  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 non-linear
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 CCAE 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.
