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

convolutional neural network

deep learning

galewesky test case

hybrid modeling

numerical ocean model ICON

shallow water equation

super-resolution

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

Publication version

publishedVersion

Lizenz

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

Name

Witte_2025_Mach._Learn.__Sci._Technol._6_015060.pdf

Size

4.21 MB

Format

Adobe PDF

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