Improving ideal MHD equilibrium accuracy with physics-informed neural networks

TL;DR

This paper introduces a physics-informed neural network approach to compute 3D MHD equilibria, achieving competitive accuracy and establishing a new lower bound for force residuals compared to traditional solvers.

Contribution

It presents a novel neural network-based method for MHD equilibrium computation that minimizes the nonlinear force residual, offering potential improvements over conventional solvers.

Findings

Neural networks achieve comparable residuals to existing codes.

Lower residual minima are obtained with neural networks, setting a new lower bound.

Method shows promise for computing equilibria over continuous distributions.

Abstract

We present a novel approach to compute three-dimensional Magnetohydrodynamic equilibria by parametrizing Fourier modes with artificial neural networks and compare it to equilibria computed by conventional solvers. The full nonlinear global force residual across the volume in real space is then minimized with first order optimizers. Already,we observe competitive computational cost to arrive at the same minimum residuals computed by existing codes. With increased computational cost,lower minima of the residual are achieved by the neural networks,establishing a new lower bound for the force residual. We use minimally complex neural networks,and we expect significant improvements for solving not only single equilibria with neural networks,but also for computing neural network models valid over continuous distributions of equilibria.