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High-$\langle \beta \rangle$ operations require a fast and robust inference of plasma parameters with a self-consistent MHD equilibrium. Precalculated MHD equilibria are usually employed at W7-X due to the high computational cost. To address this, we couple a physics-regularized NN model that approximates the ideal-MHD equilibrium with the Bayesian modeling framework Minerva. We show the fast and robust inference of plasma profiles (electron temperature and density) with a self-consistent MHD equilibrium approximated by the NN model. We investigate the robustness of the inference across diverse synthetic W7-X plasma scenarios. The inferred plasma parameters and their uncertainties are compatible with the parameters inferred using the VMEC, and the inference time is reduced by more than two orders of magnitude. This work suggests that MHD self-consistent inferences of plasma parameters can be performed between shots., Comment: 18 pages, 6 figures

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., Comment: 47 pages, 28 figures, published in Nuclear Fusion

In magnetic confinement fusion research, the achievement of high plasma pressure is key to reaching the goal of net energy production. The magnetohydrodynamic (MHD) model is used to self-consistently calculate the effects the plasma pressure induces on the magnetic field used to confine the plasma. Such MHD calculations serve as input for the assessment of a number of important physics questions. The VMEC code is the most widely used to evaluate 3D ideal-MHD equilibria, as prominently present in stellarators. However, considering the computational cost, it is rarely used in large-scale or online applications. Access to fast MHD equilbria is a challenging problem in fusion research, one which machine learning could effectively address. In this paper, we present artificial neural network (NN) models able to quickly compute the equilibrium magnetic field of W7-X. Magnetic configurations that extensively cover the device operational space, and plasma profiles with volume averaged normalized plasma pressure $\langle \beta \rangle$ ($\beta$ = $\frac{2 \mu_0 p}{B^2}$) up to 5% and non-zero net toroidal current are included in the data set. By using convolutional layers, the spectral representation of the magnetic flux surfaces can be efficiently computed with a single network. To discover better models, a Bayesian hyper-parameter search is carried out, and 3D convolutional neural networks are found to outperform feed-forward fully-connected neural networks. The achieved normalized root-mean-squared error ranges from 1% to 20% across the different scenarios. The model inference time for a single equilibrium is on the order of milliseconds. Finally, this work shows the feasibility of a fast NN drop-in surrogate model for VMEC, and it opens up new operational scenarios where target applications could make use of magnetic equilibria at unprecedented scales., Comment: 24 pages, 16 figures. Accepted for publication to Nuclear Fusion