Predictive Deep Learning for High-Dimensional Inverse Modeling of Hydraulic Tomography in Gaussian and Non-Gaussian Fields

Abstract

Inverse modeling of hydraulic tomography (HT) is computationally expensive for estimating high-dimensional hydrogeologic parameter fields. In this work, we develop a novel method called HT-INV-NN, which combines dimensionality reduction techniques with a predictive deep learning (DL) model to estimate high-dimensional Gaussian and non-Gaussian channel fields. The HT-INV-NN model consists of a predictor that directly learns the inverse process from hydraulic head measurements to latent variables of random fields, and a decoder that generates high-dimensional parameter fields from predicted latent variables. For Gaussian spatially correlated fields, the decoder utilizes principal components derived from spatial covariance, and for non-Gaussian channel fields, a generative adversarial network (GAN) is trained using generated realizations based on a training image (TI). The predictor is a deep neural network calibrated using the reference data obtained from HT forward simulations, which can be implemented in parallel. HT-INV-NN is successfully tested in multiple numerical experiments including steady-state and transient HT for estimating Gaussian fields in 2D and 3D, as well as binary discontinuous or continuous non-Gaussian channel fields. The training process is efficient, and the model structure demonstrates robustness for input data with perturbations. The model performance on multiple validation data sets are satisfactory when compared with other numerical and deep learning methods.