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The incorporation of hard data in geostatistical modeling is crucial for enhancing the accuracy of interpolating or stochastically estimating subsurface spatial features. The hard data at specified points in the model domain serve as a guide in optimizing the unknown parameters to follow the patterns of the hard data. Recently, a novel approach to solving hydrogeologic/reservoir modeling problems has emerged by using deep generative models, specifically generative adversarial networks (GANs), to generate realistic and diverse images of channelized aquifers. This subsequently can be coupled with inverse models to solve parameter estimation problems. This study focused on using an improved GAN, called a progressive growing generative adversarial network (PGGAN), conditioned with hard data to perform parameter estimation of complex facies models by coupling an ensemble smoother with multiple data assimilation (ES-MDA). First, the PGGAN was trained to an image with 128 × 128 resolution. The trained PGGAN was used to generate hydraulic conductivity fields when fed an ensemble of latent variables and hard data. The ES-MDA then was used to update the latent variable with the help of hydraulic head data obtained from the groundwater model. The approach was tested on synthetic hydraulic conductivity data. Results show that this approach was able to perform efficient estimation of an unknown facies model domain. Additionally, the proposed method was applied to a different test case of a facies model exhibiting different statistical characteristics. The results were satisfactory, demonstrating that the method is not constrained to the particular hydraulic conductivity fields introduced in the generator's training. • Coupling deep learning with data assimilation for groundwater modeling. • Both hard data and soft data are conditioned. • Synthetic examples are used to demonstrate the effectiveness. [ABSTRACT FROM AUTHOR]

• This paper introduces the concept of Traveling Pilot Points (TRIPS) for solving the categorical inverse problem • The TRIPS methodology combined with subspace methods is used to identify channel structures in a categorical aquifer system while honoring calibration and prior constraints • Tests on a synthetic example suggest that the TRIPS methodology has promise and could be tested on more complicated problems Categorical parameter distributions are common-place in hydrogeological systems consisting of geologic facies/categories with distinct properties, e.g., high-permeability channels embedded in a low-permeability matrix. Parameter estimation is difficult in such systems because the discontinuities in the parameter space hinder the inverse problem. Previous research in this area has been focused on the use of stochastic methods. In this paper, we present a novel approach based on Traveling Pilot points (TRIPS) combined with subspace parameter estimation methods to generate realistic categorical parameter distributions that honor calibration constraints (e.g., - measured water levels). In traditional implementations, aquifer properties (e.g., hydraulic conductivity) are estimated at fixed pilot point locations. In the TRIPS implementation, both the properties associated with the pilot points and their locations are estimated. Tikhonov regularization constraints are incorporated in the parameter estimation process to produce realistic parameter depictions. For a synthetic aquifer system, we solved the categorical inverse problem by combining the TRIPS methodology with two subspace methods: Null Space Monte Carlo (NSMC) and Posterior Covariance (PC). A posterior ensemble developed with the rejection sampling (RS) method is compared against the TRIPS ensembles. The comparisons indicated similarities between the various ensembles and to the reference parameter distribution. Between the two subspace methods, the NSMC method produced an ensemble with more variability than the PC method. These preliminary results suggest that the TRIPS methodology has promise and could be tested on more complicated problems. [ABSTRACT FROM AUTHOR]