Dual-Domain Deep Learning Method to Accelerate Local Basis Functions Computation for Reservoir Simulation in High-Contrast Porous Media

TL;DR

The paper addresses the computational bottleneck in MGMsFEM for Darcy flow in high-contrast porous media by introducing a dual-domain neural operator that extracts features in both frequency and spatial domains to rapidly predict multiple multiscale basis functions. The method blends a Fourier-based frequency-domain extractor with a two-path spatial extractor and a smooth TeLU activation, followed by a ridge-regularized decoder to deliver offline basis functions with high fidelity. Numerical experiments on KLE-generated permeability fields show MSE around $1\times10^{-3}$ and $R^2$ above $0.98$, with near-orthogonality preserved, while achieving substantial speedups over traditional MGMsFEM basis construction. This approach offers a scalable pathway to efficient reservoir simulations and can be extended to 3D and multiphase problems, particularly when integrated with physics-informed constraints.

Abstract

In energy science, Darcy flow in heterogeneous porous media is a central problem in reservoir sim-ulation. However, the pronounced multiscale characteristics of such media pose significant challenges to conventional numerical methods in terms of computational demand and efficiency. The Mixed Generalized Multiscale Finite Element Method (MGMsFEM) provides an effective framework for addressing these challenges, yet the construction of multiscale basis functions remains computationally expensive. In this work, we propose a dual-domain deep learning framework to accelerate the computation of multiscale basis functions within MGMsFEM for solving Darcy flow problems. By extracting and decoding permeability field features in both the frequency and spatial domains, the method enables rapid generation of numerical matrices of multiscale basis functions. Numerical experiments demonstrate that the proposed framework achieves significant computational acceleration while maintaining high approximation accuracy, thereby offering the potential for future applications in real-world reservoir engineering.

Figures (5)

• Figure 1: Network structure for our deep learning method. It can be divided into four parts: Data preprocessing, Feature Extraction in two domains, and Fully-Connected Decoder. Specially, the part ‘Feature Extraction in Frequency Domain’ also refers to FNO with TeLU function. The relevant abbreviations are explained in the lower right corner of the picture.
• Figure 2: An example of our permeability field. Left: the field generated by KLE, with size $30 \times 30$. The yellow part represents the fissure, and the dark blue part represents the matrix. Right: reshaped permeability field. Each column refers to a coarse block. The coarse grid framed by the red line in the left figure is the coarse grid used for the subsequent display of multi-scale basis functions, one with cracks and one without.
• Figure 3: Learning curve of the training process. Left: the change of loss in total 300 epochs. Right: The loss curve of the last 10 epochs.
• Figure 4: The contour plots of our multiscale basis functions, which are for the coarse block with no fractures in Figure \ref{['fig:data_sample']}. Top: basis functions generated from MGMsFEM. Bottom: basis functions generated from our deep learning model.
• Figure 5: The contour plots of our multiscale basis functions, which are for the coarse block with fractures in Figure \ref{['fig:data_sample']}. Top: basis functions generated from MGMsFEM. Bottom: basis functions generated from our deep learning model.