Deep-Learning based Inverse Modeling Approaches: A Subsurface Flow Example

Abstract

Deep-learning has achieved good performance and shown great potential for solving forward and inverse problems. In this work, two categories of innovative deep-learning based inverse modeling methods are proposed and compared. The first category is deep-learning surrogate-based inversion methods, in which the Theory-guided Neural Network (TgNN) is constructed as a deep-learning surrogate for problems with uncertain model parameters. By incorporating physical laws and other constraints, the TgNN surrogate can be constructed with limited simulation runs and accelerate the inversion process significantly. Three TgNN surrogate-based inversion methods are proposed, including the gradient method, the iterative ensemble smoother (IES), and the training method. The second category is direct-deep-learning-inversion methods, in which TgNN constrained with geostatistical information, named TgNN-geo, is proposed for direct inverse modeling. In TgNN-geo, two neural networks are introduced to approximate the respective random model parameters and the solution. Since the prior geostatistical information can be incorporated, the direct-inversion method based on TgNN-geo works well, even in cases with sparse spatial measurements or imprecise prior statistics. Although the proposed deep-learning based inverse modeling methods are general in nature, and thus applicable to a wide variety of problems, they are tested with several subsurface flow problems. It is found that satisfactory results are obtained with a high efficiency. Moreover, both the advantages and disadvantages are further analyzed for the proposed two categories of deep-learning based inversion methods.

arXiv comment53 pages, 22 figures, 7 tables

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• Weak Form Theory-guided Neural Network (TgNN-wf) for Deep Learning of Subsurface Single and Two-phase Flow
• Surrogate and inverse modeling for two-phase flow in porous media via theory-guided convolutional neural network
• Probabilistic model-error assessment of deep learning proxies: an application to real-time inversion of borehole electromagnetic measurements
• Direct multi-modal inversion of geophysical logs using deep learning
• Transfer learning-based physics-informed convolutional neural network for simulating flow in porous media with time-varying controls