Parametrization of Stochastic Inputs Using Generative Adversarial Networks With Application in Geology

Chan, Shing; Elsheikh, Ahmed H.

doi:10.3389/frwa.2020.00005

Cited by 39 publications

(21 citation statements)

References 77 publications

(64 reference statements)

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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

249

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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

249

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“…Moreover, these latent variables are usually normally distributed, which satisfy the stationarity assumption of traditional inversion methods (e.g., ESMDA—Ensemble Smoother with Multiple Data Assimilation, Emerick & Reynolds, 2013). In hydrogeology and reservoir simulation, many recent studies have applied deep‐learning methods to parameterize the channelized nonGaussian hydraulic conductivity fields (e.g., Canchumuni et al., 2020, 2019b, 2019a; Chan & Elsheikh, 2020; Laloy et al., 2018, 2017; Y. Liu et al., 2019; M. Liu and Grana, 2018; Mo et al., 2020; Mosser et al., 2020; Tang et al., 2020). Deep neural networks were used after training to generate new conductivity realizations having similar features with those found in the training set.…”

Section: Introductionmentioning

confidence: 99%

Hydrogeophysical Characterization of Nonstationary DNAPL Source Zones by Integrating a Convolutional Variational Autoencoder and Ensemble Smoother

Kang

Kokkinaki

Kitanidis

et al. 2021

Water Resources Research

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Detailed characterization of dense nonaqueous phase liquid (DNAPL) source zone architecture (SZA) is essential for designing efficient remediation strategies. However, it is difficult to characterize a highly irregular and localized SZA, because traditional drilling investigations provide limited information. With limited data, the estimation accuracy of traditional geostatistical methods is strongly affected by the parameterization of the prior description of the SZA. To improve characterization performance, we parameterized the DNAPL saturation field using a physics‐based approach. We trained a convolutional variational autoencoder (CVAE) using data from multiphase modeling that captures the physics of DNAPL infiltration. The trained CVAE network was used in SZA inversion to obtain an improved prior DNAPL saturation field, instead of the typical stationary prior covariances. We then integrated the CVAE network into an iterative ensemble smoother (ES), to formulate a joint inversion framework. To overcome difficulties from limited/sparse data, we incorporated hydrogeological and geophysical datasets in the proposed inversion framework. To evaluate the performance of our method, we conducted numerical experiments in a hypothetical heterogeneous aquifer with an intricate SZA. The results show that the CVAE was an effective and efficient parameterization method which can capture the DNAPL infiltration patterns better than a Gaussian prior. The improved prior, combined with multisource datasets, can result in better resolution, and overall improved SZA characterization. In contrast to the standard ES method, the proposed framework reconstructed the SZA more accurately. We also demonstrated that DNAPL depletion behavior and dissolved concentration profiles can be predicted accurately using the estimated SZA.

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“…While these methods are well suited for Gaussian random fields, their performance for complex non‐Gaussian fields deserves further improvement (Canchumuni et al, ; Chan & Elsheikh, ; Laloy et al, ; Liu et al, ). Inspired by the recent success of deep learning in various areas including Earth science (Bergen et al, ; Reichstein et al, ; Zuo et al, ) and hydrology (Shen, ), its application in parameterization of non‐Gaussian conductivity fields has been reported in many recent studies (Canchumuni et al, , ; Chan & Elsheikh, , , ; Laloy et al, , ; Liu et al, ). Among these applications, generative adversarial network (GAN) (Goodfellow et al, ) and variational antoencoder (VAE) (Kingma & Welling, ) are the two most popular network architectures.…”

Section: Introductionmentioning

confidence: 99%

Integration of Adversarial Autoencoders With Residual Dense Convolutional Networks for Estimation of Non‐Gaussian Hydraulic Conductivities

Zabaras

Shi

et al. 2020

Water Resources Research

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Inverse modeling for the estimation of non‐Gaussian hydraulic conductivity fields in subsurface flow and solute transport models remains a challenging problem. This is mainly due to the non‐Gaussian property, the nonlinear physics, and the fact that many repeated evaluations of the forward model are often required. In this study, we develop a convolutional adversarial autoencoder (CAAE) to parameterize non‐Gaussian conductivity fields with heterogeneous conductivity within each facies using a low‐dimensional latent representation. In addition, a deep residual dense convolutional network (DRDCN) is proposed for surrogate modeling of forward models with high‐dimensional and highly complex mappings. The two networks are both based on a multilevel residual learning architecture called residual‐in‐residual dense block. The multilevel residual learning strategy and the dense connection structure ease the training of deep networks, enabling us to efficiently build deeper networks that have an essentially increased capacity for approximating mappings of very high complexity. The CAAE and DRDCN networks are incorporated into an iterative ensemble smoother to formulate an inversion framework. The numerical experiments performed using 2‐D and 3‐D solute transport models illustrate the performance of the integrated method. The obtained results indicate that the CAAE is a robust parameterization method for non‐Gaussian conductivity fields with different heterogeneity patterns. The DRDCN is able to obtain accurate approximations of the forward models with high‐dimensional and highly complex mappings using relatively limited training data. The CAAE and DRDCN methods together significantly reduce the computation time required to achieve accurate inversion results.

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Parametrization of Stochastic Inputs Using Generative Adversarial Networks With Application in Geology

Cited by 39 publications

References 77 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

Hydrogeophysical Characterization of Nonstationary DNAPL Source Zones by Integrating a Convolutional Variational Autoencoder and Ensemble Smoother

Integration of Adversarial Autoencoders With Residual Dense Convolutional Networks for Estimation of Non‐Gaussian Hydraulic Conductivities

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