Approximating Families of Sharp Solutions to Fisher's Equation with Physics-Informed Neural Networks

This paper employs physics-informed neural networks (PINNs) to solve Fisher's equation, a fundamental representation of a reaction-diffusion system with both simplicity and significance. The focus lies specifically in investigating Fisher's equation under conditions of large reaction rate coefficients, wherein solutions manifest as traveling waves, posing a challenge for numerical methods due to the occurring steepness of the wave front. To address optimization challenges associated with the standard PINN approach, a residual weighting scheme is introduced. This scheme is designed to …

challenge cs.lg diffusion equation families fisher focus lies manifest networks neural networks paper physics physics-informed rate representation significance simplicity solutions solve