Parametrization of subgrid scales in long-term simulations of the shallow-water equations using machine learning and convex limiting

ArXi:2602.00378v2 Announce Type: replace-cross We present a method for parametrizing sub-grid processes in the Shallow Water equations. We define coarse variables and local spatial averages and use a feed-forward neural network to learn sub-grid fluxes. Our method results in a local parametrization that uses a four-point computational stencil, which has several advantages over globally coupled parametrizations. We nstrate numerically that our method improves energy balance in long-term turbulent simulations and also accurately reproduces individual solutions.