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

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 neu...

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Bibliographic Details
Published in:arXiv.org 2018-10
Main Authors: Vasilyeva, Maria, Tyrylgin, Aleksey
Format: Article
Language:English
Subjects:
Artificial neural networks
Elasticity
Machine learning
Mathematical analysis
Mathematical models
Neural networks
Poroelasticity
Properties (attributes)
Tensors
Three dimensional models
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Summary: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.
ISSN:2331-8422