Efficient Deep Learning Techniques for Multiphase Flow Simulation in Heterogeneous Porous Media

Abstract

We present efficient deep learning techniques for approximating flow and transport equations for both single phase and two-phase flow problems. The proposed methods take advantages of the sparsity structures in the underlying discrete systems and can be served as efficient alternatives to the system solvers at the full order. In particular, for the flow problem, we design a network with convolutional and locally connected layers to perform model reductions. Moreover, we employ a custom loss function to impose local mass conservation constraints. This helps to preserve the physical property of velocity solution which we are interested in learning. For the saturation problem, we propose a residual type of network to approximate the dynamics. Our main contribution here is the design of custom sparsely connected layers which take into account the inherent sparse interaction between the input and output. After training, the approximated feed-forward map can be applied iteratively to predict solutions in the long range. Our trained networks, especially in two-phase flow where the maps are nonlinear, show their great potential in accurately approximating the underlying physical system and improvement in computational efficiency. Some numerical experiments are performed and discussed to demonstrate the performance of our proposed techniques.

References in corpus (19)

• Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data
• Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations
• Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification
• Generalized Multiscale Finite Element Methods (GMsFEM)
• Neural Ordinary Differential Equations
• Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations
• Data Driven Governing Equations Approximation Using Deep Neural Networks
• Deep Fluids: A Generative Network for Parameterized Fluid Simulations
• An adaptive GMsFEM for high-contrast flow problems
• Non-local Multi-continua Upscaling for Flows in Heterogeneous Fractured Media
• Learning Functions: When Is Deep Better Than Shallow
• Global-Local Nonlinear Model Reduction for Flows in Heterogeneous Porous Media
• A multiscale neural network based on hierarchical matrices
• Deep Multiscale Model Learning
• A Multiscale Method for Porous Microstructures
• Generalized Multiscale Finite Element Method for Elasticity Equations
• Multiscale Empirical Interpolation for Solving Nonlinear PDEs using Generalized Multiscale Finite Element Methods
• Deep Global Model Reduction Learning in Porous Media Flow Simulation
• Prediction of Discretization of GMsFEM using Deep Learning

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• ML-LBM: Machine Learning Aided Flow Simulation in Porous Media
• Physics-informed Neural Networks for Solving Inverse Problems of Nonlinear Biot's Equations: Batch Training
• Bayesian Sparse learning with preconditioned stochastic gradient MCMC and its applications
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• MFPC-Net: Multi-fidelity Physics-Constrained Neural Process