# Mathematics Colloquium - Qingguo Hong

This event is in the past.

**When:**

January 19, 2023

2:45 p.m. to 3:45 p.m.

2:45 p.m. to 3:45 p.m.

**Event category:**Lecture

In-person

**Speaker:**Qinqguo Hong (Pennsylvania State University)

**Title:**Neural Networks for Fitting Data and Solving PDEs

**Abstract:**We develop new neural networks which are much easier to train for fitting data. These newly developed neural networks are motivated by finite element and spectral analysis. In addition, we apply neural networks for solving PDEs. We provide an a priori error analysis. We first show that the generalization error arising from discretizing the energy integrals is bounded. Then we show that the resulting constrained optimization problem can be efficiently solved using a greedy algorithm, which replaces gradient descent. These importantly give a consistent analysis which incorporates the optimization, approximation, and generalization aspects of the problem. Some numerical results will be presented.

## Contact

Department of Mathematics

3135772479

math@wayne.edu