Homotopy Methods for Solving Nonlinear Systems: from Nonlinear PDE to Machine Learning

Date
3/18/2019
Location
4:30PM at REC 113
Speaker
Prof. Wenrui Hao, Penn State University.
Title
Homotopy Methods for Solving Nonlinear Systems: from Nonlinear PDE to Machine Learning
Host
Guang Lin
Description

This talk will cover some recent progress on homotopy methods to solve nonlinear systems. I will start with homotopy methods for solving nonlinear PDEs with multiple solutions and bifurcations by coupling with domain decomposition and reduced basis methods. Examples from hyperbolic systems and free boundary problems will be used to demonstrate the ideas. Then a homotopy method will be introduced for solving maximum entropy problem to reconstruct probability density functions based on given data. I will also talk about a homotopy training algorithm for nonlinear optimization arising from machine learning.