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Science and Mathematics

Special Lecture Series in Mathematics

March 29, 2024 at 3:00pm – 4:00pm EDT

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Title: Numerical Analysis with Deep Neural Networks

Speaker: Yuesheng Xu

Abstract: This four-hour short course is to present to graduate students in applied mathematics and engineering an introduction to 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. This talk 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

Date: March 29, April 5, April 12 and April 19 (Friday every week) via Zoom.

Short Bio: Prof. Yuesheng Xu is a professor emeritus at Syracuse University and Professor of Data Science and Mathematics at Old Dominion University. He was the Managing Editor and is an Associate Editor of Advances in Computational Mathematics. His research interest includes multiscale methods for Fredholm integral equations, wavelet analysis, signal/image processing, machine learning and neural networks. His research is currently supported by NSF and NIH.

The “Special Lecture in Mathematics” series is partly supported by the Douglas R. Anderson Faculty Scholarship.

This event was published on March 21, 2024.

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