Deep Autoregressive Neural Networks for High‐Dimensional Inverse Problems in Groundwater Contaminant Source Identification

Mo, Shaoxing; Zabaras, Nicholas; Shi, Xiaoqing; Wu, Jichun

doi:10.1029/2018wr024638

Cited by 217 publications

(119 citation statements)

References 64 publications

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“…Zhu and Zabaras [5] devised a fully convolutional encoder-decoder architecture to capture pressure and velocity maps for single-phase flow problems characterized by random 2D Gaussian permeability fields. In later work, an autoregressive strategy was integrated with a fully convolutional encoder-decoder architecture for the prediction of time-dependent transport in 2D problems [6]. Tang et al [3] proposed a combination of a residual U-Net with convLSTM to capture the saturation and pressure evolution in 2D oil-water problems, with wells operating under wellbore pressure control.…”

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

250

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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

250

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“…Here,

{boldC}_{MM}

is the autocovariance matrix of the input parameters in

boldM

J_{d}^{\max}

and

J_{m}^{\max}

are the maximum values of

J_{d} false(\cdot false)

and

J_{m} false(\cdot false)

, respectively. Based on the

J

values, we select

N_{l} = β_{l} N_{e}, false(β_{l} \in false(0, 1 false] false)

samples as the local ensemble of

{bold-italicm}_{i}

using a roulette wheel selection operator (Lipowski & Lipowska, ), in which the selection probability of the

i

th individual is given as

P_{i} = ρ_{i} false/ \sum_{j = 1}^{N_{e}} ρ_{j}

i = 1, \dots, N_{e}

, where

ρ_{j} = 1 false/ J false({bold-italicm}_{j} false)

(Mo et al, ). A local ensemble factor of

β_{l} = 0.1

suggested in Zhang et al () is used.…”

Section: Methodsmentioning

confidence: 99%

“…The two factors together make the commonly used surrogate methods, such as Gaussian processes (Rasmussen & Williams, ) and polynomial chaos expansion (Xiu & Karniadakis, ), difficult to work. Deep neural networks have already exhibited a promising and impressive performance for surrogate modeling of forward models with high‐dimensional input and output fields (Kani & Elsheikh, ; Mo, Zabaras, et al, ; Mo, Zhu, et al ; Sun, ; Tripathy & Bilionis, ; Zhong et al, ; Zhu & Zabaras, ; Zhu et al, ). For example, in Tripathy and Bilionis () a deep neural network was proposed to build a surrogate model for a single‐phase flow forward model.…”

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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“…S. Li et al (2020) proposed an end-to-end seismic inversion network (SeisInvNet), which takes advantage of all seismic data for reconstruction of velocity models. In hydrology, Mo et al (2019) developed a deep autoregressive neural network-based surrogate as a forward groundwater contaminant transport model, and the iterative local updating ensemble smoother is adopted for groundwater contaminant source identification. Deep-learning techniques have also been used in parameterization of geological media, such as the Variational AutoEncoder (VAE) (Laloy et al, 2017) and the Generative Adversarial Network (GAN) (Laloy et al, 2018), which constitutes an important step for geological media property inversion.…”

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confidence: 99%

Deep‐Learning‐Based Inverse Modeling Approaches: A Subsurface Flow Example

2021

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Inverse modeling aims to infer uncertain parameters of a system with noisy observations of the system response, which has been widely utilized in various scientific and engineering practices, such as seismic inversion (Bunks et al., 1995), petroleum reservoir history matching (Oliver et al., 2008), aquifer parameter estimation (Carrera & Neuman, 1986a, 1986b, 1986c), and medical imaging (Arridge, 1999). Under certain conditions, inverse problems can be viewed as optimization problems, in which the model parameters are modified, such that the predictions from forward models can match the measurements. In addition, prior knowledge can be used to regularize the objective function and to obtain the maximum a posteriori estimate of the model parameters. The gradient-based method is a straightforward and common way to perform inverse modeling tasks. Anterion et al. (1989) presented a rigorous analytical method to calculate the gradients of observations with respect to reservoir characteristics, which can then be used to assist the process of parameter adjustment for history matching. For calculating the required gradients in inverse modeling, the adjoint method is a frequently utilized technique (

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Deep Autoregressive Neural Networks for High‐Dimensional Inverse Problems in Groundwater Contaminant Source Identification

Cited by 217 publications

References 64 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

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

Deep‐Learning‐Based Inverse Modeling Approaches: A Subsurface Flow Example

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