Residual-based adaptivity for two-phase flow simulation in porous media using Physics-informed Neural Networks

This paper aims to provide a machine learning framework to simulate two-phase flow in porous media. The proposed algorithm is based on Physics-informed neural networks (PINN). A novel residual-based adaptive PINN is developed and compared with traditional PINN having fixed collocation points. The proposed algorithm is expected to have great potential to be applied to different fields where adaptivity is needed. In this paper, we focus on the two-phase flow in porous media problem. We provide a numerical example to show the effectiveness of the new algorithm. It is found that adaptivity is essential to capture moving flow fronts. We show how the results obtained through this approach are more accurate than classical PINN, while having a comparable computational cost.