Accelerating multigrid solver with generative super-resolution
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910364742975488 |
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| author | Holguin, Francisco Sidharth, GS Portwood, Gavin |
| author_facet | Holguin, Francisco Sidharth, GS Portwood, Gavin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_07936 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Accelerating multigrid solver with generative super-resolution Holguin, Francisco Sidharth, GS Portwood, Gavin Numerical Analysis 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. |
| title | Accelerating multigrid solver with generative super-resolution |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2403.07936 |