Prediction of Multiscale Features Using Deep Learning-based Preconditioner-Solver Architecture for Darcy Equation in High-Contrast Media

TL;DR

This paper introduces FP-HMsNet, a deep learning architecture combining Fourier Neural Operators and multi-scale networks, achieving state-of-the-art accuracy and efficiency in modeling high-contrast subsurface fluid flow for Darcy equations.

Contribution

The paper presents a novel hierarchical preconditioner-learner architecture that effectively reconstructs multiscale basis functions, outperforming existing models in accuracy and computational efficiency.

Findings

Achieved an MSE of 0.0036 and R2 of 0.9716 on test data.

Maintained stability under various noise levels.

Demonstrated faster convergence and improved efficiency.

Abstract

Modeling subsurface fluid flow in porous media is crucial for applications such as oil and gas exploration. However, the inherent heterogeneity and multi-scale characteristics of these systems pose significant challenges in accurately reconstructing fluid flow behaviors. To address this issue, we proposed Fourier Preconditioner-based Hierarchical Multiscale Net (FP-HMsNet), an efficient hierarchical preconditioner-learner architecture that combines Fourier Neural Operators (FNO) with multi-scale neural networks to reconstruct multi-scale basis functions of high-dimensional subsurface fluid flow. Using a dataset comprising 102,757 training samples, 34,252 validation samples, and 34,254 test samples, we ensured the reliability and generalization capability of the model. Experimental results showed that FP-HMsNet achieved an MSE of 0.0036, an MAE of 0.0375, and an R2 of 0.9716 on the testing set, significantly outperforming existing models and demonstrating exceptional accuracy and generalization ability. Additionally, robustness tests revealed that the model maintained stability under various levels of noise interference. Ablation studies confirmed the critical contribution of the preconditioner and multi-scale pathways to the model's performance. Compared to current models, FP-HMsNet not only achieved lower errors and higher accuracy but also demonstrated faster convergence and improved computational efficiency, establishing itself as the state-of-the-art (SOTA) approach. This model offers a novel method for efficient and accurate subsurface fluid flow modeling, with promising potential for more complex real-world applications.