Groundwater flow models are usually subject to uncertainty as a consequence of the random representation of the conductivity field. In this paper, we use a Gaussian process model based on the simultaneous dimension reduction in the conductivity input and flow field output spaces in order quantify the uncertainty in a model describing the flow of an incompressible liquid in a random heterogeneous porous medium. We show how to significantly reduce the dimensionality of the high-dimensional input and output spaces while retaining the qualitative features of the original model, and secondly how to build a surrogate model for solving the reduced-order stochastic model. A Monte Carlo uncertainty analysis on the full-order model is used for validation of the surrogate model.

中文翻译：

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基于同时随机模型降维的高度非均质多孔介质中流动和输运的不确定性量化

由于电导率场的随机表示，地下水流模型通常会受到不确定性的影响。在本文中，我们使用基于电导率输入和流场输出空间中同时降维的高斯过程模型来量化描述随机非均质多孔介质中不可压缩液体流动的模型中的不确定性。我们展示了如何在保留原始模型的定性特征的同时显着降低高维输入和输出空间的维数，其次如何构建用于求解降阶随机模型的代理模型。对全阶模型的蒙特卡罗不确定性分析用于验证代理模型。