[PAST EVENT] Mathematics Colloquium - Wenrui Hao, Penn State University

November 10, 2023
2pm - 3pm
Jones Hall, Room 302
200 Ukrop Way
Williamsburg, VA 23185Map this location
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  • Open to the public
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Title: Exploring Solution Structures in Nonlinear Models of Pattern Formation


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.


Junping Shi