top of page
Simultaneous Neural Network Approximations for Smooth Functions
We establish in this talk approximation results of deep neural networks for smooth functions measured in Sobolev norms, motivated by recent development of numerical solvers for partial differential equations using deep neural networks. Our approximation results are nonasymptotic in the sense that the error bounds are explicitly characterized in terms of both the width and depth of the networks simultaneously with all involved constants explicitly determined. This is joint work Haizhao Yang (University of Maryland).
Dr. Sean Y S HON is now an Assistant Professor at Hong Kong Baptist University. He has a keen interest in numerical analysis and mathematics of data science.Sean's current research focuses on developing theory and numerical methods for evolutionary partial differential equations and deep learning. Dr. Sean is also interested in efficient solvers for interfacial motions and preconditioning on Toeplitz-related systems. These research areas play crucial roles in scientific computation. For example, accurate numerical methods are needed for modelling multi-phase flow and spiral crystal growth, and image segmentation. Since the exact solutions of these problems are often unavailable, it is of great importance to develop efficient yet flexible methods which provide numerical approximations. As for Toeplitz-related systems, they are ubiquitous in maths and physics: they arise in numerical partial differential equations, approximation theory, compressed sensing, image processing, to name just a few. Thus it is essential to develop preconditioners to speed up the matrix inversion that involves such Toeplitz structure.
bottom of page