Deep Learning for Simultaneous Inference of Hydraulic and Transport Properties

Identification of a heterogeneous conductivity field and reconstruction of a contaminant release history are key aspects of subsurface remediation. These two goals are achieved by combining model predictions with sparse and noisy hydraulic head and concentration measurements. Solution of this inverse problem is notoriously difficult due to, in part, high dimensionality of the parameter space and high computational cost of repeated forward solves. We use a convolutional adversarial autoencoder (CAAE) to parameterize a heterogeneous non-Gaussian conductivity field via a low-dimensional latent representation. A three-dimensional dense convolutional encoder-decoder (DenseED) network serves as a forward surrogate of the flow and transport model. The CAAE-DenseED surrogate is fed into the ensemble smoother with multiple data assimilation (ESMDA) algorithm to sample from the Bayesian posterior distribution of the unknown parameters, forming a CAAE-DenseED-ESMDA inversion framework. The resulting CAAE-DenseED-ESMDA inversion strategy is used to identify a three-dimensional contaminant source and conductivity field. A comparison of the inversion results from CAAE-ESMDA with physical flow and transport simulator and from CAAE-DenseED-ESMDA shows that the latter yields accurate reconstruction results at the fraction of the computational cost of the former.