W7-X中电子尺度湍流建模的机器学习方法
Machine Learning for Electron-Scale Turbulence Modeling in W7-X
AI总结：
针对Wendelstein 7-X仿星器中电子温度梯度湍流，利用主动学习回归构建物理引导的标度律降阶模型，预测热流并评估插值与外推性能。
摘要：
构建湍流输运的降阶模型对于加速剖面预测和实现参数探索、设计优化等多查询任务至关重要。本文研究了Wendelstein 7-X (W7-X)仿星器中电子温度梯度(ETG)湍流的机器学习驱动降阶模型。我们开发了物理引导的标度律，以预测七个径向位置处的ETG热流作为三个关键等离子体参数的函数：归一化电子温度梯度($ω_{T_e}$)、归一化电子温度与密度梯度之比($η_e$)以及电子与离子温度比($τ$)。模型系数通过回归结合主动学习策略确定。该过程使用低基数稀疏网格训练数据初始化标度律，并通过从现有模拟数据库中选择信息量最大的样本迭代丰富训练集。使用每个径向位置超过393个点的样本外数据集评估模型的预测性能。利用在七个训练径向位置识别的系数，我们进一步推导了标度律系数作为径向位置函数的回归参数化。然后在训练中未使用的三个额外径向位置评估所得模型，包括插值和适度外推情况。总体而言，我们的降阶模型表现出良好的预测性能，并达到与原始参考模拟相当的精度，包括在插值和适度外推范围内。一个重要发现是，单一的径向无关模型无法充分描述W7-X核心区的ETG输运，表明存在当前公式未捕捉的几何依赖物理。
英文摘要：
Constructing reduced models for turbulent transport is essential for accelerating profile predictions and enabling many-query tasks such as parameter exploration and design optimization. This work investigates machine-learning-driven reduced models for Electron Temperature Gradient (ETG) turbulence in the Wendelstein 7-X (W7-X) stellarator. We develop physics-guided scaling laws to predict the ETG heat flux at seven radial locations as functions of three key plasma parameters: the normalized electron temperature gradient ($ω_{T_e}$), the ratio of normalized electron temperature and density gradients ($η_e$), and the electron-to-ion temperature ratio ($τ$). The model coefficients are determined through regression combined with an active learning strategy. The procedure initializes the scaling laws using low-cardinality sparse-grid training data and iteratively enriches the training set by selecting maximally informative samples from an existing simulation database. The predictive performance of the models is assessed using out-of-sample datasets comprising more than $393$ points per radial location. Using the coefficients identified at the seven training radial locations, we further derive regression-based parameterizations for the scaling-law coefficients as functions of radial position. The resulting models are then evaluated at three additional radial locations not used during training, including both interpolation and moderate extrapolation cases. Overall, our reduced models demonstrate good predictive performance and achieve accuracy comparable to the original reference simulations, including in interpolation and moderate extrapolation regimes. An important finding is that a single radius-independent model cannot adequately describe ETG transport across the W7-X core, suggesting the presence of geometry-dependent physics not captured by the present formulation.
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