Generative adversarial network as a stochastic subsurface model reconstruction

Azevedo, Leonardo; Paneiro, Gustavo; Santos, A. S.; Soares, Amílcar

doi:10.1007/s10596-020-09978-x

Cited by 37 publications

(14 citation statements)

References 21 publications

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“…Tools based on deep-learning have been shown to be applicable for such geological parameterizations. Specific approaches include those based on variational autoencoders (VAEs) [18,19] and generative adversarial networks (GANs) [20,21,22,23,24,25,26,27]. Algorithms based on a combination of VAE and GAN have also been devised [7].…”

Section: Introductionmentioning

confidence: 99%

A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problems

Tang

Liu

Durlofsky

2020

Journal of Computational Physics

228

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A deep-learning-based surrogate model is developed and applied for predicting dynamic subsurface flow in channelized geological models. The surrogate model is based on deep convolutional and recurrent neural network architectures, specifically a residual U-Net and a convolutional long short term memory recurrent network. Training samples entail global pressure and saturation maps, at a series of time steps, generated by simulating oil-water flow in many (1500 in our case) realizations of a 2D channelized system. After training, the 'recurrent R-U-Net' surrogate model is shown to be capable of accurately predicting dynamic pressure and saturation maps and well rates (e.g., time-varying oil and water rates at production wells) for new geological realizations. Assessments demonstrating high surrogatemodel accuracy are presented for an individual geological realization and for an ensemble of 500 test geomodels. The surrogate model is then used for the challenging problem of data assimilation (history matching) in a channelized system. For this study, posterior reservoir models are generated using the randomized maximum likelihood method, with the permeability field represented using the recently developed CNN-PCA parameterization. The flow responses required during the data assimilation procedure are provided by the recurrent R-U-Net. The overall approach is shown to lead to substantial reduction in prediction uncertainty. High-fidelity numerical simulation results for the posterior geomodels (generated by the surrogate-based data assimilation procedure) are shown to be in essential agreement with the recurrent R-U-Net predictions. The accuracy and dramatic speedup provided by 1 arXiv:1908.05823v1 [cs.LG] 16 Aug 2019 the surrogate model suggest that it may eventually enable the application of more formal posterior sampling methods in realistic problems. our case), this surrogate model can provide flow predictions in close agreement with the underlying flow simulator, but with a significant reduction in computational cost. Thus this approach enables the application of accurate but computationally demanding inverse modeling procedures.There has been extensive research on constructing surrogate models for subsurface flow prediction. These can be generally classified, based on the mathematical formulation, into physics-based and data-driven procedures (though these categories are not mutually exclusive). The physics-based methods typically neglect or simplify physical or numerical aspects of the problem, through, for example, reduced-physics modeling, coarse-grid modeling, or proper orthogonal decomposition (POD) based reduced-order modeling (ROM). A variety of POD-based ROMs, in which the state variables and the system of equations are projected into low-dimensional space and then solved, have been applied for a range of subsurface flow problems [1, 2, 3, 4, 5]. These ROMs can be effective, although they are generally only accurate when new (test) runs are sufficiently 'close' to training runs. In addition, the applicat...

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Section: Introductionmentioning

confidence: 99%

A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problems

Tang

Liu

Durlofsky

2020

Journal of Computational Physics

228

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“…CNN-based algorithms are, in general, more efficient and scalable. Examples involving CNNs include convolutional variational autoencoders (VAE) (Laloy et al 2017;Canchumun et al 2019) and deep convolutional generative adversarial networks (GAN) Elsheikh 2017, 2018;Dupont et al 2018;Mosser et al 2018;Laloy et al 2018Laloy et al , 2019Chan and Elsheikh 2020;Azevedo et al 2020). The combination of VAE and GAN has also been proposed by Mo et al (2020) and Canchumun et al (2020).…”

Section: Introductionmentioning

confidence: 99%

A Deep-Learning-Based Geological Parameterization for History Matching Complex Models

2019

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A new low-dimensional parameterization based on principal component analysis (PCA) and convolutional neural networks (CNN) is developed to represent complex geological models. The CNN-PCA method is inspired by recent developments in computer vision using deep learning. CNN-PCA can be viewed as a generalization of an existing optimization-based PCA (O-PCA) method. Both CNN-PCA and O-PCA entail post-processing a PCA model to better honor complex geological features. In CNN-PCA, rather than use a histogram-based regularization as in O-PCA, a new regularization involving a set of metrics for multipoint statistics is introduced. The metrics are based on summary statistics of the nonlinear filter responses of geological models to a pre-trained deep CNN. In addition, in the CNN-PCA formulation presented here, a convolutional neural network is trained as an explicit transform function that can post-process PCA models quickly. CNN-PCA is shown to provide both unconditional and conditional realizations that honor the geological features present in reference SGeMS geostatistical realizations for a binary channelized system. Flow statistics obtained through simulation of random CNN-PCA models closely match results for random SGeMS models for a demanding case in which O-PCA models lead to significant discrepancies. Results for history matching are also presented. In this assessment CNN-PCA is applied with derivative-free optimization, and a subspace randomized maximum likelihood method is used to provide multiple posterior models. Data assimilation and significant uncertainty reduction are achieved for existing wells, and physically reasonable predictions are also obtained for new wells.Finally, the CNN-PCA method is extended to a more complex non-stationary bimodal deltaic fan system, and is shown to provide high-quality realizations for this challenging example.

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“…Artificial neural networks have proven successful at embedding multiple sources of data [30,31] and mapping complex non-linear input-outputs relationships. In particular, techniques such as generative adversarial networks have been successful at enhancing the resolution of outputs and will be used to obtain the most detailed representation of the quantities of interest [32]. In addition, Gaussian processes are known for accommodating unstructured data, interpolating in a multidimensional fashion (space-time, scale-aware, multiple variables, etc.)…”

Section: Narrativementioning

confidence: 99%

Using AI to build a hydrobiogeochemical soil model

Drewniak

2021

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Generative adversarial network as a stochastic subsurface model reconstruction

Cited by 37 publications

References 21 publications

A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problems

A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problems

A Deep-Learning-Based Geological Parameterization for History Matching Complex Models

Using AI to build a hydrobiogeochemical soil model

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