Quantifying uncertainty in predictive simulations for real-world problems is of paramount importance - and far from trivial, mainly due to the large number of stochastic parameters and significant computational requirements. Adaptive sparse grid approximations are an established approach to overcome these challenges. However, standard adaptivity is based on global information, thus properties such as lower intrinsic stochastic dimensionality or anisotropic coupling of the input directions, which are common in practical applications, are not fully exploited. We propose a novel structure-exploiting dimension-adaptive sparse grid approximation methodology using Sobol' decompositions in each subspace to introduce a sensitivity scoring system to drive the adaptive process. By employing sensitivity information, we explore and exploit the anisotropic coupling of the stochastic inputs as well as the lower intrinsic stochastic dimensionality. The proposed approach is generic, i.e., it can be formulated in terms of arbitrary approximation operators and point sets. In particular, we consider sparse grid interpolation and pseudo-spectral projection constructed on (L)-Leja sequences. The power and usefulness of the proposed method is demonstrated by applying it to the analysis of gyrokinetic microinstabilities in fusion plasmas, one of the key scientific problems in plasma physics and fusion research. In this context, it is shown that a 12D parameter space can be scanned very efficiently, gaining more than an order of magnitude in computational cost over the standard adaptive approach. Moreover, it allows for the uncertainty propagation and sensitivity analysis in higher-dimensional plasma microturbulence problems, which would be almost impossible to tackle with standard screening approaches.

量化针对现实问题的预测模拟中的不确定性至关重要-绝非易事，主要是由于大量的随机参数和大量的计算需求。自适应稀疏网格近似是克服这些挑战的既定方法。但是，标准适应性基于全局信息，因此，在实际应用中常见的诸如较低的固有随机维数或输入方向的各向异性耦合之类的属性并未得到充分利用。我们提出了一种在每个子空间中利用Sobol分解的结构利用维数的稀疏网格近似方法，以引入灵敏度评分系统来驱动自适应过程。通过使用敏感性信息，我们探索并利用了随机输入的各向异性耦合以及较低的内在随机维数。所提出的方法是通用的，即可以根据任意逼近算子和点集来表示。特别地，我们考虑在（L）-Leja序列上构造的稀疏网格插值和伪谱投影。通过将其应用于聚变等离子体中的回旋动力学微不稳定性分析，证明了该方法的强大功能和实用性，这是等离子体物理和聚变研究的关键科学问题之一。在这种情况下，显示了可以非常有效地扫描12D参数空间，比标准自适应方法获得的计算成本高出一个数量级。此外，