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

Accelerated Bayesian inference of plasma profiles with self-consistent MHD equilibria at W7-X via neural networks

“…In the proposed Minerva graph, the equilibrium model is employed only to provide the selfconsistent flux surface mapping. In this regard, [26] reports that the NN model achieves an average flux surface error of ≃ 0.6 mm. The NN model was trained on a large set of W7-X magnetic configurations, including the reference W7-X configurations [34], pressure profiles with 〈𝛽〉 up to 5%, and toroidal current profiles with 𝐼 tor up to 20 kA.…”

“…Function parametrization was used at W7-AS [14,22] and at W7-X [23][24][25]. More recently, [26] proposed a physics-regularized artificial neural network (NN) to approximate the ideal-MHD solution operator in W7-X configurations. Adopting machine learning (ML) models to approximate experimental equilibria can drastically accelerate sample-intensive applications (e.g., Bayesian inference) that require the computation of a MHD equilibrium.…”

“…In this paper, we show the fast (O (10 2 s)) and robust inference of plasma profiles (electron temperature and density) based on the Thomson scattering (TS) [27,28] and single channel dispersion interferometer (DI) [29] diagnostics with a self-consistent MHD equilibrium. The self-consistent MHD equilibrium is approximated by the physics-regularized NN model proposed in [26]. The NN model allows the efficient exploration of the full posterior distribution of plasma profiles with self-consistent MHD equilibria, yielding an estimation of the profile uncertainties.…”

“…This work considers two MHD equilibrium models: VMEC [32] and a physics-regularized NN [26]. The NN model has been integrated into Minerva with the ONNX Runtime framework [33].…”

“…W7-X experimental conditions in previous operational campaigns are well within the training data set [35]. For further information on the model architecture, training, and evaluation, please refer to [26].…”