Dynamic Deep Learning Based Super-Resolution For The Shallow Water Equations
<|reference_start|>Dynamic Deep Learning Based Super-Resolution For The Shallow Water Equations: 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.<|reference_end|>
@article{witte2024dynamic,
    title={Dynamic Deep Learning Based Super-Resolution For The Shallow Water
  Equations},
    author={Maximilian Witte, Fabricio Rodrigues Lapolli, Philip Freese, Sebastian
  G"otschel, Daniel Ruprecht, Peter Korn, Christopher Kadow},
    journal={arXiv preprint arXiv:2404.06400},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.06400},
    primaryClass={cs.LG physics.comp-ph physics.flu-dyn}
}