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Variational Autoencoder or Generative Adversarial Networks? A Comparison of Two Deep Learning Methods for Flow and Transport Data Assimilation

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Abstract

Groundwater modeling is an important tool for water resources management and aquifer remediation. However, the inherent strong heterogeneity of the subsurface and scarcity of observed data pose major challenges for groundwater flow and contaminant transport modeling. Data assimilation such as the Ensemble Smoother with Multiple Data Assimilation (ES-MDA) can be used to improve the understanding of the subsurface by integrating a variety of data into the modeling. For highly heterogeneous aquifers such as fluvial deposits, traditional data assimilation methods cannot preserve geological structures. In this work, two of the most popular deep learning methods, Variational Autoencoder (VAE) and Generative Adversarial Network (GAN), are compared for identifying geological structures using flow and transport data assimilation. Specifically, VAE and GAN are used to re-parameterize the hydraulic conductivity fields with low dimensional latent variables. The ES-MDA then is used to update the latent variables by assimilating the observed data such as hydraulic head and contaminant concentration into the model. Synthetic examples of both categorical and continuous variables are conducted to test the performance of coupling ES-MDA with VAE or GAN. The results demonstrate that the generating quality of GAN is better such that channels are generated with similar properties as in the training image, while VAE has the advantage that data assimilation is more successful in allowing better localization of the actual channels for the considered inverse problem.

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Acknowledgements

This work has been supported through a grant from the National Science Foundation (OIA-1833069). The authors wish to thank the associate editor and two anonymous reviewers for their comments, which substantially helped to improve the final version of the manuscript.

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  1. Department of Geology and Geological Engineering, South Dakota School of Mines and Technology, Rapid City, 57701, USA

    Jichao Bao, Liangping Li & Arden Davis

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  1. Jichao Bao
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  2. Liangping Li
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  3. Arden Davis
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Correspondence to Liangping Li.

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Bao, J., Li, L. & Davis, A. Variational Autoencoder or Generative Adversarial Networks? A Comparison of Two Deep Learning Methods for Flow and Transport Data Assimilation. Math Geosci 54, 1017–1042 (2022). https://doi.org/10.1007/s11004-022-10003-3

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