Parametrization of subgrid scales in long-term simulations of the shallow-water equations using machine learning and convex limiting
This work addresses the challenge of accurate and stable long-term simulations in fluid dynamics, particularly for climate and weather modeling, though it appears incremental as it builds on existing machine learning approaches for parametrization.
The authors tackled the problem of parametrizing subgrid-scale processes in shallow-water equations for long-term turbulent simulations, resulting in a method that improves energy balance and accurately reproduces solutions, with reliable performance even in untrained dynamical regimes.
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 demonstrate numerically that our method improves energy balance in long-term turbulent simulations and also accurately reproduces individual solutions. The neural network parametrization can be easily combined with flux limiting to reduce oscillations near shocks. More importantly, our method provides reliable parametrizations, even in dynamical regimes that are not included in the training data.