Integration of adversarial autoencoders with residual dense convolutional networks for estimation of non-Gaussian hydraulic conductivities

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.