PNNL

Abstract

Data assimilation for parameter and state estimation in subsurface transport problems remains a significant challenge due to the sparsity of measurements, the porous media heterogeneity, and high computational cost of forward numerical models. We present a physics-informed deep neural networks (DNNs) machine learning method for estimating space-dependent hydraulic conductivity, hydraulic head, and concentration fields from sparse measurements. In this approach, we employ individual DNNs to approximate the unknown parameters (e.g., hydraulic conductivity) and states (e.g., hydraulic head and concentration) of a physical system, and jointly train these DNNs by minimizing the loss function consisting of the residuals of the governing equations in addition to the error with respect to measurement data. We apply this approach to assimilate conductivity, hydraulic head, and concentration measurements for joint inversion of the conductivity, hydraulic head, and concentration fields in a steady-state advection-dispersion problem. We study the accuracy of the physics-informed DNN approach with respect to data size, number of variables (conductivity and head versus conductivity, head, and concentration), DNNs size, and DNN initialization during training. We demonstrate that the physics-informed DNNs are significantly more accurate than standard data-driven DNNs when the training set consists of sparse data. We also show that the accuracy of parameter estimation increases as more different types of data are inverted jointly.