Title: Accelerating Multiscale Discretization in High-Contrast Media for Subsurface Flow Simulation via Attention-Enhanced Hybrid Networks and Two-Grid Preconditioning

Abstract:

This study investigates an efficient numerical strategy for solving Darcy equations within strongly heterogeneous media characterized by high-contrast permeability. We introduce a hybrid framework that integrates machine learning with multiscale numerical techniques. Specifically, the learning module is employed to predict multiscale basis functions for the mixed generalized multiscale finite element method (mixed GMsFEM), aiming to minimize the repetitive local computations typically required during the offline phase. Following the prediction of these basis functions, the global system is assembled, and the pressure field is determined using a two-grid preconditioned solver. This approach significantly speeds up the computationally expensive local basis-construction process while maintaining the multiscale discretization and preconditioned iterative architecture of the original solver.

Numerical experiments conducted on two-dimensional heterogeneous Darcy problems demonstrate that the proposed framework achieves superior accuracy in final pressure reconstruction compared to several existing learning-based methods. Furthermore, the method exhibits robust stability under conditions of strong heterogeneity and high-contrast coefficients. When compared to the traditional mixed GMsFEM, the primary benefit of this new approach is the enhanced efficiency of the basis-generation stage. Meanwhile, the two-grid preconditioner ensures the high quality of the global solution. These findings suggest that leveraging learning to accelerate multiscale basis construction, while relying on a well-established numerical solver for the global problem, offers a promising pathway for high-resolution Darcy-type simulations.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC