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

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 desirable 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.