Numerical methods for solving nonlinear differential equations from homotopy methods to machine learning

Wenrui Hao (Pennsylvania State University)

Abstract

Many systems of nonlinear differential equations 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 differential equations. First, 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 use the machine learning techniques to solve nonlinear differential equations and learn the multiple solutions by developing a randomized Newton's method for the neural network discretization. Several benchmark problems will be used to illustrate these ideas.

Zoom Link: https://ccny.zoom.us/j/92057419965

Zoom ID: 92057419965