报告人:金石
报告人单位:上海交通大学
报告时间:4月23日14:00
报告网址:Zoom会议 ID:927 3506 6290 密码:005266
报告摘要:
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.
报告人简介:
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。先后获北京大学学士学位,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。