Journal Article

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

Freese, Philip, Ruprecht, Daniel, Kadow, Christopher, Lapolli, Fabrício R, Witte, Maximilian, Götschel, Sebastian, Korn, Peter

2025

Overview

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 L 2 -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.

• Publisher: IOP Publishing
• Subject: convolutional neural network / Deep learning / Error correction / galewesky test case / hybrid modeling / Image resolution / Kinetic energy / Neural networks / numerical ocean model ICON / Ocean models / shallow water equation / Shallow water equations / Simulation / Spatial resolution / super-resolution / Turbulence / Turbulent flow