报告题目：Theoretical guarantees of machine learning methods for statistical

sampling and PDEs in high dimensions

报告人：Yulong Lu  Assistant Professor，Department of Mathematics and Statistics
University of Massachusetts

报告时间：2020年11月30日 星期一上午10：00-12：00

报告地点：腾讯会议 ID：985 927 218

报告摘要： Neural network-based machine learning methods, inlcuding the most

notably deep learning have achieved extraordinary successes in numerious  fields.

In spite of the rapid development of learning  algorithms based on neural networks, their mathematical analysis are far from understood. In particular, it has been a big mystery that neural network-based machine learning methods work extremely well for solving high dimensional problems.

In this talk, I will demonstrate the power of  neural network methods for solving two classes of high dimensional problems: statistical sampling and PDEs. In the first part of the talk, I will present a universal approximation theorem of deep neural networks for representing high dimensional probability distributions. In the second part of the talk, I will discuss a generalization error bound of the Deep Ritz Method for solving high dimensional elliptic problems. For both problems,  our theoretical results show that neural networks-based methods  can overcome the curse of dimensionality.