Numerical Analysis with Deep Neural Networks

Prof. Yuesheng Xu
Old Dominion University and Syracuse University, USA

Abstract

This four-talk lecture sequence aims to introduce numerical analysis with deep neural networks. Traditional function classes used in numerical analysis include polynomials, trigonometric polynomials, splines, finite elements, wavelets, and kernels. Deep neural networks were recently employed in numerical analysis as a class of approximation functions, demonstrating advantages over traditional function classes. These talks will cover the following topics:

1. Deep neural network representation of a function
2.  Optimization problems that learn a neural network
3. Adaptive solutions of integral equations with deep neural networks
4. Adaptive solutions of partial differential equations with deep neural networks.

Schedule

September 12nd, 9.30-11.30 Aula A
September 13nd, 9.30-11.30 Aula A