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—usually done computationally—serve as input for the assessment of a number of important physics questions. The variational moments equilibrium code (VMEC) 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 (e.g. Bayesian scientific modeling, real-time plasma control). Access to fast MHD equilibria 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 Wendelstein 7-X. Magnetic configurations that extensively cover the device operational space, and plasma profiles with volume-averaged normalized plasma pressure ⟨β⟩ (β = ) 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 NNs are found to outperform feed-forward fully-connected NNs. The achieved normalized root-mean-squared error, the ratio between the regression error and the spread of the data, 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.

在磁约束聚变研究中，实现高等离子体压力是实现净能量生产目标的关键。磁流体动力学 (MHD) 模型用于自洽地计算等离子体压力对用于限制等离子体的磁场的影响。这种 MHD 计算——通常是通过计算完成的——作为评估许多重要物理问题的输入。变分矩平衡代码 (VMEC) 是最广泛用于评估 3D 理想 MHD 平衡的，在仿星器中尤为突出。然而，考虑到计算成本，它很少用于大规模或在线应用（例如贝叶斯科学建模、实时等离子体控制）。获得快速 MHD 平衡是融合研究中的一个具有挑战性的问题，一种机器学习可以有效解决的问题。在本文中，我们提出了能够快速计算 Wendelstein 7-X 平衡磁场的人工神经网络 (NN) 模型。广泛覆盖设备操作空间的磁性配置，以及具有体积平均归一化等离子体压力的等离子体轮廓 ⟨β ⟩ ( β =) 高达 5% 的非零净环形电流包含在数据集中。通过使用卷积层，可以使用单个网络有效地计算磁通量表面的频谱表示。为了发现更好的模型，进行了贝叶斯超参数搜索，发现 3D 卷积神经网络优于前馈全连接神经网络。实现的归一化均方根误差（回归误差与数据分布之间的比率）在不同场景中的范围从 1% 到 20%。单个均衡的模型推理时间为毫秒级。最后，这项工作展示了用于 VMEC 的快速 NN 替代模型的可行性，并开辟了新的操作场景，其中目标应用程序可以以前所未有的规模利用磁平衡。