Physics Informed Neural Networks – A Methodology Review

We investigate methodologies for improving the results of Physics Informed Neural Networks – Neural Networks that are trained with the supervision of relevant physical laws to solve specific problems. The methods we look into in this work are implementing the ResNet architecture and implementing Fourier Feature Mapping to allow the network to learn high-frequency features. We implement these methods to train a PINN on the 1D Burger's Equation. The predictions of the PINNs are compared against the solution from a Finite Difference Method based solver along with a baseline performance of a simple densely connected network.