Constructing reduced models for turbulent transport is essential for accelerating profile predictions and enabling many-query tasks such as uncertainty quantification, parameter scans, and design optimization. This paper presents machine-learning-driven reduced models for Electron Temperature Gradient (ETG) turbulence in the Wendelstein 7-X (W7-X) stellarator. Each model predicts the ETG heat flux as a function of three plasma parameters: the normalized electron temperature radial gradient ($ω_{T_e}$), the ratio of normalized electron temperature and density radial gradients ($η_e$), and the electron-to-ion temperature ratio ($τ$). We first construct models across seven radial locations using regression and an active machine-learning-based procedure. This process initializes models using low-cardinality sparse-grid training data and then iteratively refines their training sets by selecting the most informative points from a pre-existing simulation database. We evaluate the prediction capabilities of our models using out-of-sample datasets with over $393$ points per location, and $95\%$ prediction intervals are estimated via bootstrapping to assess prediction uncertainty. We then investigate the construction of generalized reduced models, including a generic, position-independent model, and assess their heat flux prediction capabilities at three additional locations. Our models demonstrate robust performance and predictive accuracy comparable to the original reference simulations, even when applied beyond the training domain.

翻译：构建湍流输运的降阶模型对于加速剖面预测以及实现不确定性量化、参数扫描和设计优化等多查询任务至关重要。本文提出了针对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。每个模型将ETG热通量预测为三个等离子体参数的函数：归一化电子温度径向梯度（$ω_{T_e}$）、归一化电子温度与密度径向梯度之比（$η_e$）以及电子-离子温度比（$τ$）。我们首先通过回归和基于主动机器学习的方法，在七个径向位置构建模型。该过程使用低基数稀疏网格训练数据初始化模型，然后通过从现有模拟数据库中选择信息量最大的点，迭代优化训练集。我们使用每个位置超过$393$个点的样本外数据集评估模型的预测能力，并通过自助法估计$95\\%$预测区间以评估预测不确定性。随后，我们研究广义降阶模型的构建，包括通用的位置无关模型，并评估其在三个额外位置的热通量预测能力。即使在训练域外应用时，我们的模型仍展现出稳健的性能和与原始参考模拟相当的预测精度。