Learning finite difference methods for reaction-diffusion type equations with FCNN

In this paper, we propose Five-point stencil CNN (FCNN) containing a five-point stencil kernel and a trainable approximation function. We consider reaction-diffusion type equations including heat, Fisher's, Allen-Cahn equations, and reaction-diffusion equations with trigonometric functions. Our proposed FCNN is trained well using few data and then can predict reaction-diffusion evolutions with unseen initial conditions. Also, our FCNN is trained well in the case of using noisy train data. We present various simulation results to demonstrate that our proposed FCNN is working well.