In this paper, we consider a coarse grid approximation (numerical homogenization and multiscale finite element method) for the poroelasticity problem with stochastic properties. The proposed method is based on the construction of deep neural network for fast calculation of macroscopic parameters for a coarse grid approximation of the problem. We train neural networks on a set of selected realizations of local microscale stochastic fields and macroscale characteristics (effective property tensor or local matrix). We construct a deep learning method through a convolutional neural network (CNN) to learn a map between stochastic fields and macroscopic parameters. Numerical results are presented for two and three-dimensional model problems and show that the proposed method provides fast and accurate effective property predictions.

在本文中，我们考虑具有随机性质的多孔弹性问题的粗网格近似（数值均化和多尺度有限元方法）。所提出的方法是基于深度神经网络的构建，用于快速计算宏观参数，以实现问题的粗网格近似。我们在局部微观随机场和宏观特征（有效属性张量或局部矩阵）的一组选定实现上训练神经网络。我们通过卷积神经网络（CNN）构建深度学习方法，以学习随机场与宏观参数之间的映射。给出了二维和三维模型问题的数值结果，表明该方法提供了快速，准确的有效性能预测。