Hybrid Two-Stage Reconstruction of Multiscale Subsurface Flow with Physics-informed Residual Connected Neural Operator

TL;DR

This paper introduces a hybrid two-stage neural network framework combining multiscale basis functions and physics-informed learning to accurately reconstruct subsurface flow in high-contrast fractured media, ensuring physical consistency.

Contribution

It develops a novel hybrid framework integrating multiscale basis functions with physics-guided neural networks for subsurface flow modeling.

Findings

Achieved R2 > 0.9 in basis and pressure reconstruction

Residual indicator around 1e-4, indicating high accuracy

Validated framework's effectiveness across different datasets

Abstract

The novel neural networks show great potential in solving partial differential equations. For single-phase flow problems in subsurface porous media with high-contrast coefficients, the key is to develop neural operators with accurate reconstruction capability and strict adherence to physical laws. In this study, we proposed a hybrid two-stage framework that uses multiscale basis functions and physics-guided deep learning to solve the Darcy flow problem in high-contrast fractured porous media. In the first stage, a data-driven model is used to reconstruct the multiscale basis function based on the permeability field to achieve effective dimensionality reduction while preserving the necessary multiscale features. In the second stage, the physics-informed neural network, together with Transformer-based global information extractor is used to reconstruct the pressure field by integrating the physical constraints derived from the Darcy equation, ensuring consistency with the physical laws of the real world. The model was evaluated on datasets with different combinations of permeability and basis functions and performed well in terms of reconstruction accuracy. Specifically, the framework achieves R2 values above 0.9 in terms of basis function fitting and pressure reconstruction, and the residual indicator is on the order of $1\times 10^{-4}$. These results validate the ability of the proposed framework to achieve accurate reconstruction while maintaining physical consistency.