### Numerical methods for solving nonlinear PDEs from homotopy methods to machine learning

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, October 12, 2020 - 14:00 for 1 hour (actually 50 minutes)
- Location
- https://bluejeans.com/884917410
- Speaker
- Wenrui Hao – Penn State University – wxh64@psu.edu

Many systems of nonlinear PDEs are arising from engineering and biology and have attracted research scientists to study the multiple solution structure such as pattern formation. In this talk, I will present several methods to compute the multiple solutions of nonlinear PDEs. In specific, I will introduce the homotopy continuation technique to compute the multiple steady states of nonlinear differential equations and also to explore the relationship between the number of steady-states and parameters. Then I will also introduce a randomized Newton's method to solve the nonlinear system arising from neural network discretization of the nonlinear PDEs. Several benchmark problems will be used to illustrate these ideas.