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Machine learning for accelerating macroscopic parameters prediction for poroelasticity problem in stochastic media. (English) Zbl 07308036
Summary: 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.

MSC:
74 Mechanics of deformable solids
82 Statistical mechanics, structure of matter
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