Numerical solution of reaction-diffusion equations by machine learning techniques. The case of zero Neumann boundary conditions and long integration times.

Reaction-Diffusion systems are very important to understand nonlinear phenomena. In the present talk, we discuss two issues when solving RD systems using machine learning methods. The first issue is related to the implementation of zero Neumann boundary conditions. The second issue is related to the long integration time of an equation. For the first problem, and based on the PINN idea, we explore four different methods to implement the boundary conditions. For the second issue, we present a multidomain approach. To understand the presented
techniques, three equations are solved. The diffusion, bistable and Gray-Scott equations. We end up with a discussion about the comparison of the methods.