Solving the Magnetohydrostatic Equations with Physics-Informed Neural Nets

We present a novel Physics-Informed Neural Network (PINN) which is trained on output from a numerical magnetohydrostatic model. The architecture and construction of the PINN are discussed in detail. We demonstrate results on both analytic solutions and ones extrapolated numerically from boundary conditions in the SHARP dataset. We discuss the tradeoff between accuracy and speed of the Machine Learning approach, and a possible application in space weather prediction.