Nov 10, 2023
Contact: Junping Shi
Summary
{{https://sites.psu.edu/whao/, Wenrui Hao}} (Penn State University)
Full Description
Title: Exploring Solution Structures in Nonlinear Models of Pattern Formation
Abstract:
Within the field of math biology, numerous nonlinear systems, particularly those pertaining to pattern formation described by nonlinear differential equations, present intricate challenges. In this talk, I will introduce a systematic computational approach designed to tackle these complex nonlinear biological systems. Specifically, I will introduce the application of the homotopy continuation technique, a powerful tool for computing multiple steady states in nonlinear differential equations, and explore the relationship between these steady states and various parameters. To illustrate these concepts, I will employ several benchmark problems in pattern formation. Additionally, I will demonstrate the utility of neural networks in overcoming the curse of dimensionality introduced by the homotopy method when solving large-scale systems, thereby enhancing the efficiency and effectiveness of our computational approach.
