Accelerating multigrid solver with generative super-resolution
<|reference_start|>Accelerating multigrid solver with generative super-resolution: The geometric multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared to iterative methods such as Gauss-Seidel. The prolongation or coarse-to-fine interpolation operator within the multigrid algorithm, lends itself to a data-driven treatment with deep learning super-resolution, commonly used to increase the resolution of images. We (i) propose the integration of a super-resolution generative adversarial network (GAN) model with the multigrid algorithm as the prolongation operator and (ii) show that the GAN-interpolation can improve the convergence properties of multigrid in comparison to cubic spline interpolation on a class of multiscale PDEs typically solved in fluid mechanics and engineering simulations. We also highlight the importance of characterizing hybrid (machine learning/traditional) algorithm parameters.<|reference_end|>
@article{holguin2024accelerating,
    title={Accelerating multigrid solver with generative super-resolution},
    author={Francisco Holguin, GS Sidharth, Gavin Portwood},
    journal={arXiv preprint arXiv:2403.07936},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.07936},
    primaryClass={math.NA cs.NA}
}