Prediction of Discretization of GMsFEM using Deep Learning
For researchers working on multiscale simulations of flow in porous media, this work offers a faster alternative to recomputing GMsFEM ingredients when media properties change, though it is incremental as it applies existing deep learning techniques to a known bottleneck.
This paper uses deep learning to predict GMsFEM discretizations for multiscale flow problems in heterogeneous porous media, enabling fast recomputation for varying media. Numerical experiments demonstrate the neural network's predictive power and the resulting multiscale model's effectiveness in channelized flow problems.
In this paper, we propose a deep-learning-based approach to a class of multiscale problems. THe Generalized Multiscale Finite Element Method (GMsFEM) has been proven successful as a model reduction technique of flow problems in heterogeneous and high-contrast porous media. The key ingredients of GMsFEM include mutlsicale basis functions and coarse-scale parameters, which are obtained from solving local problems in each coarse neighborhood. Given a fixed medium, these quantities are precomputed by solving local problems in an offline stage, and result in a reduced-order model. However, these quantities have to be re-computed in case of varying media. The objective of our work is to make use of deep learning techniques to mimic the nonlinear relation between the permeability field and the GMsFEM discretizations, and use neural networks to perform fast computation of GMsFEM ingredients repeatedly for a class of media. We provide numerical experiments to investigate the predictive power of neural networks and the usefulness of the resultant multiscale model in solving channelized porous media flow problems.