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

• URL: http://arxiv.org/abs/2602.00378v1
• Date: Fri, 30 Jan 2026 22:57:32 GMT
• Title: Parametrization of subgrid scales in long-term simulations of the shallow-water equations using machine learning and convex limiting
• Authors: Md Amran Hossan Mojamder, Zhihang Xu, Min Wang, Ilya Timofeyev,
• Abstract summary: We present a method for parametrizing sub-grid processes in the Shallow Water equations.<n>We define coarse variables and local spatial averages and use a feed-forward neural network to learn sub-grid flux.<n>Our method results in a local parametrization that uses a four-point computational stencil, which has several advantages over globally coupled parametrizations.
• Score: 2.612594175980954
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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