Physics-regularized neural network of the ideal-MHD solution operator in Wendelstein 7-X configurations

TL;DR

This paper introduces a neural network model that efficiently approximates the ideal-MHD solution operator for Wendelstein 7-X stellarator configurations, enabling fast and accurate equilibrium reconstructions and optimization.

Contribution

The work presents a physics-regularized neural network that accurately models the 3D ideal-MHD solution operator, incorporating equilibrium symmetries and MHD constraints.

Findings

High accuracy in predicting equilibrium solutions

Faithful reconstruction of global equilibrium quantities

Effective optimization of stellarator magnetic configurations

Abstract

The computational cost of constructing 3D magnetohydrodynamic (MHD) equilibria is one of the limiting factors in stellarator research and design. Although data-driven approaches have been proposed to provide fast 3D MHD equilibria, the accuracy with which equilibrium properties are reconstructed is unknown. In this work, we describe an artificial neural network (NN) that quickly approximates the ideal-MHD solution operator in Wendelstein 7-X (W7-X) configurations. This model fulfils equilibrium symmetries by construction. The MHD force residual regularizes the solution of the NN to satisfy the ideal-MHD equations. The model predicts the equilibrium solution with high accuracy, and it faithfully reconstructs global equilibrium quantities and proxy functions used in stellarator optimization. We also optimize W7-X magnetic configurations, where desiderable configurations can be found in terms of fast particle confinement. This work demonstrates with which accuracy NN models can approximate the 3D ideal-MHD solution operator and reconstruct equilibrium properties of interest, and it suggests how they might be used to optimize stellarator magnetic configurations.