Improving ideal MHD equilibrium accuracy with physics-informed neural networks

Abstract

We present a novel approach to compute three-dimensional magnetohydrodynamic equilibria with isotropic pressure profiles and nested surfaces by parametrizing Fourier modes with artificial neural networks (NNs). The full nonlinear global force residual of single equilibria across the volume in real space is then minimized with first order optimizers and compared to equilibria computed by conventional solvers. Already, we observe competitive computational cost to arrive at the same minimum residuals computable with existing codes. With increased computational cost, lower minima of the residual are computable with the NNs than with any other tested solver, establishing a new lower bound for the force residual. We use minimally complex NNs, and we expect significant improvements for solving not only single equilibria with NNs, but also for creating NN models valid over continuous distributions of equilibria.