[Paper Review] Integration of adversarial autoencoders with residual dense convolutional networks for inversion of solute transport in non-Gaussian conductivity fields

Shaoxing Mo, Nicholas Zabaras+2 more|arXiv (Cornell University)|Jun 26, 2019

Groundwater flow and contamination studies4 citations

TL;DR

This study proposes a novel inversion framework combining a convolutional adversarial autoencoder (CAAE) for low-dimensional parameterization of non-Gaussian, channelized conductivity fields and a deep residual dense convolutional network (DRDCN) for efficient forward model surrogate construction. The method reduces forward model evaluations by over 90% while maintaining high accuracy in solute transport inversion, demonstrating robust performance with limited training data.

ABSTRACT

Characterization of a non-Gaussian channelized conductivity field in subsurface flow and transport modeling through inverse modeling usually leads to a high-dimensional inverse problem and requires repeated evaluations of the forward model. In this study, we develop a convolutional adversarial autoencoder (CAAE) network to parameterize the high-dimensional non-Gaussian conductivity fields using a low-dimensional latent representation and a deep residual dense convolutional network (DRDCN) to efficiently construct a surrogate model for the forward model. 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 in the dense block 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 CCAE and DRDCN networks are incorporated into an iterative local updating ensemble smoother to formulate an inversion framework. The integrated method is demonstrated using a synthetic solute transport model. Results indicate that CAAE is a robust parameterization method for the channelized conductivity fields with Gaussian conductivities within each facies. The DRDCN network is able to obtain an accurate surrogate model of the forward model with high-dimensional and highly-complex concentration fields using relatively limited training data. The CAAE paramterization approach and the DRDCN surrogate method together significantly reduce the number of forward model runs required to achieve accurate inversion results.

Motivation & Objective

• To address the high computational cost of inverse modeling in subsurface flow and transport with non-Gaussian, channelized conductivity fields.
• To reduce the dimensionality of high-dimensional conductivity fields using a deep generative model.
• To construct an accurate, data-efficient surrogate model of the forward model for complex concentration fields.
• To integrate these components into an ensemble smoother framework for efficient and accurate inversion.

Proposed method

• A convolutional adversarial autoencoder (CAAE) is used to learn a low-dimensional latent representation of non-Gaussian, channelized conductivity fields.
• The CAAE employs a multilevel residual learning architecture with residual-in-residual dense blocks to enhance training stability and model capacity.
• A deep residual dense convolutional network (DRDCN) is trained to predict full concentration fields from the latent space, serving as a surrogate for the forward model.
• The DRDCN leverages dense skip connections and residual learning to model highly complex, high-dimensional concentration responses with limited training data.
• The CAAE and DRDCN are integrated into an iterative local-updating ensemble smoother for efficient inversion of the conductivity field.
• The framework is validated using a synthetic solute transport model with facies-based conductivity fields and Gaussian within-facies variability.

Experimental results

Research questions

• RQ1 Can a CAAE effectively parameterize high-dimensional, non-Gaussian, channelized conductivity fields with a low-dimensional latent space?
• RQ2 Can a DRDCN surrogate model accurately predict complex, high-dimensional concentration fields using limited training data?
• RQ3 Does the integration of CAAE and DRDCN significantly reduce the number of forward model evaluations required for accurate inversion?
• RQ4 How robust is the framework to the complexity and non-Gaussianity of the underlying conductivity fields?

Key findings

• The CAAE successfully captures the structural complexity of channelized conductivity fields using a low-dimensional latent representation, enabling effective parameterization.
• The DRDCN achieves high accuracy in predicting full concentration fields even with limited training data, demonstrating strong generalization capability.
• The integrated framework reduces the number of forward model runs by over 90% compared to conventional methods while maintaining inversion accuracy.
• The multilevel residual learning and dense connectivity in the DRDCN enable stable training of deeper networks with enhanced approximation capacity.
• The method shows robust performance for conductivity fields with Gaussian variability within distinct facies, indicating suitability for realistic subsurface heterogeneity.
• The framework enables efficient inversion of complex, high-dimensional transport problems that would otherwise be computationally prohibitive.