  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.
