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.

翻译：构建湍流输运的简化模型对于加速剖面预测及实现参数探索与设计优化等多次查询任务至关重要。本文研究了温德尔施泰因7-X（W7-X）仿星器中电子温度梯度（ETG）湍流的机器学习驱动简化模型。我们发展了物理引导的标度律，以预测七个径向位置处ETG热通量随三个关键等离子体参数的变化：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。该流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取信息最丰富的样本迭代丰富训练集。利用包含每个径向位置超过$393$个点的离群数据集评估模型预测性能。基于七个训练径向位置确定的系数，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。随后在训练中未使用的三个额外径向位置（包括插值和适度外推情况）评估所得模型。总体而言，我们的简化模型展现出良好的预测性能，并在插值与适度外推区间内达到与原始参考模拟相当的精度。一个关键发现是：单一半径无关模型无法充分描述W7-X芯部ETG输运，表明当前公式未捕捉到依赖于几何结构的物理机制。