报告地点：行健楼学术活动室526
邀请人：汪艳秋教授
摘要：
Neural networks (NNs) have demonstrated remarkable performance in computer vision, natural language processing, and many other tasks of artificial intelligence. Recently, there has been a growing interest in leveraging NNs to solve partial differential equations (PDEs). Despite the rapid proliferation of articles in recent years, research on NN-based numerical methods for solving PDEs in the context of science and engineering is still in its early stages. Numerous critical open problems remain to be addressed before these methods can be broadly applied to solve computationally challenging problems.
In this talk, I will first give a brief introduction of ReLU NNs from numerical analysis perspective. I will then discuss our works on addressing some of critical questions such as
• why use NNs instead of finite elements in scientific computing? or for what applications, are NNs better than finite elements in approximation?
• how to develop NN discretization methods that are not only physics-informed but more importantly physics-preserved?
• how to develop reliable and efficient “training” algorithms for NN discretization (non-convex optimization)?
• for a given task, how to design a nearly optimal NN architecture within a prescribed accuracy?
个人简介：
蔡智强教授，国家重大人才项目入选者，现任大湾区大学讲席教授。自1996年起，他在美国普渡大学（Purdue University）先后任副教授、教授；此前任教于南加州大学（University of Southern California），并在纽约大学柯朗数学科学研究所（Courant Institute of Mathematical Science at New York University）和布鲁克海文国家实验室（Brookhaven National Laboratory）从事博士后研究。此外，蔡教授连续二十余年担任劳伦斯利弗莫尔国家实验室（Lawrence Livermore National Laboratory）暑期访问学者。
蔡智强教授长期专注于偏微分方程的数值求解及其在流体力学、固体力学、电磁学和多 孔介质流动等领域的应用。其研究涵盖多种离散化方法（如有限体积法、有限元法、多尺度有限元法、最小二乘法等），以及计算模拟的精度控制和复杂系统的自适应算法等。 近年来，他的研究重点转向运用科学机器学习（scientific machine learning）方法解决科学计算中的高复杂度问题。
