Transolver-GMsFEM: A Hybrid Framework for High-Contrast Multiscale PDEs on Irregular Grids

High-contrast multiscale PDE problems are common in real-world applications, yet current neural PDE solvers struggle to achieve sufficient accuracy on such tasks. The Generalized Multiscale Finite Element Method (GMsFEM) addresses this by compressing fine-scale heterogeneity into localized basis functions which are used to obtain more accurate solutions than neural PDE solvers. However, constructing these basis functions requires solving many local eigenvalue problems—the major computational bottleneck. We address this issue by proposing **Transolver-GMsFEM**, a new hybrid framework that utilizes the efficiency of neural PDE solver for predicting multiscale basis functions while preserving the solution quality of GMsFEM. Experiments on 2D/3D steady-state and time-dependent high-contrast multiscale PDEs on irregular grids show proposed method achieves over $100\times$ speedup for basis construction. Crucially, our experiments demonstrate that Transolver-GMsFEM significantly outperforms state-of-the-art neural PDE solvers in both accuracy and robustness, especially in out-of-distribution tasks where pure neural PDE solvers dramatically fail.