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

• Published in: Computer methods in applied mechanics and engineering 2022-06, Vol.396, p.115100, Article 115100
• Main Authors: Hanna, John M., Aguado, José V., Comas-Cardona, Sebastien, Askri, Ramzi, Borzacchiello, Domenico
• Format: Article
• Language: English
• Subjects: Adaptivity; Algorithms; Collocation; Computer simulation; Engineering Sciences; Flow simulation; Machine learning; Neural networks; Physics-informed neural networks; Porous media; Two phase flow
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2022.115100

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 the residual-based adaptive refinement (RAR) method and with PINN with 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 two numerical examples 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 using RAR method or PINN with fixed collocation points, while having a comparable computational cost. •A basic framework to simulate two-phase flow in porous media using PINN is suggested.•A novel residual-based adaptive PINN is developed for accurate interface predictions.•Distinct training/collocation points are obtained for different terms of the loss.