Equilibrium Solver using Physics-Informed Neural Networks

Magnetohydrodynamic (MHD) equilibrium codes are vital tools in the field of plasma physics. Often, a large number of equilibrium calculations are required for uncertainty quantification, stellarator optimization, and other inverse problems. Surrogate equilibrium solvers, such as Physics-Informed Neural Networks (PINNs), present an opportunity for addressing this class of computationally intensive problems. Here, we present initial results with PINN surrogates for the Grad-Shafranov equation. We explore the parameter space by varying the size of the model, number of collocation points, and boundary conditions, in order to map various tradeoffs (e.g., reconstruction error and computational speed).