Dynamic deep learning based super-resolution for the shallow water equations

Correctly capturing the transition to turbulence in a barotropic instability requires fine spatial resolution. To reduce computational cost, we propose a dynamic super-resolution approach where a transient simulation on a coarse mesh is frequently corrected using a U-net-type neural network. For the nonlinear shallow water equations, we demonstrate that a simulation with the Icosahedral Nonhydrostatic ocean model with a 20 km resolution plus dynamic super-resolution trained on a 2.5km resolution achieves discretization errors comparable to a simulation with 10 km resolution. The neural 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 solution every 12 h. We show that the ML-corrected coarse solution correctly maintains a balanced flow and captures the transition to turbulence in line with the higher resolution simulation. After an 8 d simulation, the L2-error of the corrected run is similar to a simulation run on a finer mesh. While mass is conserved in the corrected runs, we observe some spurious generation of kinetic energy.

Subjects

DDC Class

551: Geology, Hydrology Meteorology

519: Applied Mathematics, Probabilities

006: Special computer methods

Funding(s)

Leistungsverbesserung des ICON-O Ozeanmodells auf heterogenen Exascale-Supercomputern mit Methoden des Maschinellen Lernens

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publishedVersion

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https://creativecommons.org/licenses/by/4.0/

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Witte_2025_Mach._Learn.__Sci._Technol._6_015060.pdf

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4.21 MB

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Dynamic deep learning based super-resolution for the shallow water equations