Witte, MaximilianMaximilianWitteFreese, Jan PhilipJan PhilipFreeseGötschel, SebastianSebastianGötschelRuprecht, DanielDanielRuprechtRodrigues Lapolli, FabricioFabricioRodrigues LapolliKadow, ChristopherChristopherKadowKorn, PeterPeterKorn2025-04-042025-04-042025-03-31Machine Learning: Science and Technology 6 (1): 015060 (2025)https://hdl.handle.net/11420/55100Correctly 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.en2632-215320251https://creativecommons.org/licenses/by/4.0/convolutional neural network | deep learning | galewesky test case | hybrid modeling | numerical ocean model ICON | shallow water equation | super-resolutionNatural Sciences and Mathematics::551: Geology, Hydrology MeteorologyNatural Sciences and Mathematics::519: Applied Mathematics, ProbabilitiesComputer Science, Information and General Works::006: Special computer methodsJournal Articlehttps://doi.org/10.15480/882.1499910.1088/2632-2153/ada19f10.15480/882.14999Journal Article