Dynamic Deep Learning Based Super-Resolution For The Shallow Water Equations
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arXiv
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| Format: | Preprint |
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2024
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| author | Witte, Maximilian Lapolli, Fabricio Rodrigues Freese, Philip Götschel, Sebastian Ruprecht, Daniel Korn, Peter Kadow, Christopher |
| author_facet | Witte, Maximilian Lapolli, Fabricio Rodrigues Freese, Philip Götschel, Sebastian Ruprecht, Daniel Korn, Peter Kadow, Christopher |
| contents | Using the nonlinear shallow water equations as benchmark, we demonstrate that a simulation with the ICON-O ocean model with a 20km resolution that is frequently corrected by a U-net-type neural network can achieve discretization errors of a simulation with 10km resolution. The network, originally developed for image-based super-resolution in post-processing, is trained to compute the difference between solutions on both meshes and is used to correct the coarse mesh every 12h. Our setup is the Galewsky test case, modeling transition of a barotropic instability into turbulent flow. We show that the ML-corrected coarse resolution run correctly maintains a balance flow and captures the transition to turbulence in line with the higher resolution simulation. After 8 day of simulation, the $L_2$-error of the corrected run is similar to a simulation run on the finer mesh. While mass is conserved in the corrected runs, we observe some spurious generation of kinetic energy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06400 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamic Deep Learning Based Super-Resolution For The Shallow Water Equations Witte, Maximilian Lapolli, Fabricio Rodrigues Freese, Philip Götschel, Sebastian Ruprecht, Daniel Korn, Peter Kadow, Christopher Machine Learning Computational Physics Fluid Dynamics 65M99, 68T07, 86-08, 35-11 Using the nonlinear shallow water equations as benchmark, we demonstrate that a simulation with the ICON-O ocean model with a 20km resolution that is frequently corrected by a U-net-type neural network can achieve discretization errors of a simulation with 10km resolution. The network, originally developed for image-based super-resolution in post-processing, is trained to compute the difference between solutions on both meshes and is used to correct the coarse mesh every 12h. Our setup is the Galewsky test case, modeling transition of a barotropic instability into turbulent flow. We show that the ML-corrected coarse resolution run correctly maintains a balance flow and captures the transition to turbulence in line with the higher resolution simulation. After 8 day of simulation, the $L_2$-error of the corrected run is similar to a simulation run on the finer mesh. While mass is conserved in the corrected runs, we observe some spurious generation of kinetic energy. |
| title | Dynamic Deep Learning Based Super-Resolution For The Shallow Water Equations |
| topic | Machine Learning Computational Physics Fluid Dynamics 65M99, 68T07, 86-08, 35-11 |
| url | https://arxiv.org/abs/2404.06400 |