Using Physics-Informed Neural Networks to Solve for Permeability Field under Two-Phase Flow in Heterogeneous Porous Media

Abstract

Physics-informed neural networks (PINNs) have recently been applied to a wide range of computational physical problems. In this paper, we use PINNs to solve an inverse two-phase flow problem in heterogeneous porous media where only sparse direct and indirect measurements are available. The forward two-phase flow problem is governed by a coupled system of partial differential equations (PDEs) with initial and boundary conditions. As for inverse problems, the solutions are assumed to be known at scattered locations but some coefficients or variable functions in the PDEs are missing or incomplete. The idea is to train multiple neural networks representing the solutions and the unknown variable function at the same time such that both the underlying physical laws and the measurements can be honored. The numerical results show that our proposed method is able to recover the incomplete permeability field in different scenarios. Moreover, we show that the method can be used to forecast the future dynamics with the same format of loss function formulation. In addition, we employ a neural network structure inspired by the deep operator networks (DeepONets) to represent the solutions which can potentially shorten the time of the training process.