数学系 Seminar 第1999期
数学系“60周年”系庆系列报告
报告主题：相互作用粒子系统：快速算法和非凸优化（Interacting Particle Systems: Fast algorithms and non-convex optimization）
报告人：金 石 教授 （上海交通大学）
报告时间：2020年9月1日（周二） 9:00
参会方式：腾讯会议
https://meeting.tencent.com/s/KfkBYXjYax8f
会议ID：554 180 096
主办部门：理学院数学系
报告摘要：We first develop random batch methods for classical and quantum 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 classical particles we give a particle number independent error estimate under some special interactions. For quantum N-body Schrodinger equation, we obtain, for pair-wise random interactions, a convergence estimate for the Wigner transform of the single-particle reduced density matrix of the particle system at time t that is uniform in N > 1 and independent of the Planck constant \hbar.
We then introduce a stochastic interacting particle consensus system for global optimization of high dimensional non-convex functions. This algorithm does not use gradient of the function thus is suitable for non-smooth functions. We prove that under dimension-independent conditions on the parameters and with suitable initial data the algorithms converge to the neighborhood of the global minium almost surely.
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