题 目：Neural Networks in Scientific Computing (SciML): Basics and Challenging Questions
主讲人：蔡智强 教授
单 位：大亚湾大学
时 间：2026年3月24日 9:00
地 点：学院二楼会议室
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_x0002_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?
简 介：Before joining Great Bay University, Dongguan, Guangdong as a chair professor, Dr. Cai had been at the Purdue University since 1996 as an associate and full professor, at the University of Southern California as assistant professor, and at the Courant Institute of Mathematical Science at New York University and at Brookhaven National Laboratory as postdoc associate. He had been a summer visiting faculty at the Lawrence Livermore National Laboratory for over two decades. His research is on numerical solution of partial differential equations with applications in fluid and solid mechanics, electromagnetics, and flow in porous media. His primary interests include discretization methods (finite volume, finite element and multiscale finite element, and least-squares), accuracy control of computer simulations, and self-adaptive numerical methods for complex systems before focusing on neural network for solving challenging partial differential equations.
