We present a computational framework for dimension reduction and surrogate modeling to accelerate uncertainty quantification in computationally intensive models with high-dimensional inputs and function-valued outputs. Our driving application is multiphase flow in saturated-unsaturated porous media in the context of radioactive waste storage. For fast input dimension reduction, we utilize an approximate global sensitivity measure, for function-valued outputs, motivated by ideas from the active subspace methods. The proposed approach does not require expensive gradient computations. We generate an efficient surrogate model by combining a truncated Karhunen-Loéve (KL) expansion of the output with polynomial chaos expansions, for the output KL modes, constructed in the reduced parameter space. We demonstrate the effectiveness of the proposed surrogate modeling approach with a comprehensive set of numerical experiments, where we consider a number of function-valued (temporally or spatially distributed) QoIs.

我们提出了一个用于降维和代理建模的计算框架，以加速具有高维输入和函数值输出的计算密集型模型中的不确定性量化。我们的主要应用是在放射性废物储存环境中饱和-不饱和多孔介质中的多相流。对于快速输入降维，我们使用近似全局灵敏度度量，用于函数值输出，其灵感来自活动子空间方法的想法。所提出的方法不需要昂贵的梯度计算。我们通过将输出的截断 Karhunen-Loéve (KL) 展开与多项式混沌展开相结合来生成有效的代理模型，对于输出 KL 模式，在减少的参数空间中构建。