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

TL;DR

This paper demonstrates that a neural network-based super-resolution technique can effectively enhance coarse-resolution shallow water simulations, maintaining accuracy and physical balance comparable to finer mesh simulations.

Contribution

The study introduces a neural network correction method for shallow water simulations that improves coarse mesh results to match finer mesh accuracy, using a U-net trained on solution differences.

Findings

ML correction maintains balance flow and captures turbulence transition

Corrected coarse run achieves similar error to high-resolution simulation

Mass conservation is maintained despite some kinetic energy artifacts

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.