Ensemble-based uncertainty quantification and global sensitivity analysis of environmental models requires generating large ensembles of parameter-sets. This can already be difficult when analyzing moderately complex models based on partial differential equations because many parameter combinations cause an implausible model behavior even though the individual parameters are within plausible ranges. In this work, we apply Gaussian Process Emulators (GPE) as surrogate models in a sampling scheme. In an active-training phase of the surrogate model, we target the behavioral boundary of the parameter space before sampling this behavioral part of the parameter space more evenly by passive sampling. Active learning increases the subsequent sampling efficiency, but its additional costs pay off only for a sufficiently large sample size. We exemplify our idea with a catchment-scale subsurface flow model with uncertain material properties, boundary conditions, and geometric descriptors of the geological structure. We then perform a global-sensitivity analysis of the resulting behavioral dataset using the active-subspace method, which requires approximating the local sensitivities of the target quantity with respect to all parameters at all sampled locations in parameter space. The Gaussian Process Emulator implicitly provides an analytical expression for this gradient, thus improving the accuracy of the active-subspace construction. When applying the GPE-based preselection, 70–90% of the samples were confirmed to be behavioral by running the full model, whereas only 0.5% of the samples were behavioral in standard Monte-Carlo sampling without preselection. The GPE method also provided local sensitivities at minimal additional costs.

基于集合的不确定性量化和环境模型的全局敏感性分析需要生成大量的参数集。当基于偏微分方程分析适度复杂的模型时，这已经很困难，因为即使单个参数在合理范围内，许多参数组合也会导致难以置信的模型行为。在这项工作中，我们将高斯过程仿真器（GPE）应用为抽样方案中的替代模型。在替代模型的主动训练阶段，在通过被动采样对参数空间的这一行为部分进行更均匀采样之前，我们以参数空间的行为边界为目标。主动学习可提高随后的采样效率，但是其额外成本只有在足够大的样本量时才能得到回报。我们用集水规模的地下流动模型来说明我们的想法，该模型具有不确定的材料属性，边界条件和地质结构的几何描述。然后，我们使用活动子空间方法对所得行为数据集进行全局敏感性分析，这需要针对参数空间中所有采样位置处的所有参数，近似目标量的局部敏感性。高斯过程仿真器隐式提供了此梯度的解析表达式，从而提高了活动子空间构造的准确性。当应用基于GPE的预选时，通过运行完整模型可以确认70-90％的样本是有行为的，而在没有预选的标准蒙特卡洛采样中只有0.5％的样本是有行为的。