Deep Convolutional Autoencoders for Robust Flow Model Calibration Under Uncertainty in Geologic Continuity

Jiang, Anyue; Jafarpour, Behnam

doi:10.1029/2021wr029754

Cited by 22 publications

(16 citation statements)

References 117 publications

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“…However, the main limitation of this compression method is related to the large number of coefficients to be retained to accurately represent sharp spatial contrasts in the resistivity values. In these contexts, the DCT can be replaced by other nonlinear compression strategies (i.e., deep generative models) that can better preserve nonlinear features in the solution (Laloy et al ., 2017; Jiang and Jafarpour, 2021). However, these strategies can severely complicate the geometry of the posterior distribution (i.e.…”

Section: Discussionmentioning

confidence: 99%

Machine learning‐accelerated gradient‐based Markov chain Monte Carlo inversion applied to electrical resistivity tomography

Aleardi

Vinciguerra

Stucchi

et al. 2022

Near Surface Geophysics

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Expensive forward model evaluations and the curse of dimensionality usually hinder applications of Markov chain Monte Carlo algorithms to geophysical inverse problems. Another challenge of these methods is related to the definition of an appropriate proposal distribution that simultaneously should be inexpensive to manipulate and a good approximation of the posterior density. Here we present a gradient-based Markov chain Monte Carlo inversion algorithm that is applied to cast the electrical resistivity tomography into a probabilistic framework. The sampling is accelerated by exploiting the Hessian and gradient information of the negative log-posterior to define a proposal that is a local, Gaussian approximation of the target posterior probability. On the one hand, the computing time to run the many forward evaluations needed for both the data likelihood evaluation and the Hessian and gradient computation is decreased by training a residual neural network to predict the forward mapping between the resistivity model and the apparent resistivity value. On the other hand, the curse of dimensionality issue and the computational effort related to the Hessian and gradient manipulation are decreased by compressing data and model spaces through a discrete cosine transform. A non-parametric distribution is assumed as the prior probability density function. The method is first demonstrated on synthetic data and then applied to field measurements. The outcomes provided by the presented approach are also benchmarked against those obtained when a computationally expensive finiteelement code is employed for forward modelling , with the results of a gradient-free Markov chain Monte Carlo inversion, and also compared with the predictions of a deterministic inversion. The implemented approach not only guarantees uncertainty assessments and model predictions comparable with those achieved by more standard inversion strategies, but also drastically decreases the computational cost of the probabilistic inversion, making it similar to that of a deterministic inversion.

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Section: Discussionmentioning

confidence: 99%

Machine learning‐accelerated gradient‐based Markov chain Monte Carlo inversion applied to electrical resistivity tomography

Aleardi

Vinciguerra

Stucchi

et al. 2022

Near Surface Geophysics

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“…Both VAEs and GANs may be used to generate samples that display the training patterns by sampling from a n ‐dimensional probability distribution (where typically n ≪ N ). However, when used for inversion, the concern is not only on pattern accuracy but also on the feasibility of efficiently exploring the possible models that fit the data, or in Bayesian terms, efficiently integrating model prior information with the measured data by means of the forward operator (Canchumuni et al., 2019; Jiang & Jafarpour, 2021; Laloy et al., 2019; Mosser et al., 2018). It was recently argued that with certain choice of parameters VAEs may control both the degree of nonlinearity and the topological changes of their generative mapping, which in turn allows the gradient to be used in a computationally efficient inversion (Lopez‐Alvis et al., 2021).…”

Section: Introductionmentioning

confidence: 99%

Geophysical Inversion Using a Variational Autoencoder to Model an Assembled Spatial Prior Uncertainty

et al. 2022

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Prior information regarding subsurface spatial patterns may be used in geophysical inversion to obtain realistic subsurface models. Field experiments require prior information with sufficiently diverse patterns to accurately estimate the spatial distribution of geophysical properties in the sensed subsurface domain. A variational autoencoder (VAE) provides a way to assemble all patterns deemed possible in a single prior distribution. Such patterns may include those defined by different base training images and also their perturbed versions, for example, those resulting from geologically consistent operations such as erosion/dilation, local deformation, and intrafacies variability. Once the VAE is trained, inversion may be done in the latent space which ensures that inverted models have the patterns defined by the assembled prior. Gradient‐based inversion with both a synthetic and a field case of cross‐borehole GPR traveltime data shows that using the VAE assembled prior performs as good as using the VAE trained on the pattern with the best fit, but it has the advantage of lower computation cost and more realistic prior uncertainty. Moreover, the synthetic case shows an adequate estimation of most small‐scale structures. The absolute values of wave velocity are computed by assuming a linear mixing model which involves two additional parameters that effectively shift and scale velocity values and are included in the inversion.

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“…To provide a physics‐based statistical representation, that is, a representation that honors the physical laws guiding the spatial distribution of the unknown field, recent applications in reservoir simulation for history matching have applied deep‐learning methods to parameterize channelized geological facies (e.g., Canchumuni et al., 2019; Jiang & Jafarpour, 2021; Laloy et al., 2017; Liu and Grana, 2020). These geological facies often have similar spatial attributes as DNAPL SZs, that is, sharp interfaces, connected and tortuous channels, and a tendency, driven by physical laws, to follow a certain direction.…”

Section: Introductionmentioning

confidence: 99%

Integration of Deep Learning‐Based Inversion and Upscaled Mass‐Transfer Model for DNAPL Mass‐Discharge Estimation and Uncertainty Assessment

Kang

Kokkinaki

Shi

et al. 2022

Water Resources Research

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Dense nonaqueous phase liquid (DNAPL) contaminants present a challenging groundwater issue that has gained increasing attention worldwide since the 1980s (National Research Council, 2013). Once released to the subsurface, DNAPLs can penetrate through the groundwater table and appear as immobile liquids relative to groundwater flow, due to their physicochemical properties, that is, high density, low solubility, and low interfacial tension (Pankow and Cherry, 1996). Driven by gravity and capillary forces, a fraction of the DNAPL may become trapped within the soil pores as discontinuous ganglia, while another fraction may pool on locally low-permeability media (e.g., clay lenses) (Dekker & Abriola, 2000;Lenhard et al., 1989). These DNAPL source zones (SZ) are long-term sources that slowly release dissolved contaminant downstream until they are depleted by dissolution due to natural or imposed concentration gradients. During this time, the resulting plumes of dissolved DNAPL could pose a significant risk to humans and ecosystems. Mass discharge from DNAPL SZs is often used a remediation metrics to determine when the risk is such that warranties active remediation versus more passive approaches (National Research Council, 2013). A significant and sustained reduction in mass discharge can be used to justify less intrusive and more cost-efficient remediation. Overall, accurate prediction of DNAPL mass discharge and source longevity play a critical role in all aspects of site stewardship, from remedial program design to remedial performance assessment (Abriola et al., 2012;Kavanaugh et al., 2003).In practice, the contaminant mass discharge at a location of interest downstream is typically obtained by aggregating local measurements of concentrations and flow rates (or the local mass flux) from multilevel sampling

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Deep Convolutional Autoencoders for Robust Flow Model Calibration Under Uncertainty in Geologic Continuity

Cited by 22 publications

References 117 publications

Machine learning‐accelerated gradient‐based Markov chain Monte Carlo inversion applied to electrical resistivity tomography

Machine learning‐accelerated gradient‐based Markov chain Monte Carlo inversion applied to electrical resistivity tomography

Geophysical Inversion Using a Variational Autoencoder to Model an Assembled Spatial Prior Uncertainty

Integration of Deep Learning‐Based Inversion and Upscaled Mass‐Transfer Model for DNAPL Mass‐Discharge Estimation and Uncertainty Assessment

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