Distinguished Colloquium——Interacting Particle Systems: random batch methods for classical and quantum N-body problems and non-convex optimization
报告人：Prof. Shi Jin (Shanghai Jiao Tong University)
时间：2020-05-15 14:00-15:00
地点：会议ID：307-355-784；腾讯会议：https://meeting.tencent.com/s/5CYv2EI59b2c
Abstract: 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 initial data the algorithms converge to the neighborhood of the global minimum almost surely.
Bio: 金石，现为上海交通大学自然科学研究院院长，数学学院讲席教授。先后获tyc234cc 太阳成集团学士学位，美国亚利桑那大学博士学位，历任美国纽约大学库朗数学研究所博士后，美国佐治亚理工学院助理教授、副教授，美国威斯康星大学（麦迪逊）正教授，数学系系主任，Vilas 杰出成就教授，上海交通大学数学系讲席教授、系主任。他同时担任上海应用数学中心联合主任，上海交通大学教育部科学工程计算重点实验室主任与人工智能数学基础中心主任。他曾获得冯康科学计算奖。他是美国数学会（AMS）首批会士，工业与应用数学学会(SIAM)会士，及2018年国际数学家大会邀请报告人。他的研究方向包括动理学理论，双曲型守恒律，高频波计算，量子动力学，不确定量化，粒子系统， 计算流体力学等。
