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In this paper, we consider a numerical homogenization of the poroelasticityproblem with stochastic properties. The proposed method based on theconstruction of the deep neural network (DNN) for fast calculation of theeffective properties for a coarse grid approximation of the problem. We trainneural networks on the set of the selected realizations of the local microscalestochastic fields and macroscale characteristics (permeability and elasticitytensors). We construct a deep learning method through convolutional neuralnetwork (CNN) to learn a map between stochastic fields and effectiveproperties. Numerical results are presented for two and three-dimensional modelproblems and show that proposed method provide fast and accurate effectiveproperty predictions.

Machine learning for accelerating effective property prediction for poroelasticity problem in stochastic media