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

TL;DR

This paper introduces a residual-based adaptive PINN framework for simulating two-phase flow in porous media, demonstrating improved accuracy over fixed collocation PINNs and RAR methods with similar computational costs.

Contribution

A novel residual-based adaptive PINN algorithm is developed and validated for two-phase flow in porous media, enhancing simulation accuracy through adaptivity.

Findings

Adaptive PINN captures moving flow fronts more accurately.

The proposed method outperforms RAR and fixed PINN in accuracy.

Computational cost remains comparable to existing methods.

Abstract

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.