Physics-informed neural networks for the reaction-diffusion Brusselator model

Abstract

In this work, we are interesting in solving the 1D and 2D nonlinear stiff reaction-diffusion Brusselator system using a machine learning technique called Physics-Informed Neural Networks (PINNs). PINN has been successful in a variety of science and engineering disciplines due to its ability of encoding physical laws, given by the PDE, into the neural network loss function in a way where the network must not only conform to the measurements, initial and boundary conditions, but also satisfy the governing equations. The utilization of PINN for Brusselator system is still in its infancy, with many questions to resolve. Performance of the framework is tested by solving some one and two dimensional problems with comparable numerical or analytical results. Validation of the results is investigated in terms of absolute error. The results showed that our PINN has well performed by producing a good accuracy on the given problems.