 17.45 Room: Online ZHACM CANCELLED
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. We also improve the interacting-particle consensus system for non-convex global optimization algorithm in high dimensional machine learning problems. This method does not require taking gradient. We prove the convergence of this algorithm under suitable, dimension-independent conditions on the parameters and initial data.