Mitigating Coordinate Transformation for Solving Partial Differential Equations with Physic-Informed Neural Networks

In this work, we investigate some coordinate systems to solve partial differential equations (PDEs) using a neural network. We approximate the solution using physics-informed neural networks (PINNs) both before and after the coordinate transformation for two cases: a coordinate system with periodicity and without periodicity. We demonstrate that PINNs with Cartesian coordinate shows better approximation accuracy. This implies in PINNs training the Cartesian coordinate system is superior to the other coordinate systems derived by coordinate transformation. To the best of our knowledge, this is the first work to test training of PINNs by modifying PDEs according to the boundary shape.