报告题目：Numerical methods for solving nonlinear differential equations

报告时间：2021年6月28日，星期一，上午9:00-11:00

腾讯会议 ID：176 251 390

报告人：Wenrui Hao （郝文瑞），Pennsylvania State University

报告摘要：

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.

报告人简介：

    郝文瑞，宾州州立大学数学系助理教授。2013年获美国圣母大学理学博士学位（数学）。2013-2016年，在美国俄亥俄州立大学数学生命科学研究所博士后，2016年至今在美国宾州州立大学数学系任助理教授。主要研究方向为非线性偏微分方程的求解及其在生命科学当中的应用，已发表学术论文50多篇。