Nonlinear scientific computing arising from math biology 

Many nonlinear systems are arising from biology such as the pattern formation of nonlinear differential equations and data-driven modeling by using neural networks. In this talk, I will present a systematic computational approach to solve these nonlinear systems in biology. In specific, 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. Several benchmark problems in pattern formation will be used to illustrate the idea. Then I will also introduce a homotopy training algorithm to solve the nonlinear optimization problem of biological data-driven modeling via building the neural network adaptively. Examples of assessing cardiovascular risk by pulse wave data will be used to demonstrate the efficiency of the homotopy training algorithm.