报告人：金石教授

报告题目：

1. Random Batch Methods for interacting particle systems and molecular dynamics

2. Consensus-based High Dimensional Global Non-convex Optimization in Machine Learning

报告摘要：

1. We first develop random batch methods for classical  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.

This method is also extended to molecular dynamics with Coulomb interactions, in the framework of Ewald summation. We will show its superior performance compared to the current state-of-the-art methods (for example PPPM) for the corresponding problems, in the computational efficiency and parallelizability.

2. We 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, for fully discrete systems, that under dimension-independent conditions on the parameters, with suitable initial data, the algorithms converge to the neighborhood of the global minimum almost surely. We also introduce an Adaptive Moment Estimation (ADAM) based version to significantly improve its performance in high-space dimension. 

报告时间：6月24日上午09:00-11:30

报告地点：腾讯会议：571-158-033

报告人简介：金石教授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。他同时担任上海国家应用数学中心联合主任。他曾获冯康科学计算奖（2001），国际华人数学家大会晨兴数学银奖（2007）。他是美国数学会（AMS）首批会士（2012），工业与应用数学学会(SIAM)会士（2013），中国工业与应用数学学会（CSIAM）首批会士（2020），及2018年国际数学家大会邀请报告人。2021年他当选为欧洲人文与自然科学院(Academia Europaea)外籍院士与欧洲科学院(European Academy of Sciences)院士。

他的研究方向包括动理学理论，双曲型守恒律方程，量子动力学，不确定性量化，交互粒子系统，计算流体力学，机器学习与量子计算等。他在包含Acta Numerica等杂志发表过190余篇学术论文。