Building Flexible Physics-Informed Neural Networks with Fast Fourier Transform Analysis

Physics-Informed Neural Networks (PINNs) allow incorporating differential equations to model a system's behavior, and are well able to fit easily differentiable solutions with low-frequency components. They, however, fall short when attempting to learn high-frequency regions or boundary layers. This paper addresses one approach to fixing this by the addition of a Fourier Layer Neural Operator (FNO) to improve accuracy by better fitting regions with high frequency oscillations. We use as an example an underdamped RLC circuit, which resembles that of a boundary layer. The PINN architecture is built to be generalized over other applications, making it a flexible design for further expansion, especially for multiple layers of GPUs.