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