Neural approximation of Riemann fluxes for transient shallow water flows with wetting and drying

Introduction Hybrid approaches that integrate physically based models with neural networks are emerging as a promising route for accelerating high-fidelity simulations of shallow water flows. However, many surrogate models attempt to replace the entire solver, making it difficult to maintain physical conservation, numerical stability, and robustness over varying topography and across wet-dry fronts.Methods This work presents RimNet, a dual-branch neural Riemann flux estimator for transient shallow water flows involving wetting and drying. RimNet predicts intercell mass and momentum fluxes from locally reconstructed Riemann states while retaining the conservative update and time-stepping structure of the original Godunov-type finite volume numerical scheme.Results/Key Findings In the two benchmark tests, the resulting solver remains stable and closely follows the HLL reference across shocks and wet–dry transitions. In the indicative computatioal performance tests, replacing explicit wave-speed evaluations with batched tensor operations reduces total simulation runtime by approximately 15–30%.Conclusion These results provide preliminary evidence that learned flux evaluation can be introduced as a modular component of a conventional solver, offering insights into combining deep learning with conventional solultion frameworks for hyperbolic conservation laws.