Dynamic Deep Learning Based Super-Resolution For The Shallow Water Equations

• URL: http://arxiv.org/abs/2404.06400v2
• Date: Mon, 02 Dec 2024 09:17:21 GMT
• Title: Dynamic Deep Learning Based Super-Resolution For The Shallow Water Equations
• Authors: Maximilian Witte, Fabricio Rodrigues Lapolli, Philip Freese, Sebastian Götschel, Daniel Ruprecht, Peter Korn, Christopher Kadow,
• Abstract summary: We demonstrate that a simulation 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.<n>The network, originally developed for image-based super-resolution in post-processing, is trained to compute the difference between solutions on both meshes.
• Score: 0.4188114563181614
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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