Author(s): Jingxiao Wu; Qiuhua Liang; Huili Chen

Linked Author(s): Qiuhua Liang

Keywords: Finite-volume method; Shallow water equations; Hyperbolic conservation laws; Neural Riemann solver; Physics-guided deep learning

Abstract: Hybrid approaches that integrate physically based models with neural networks are emerging as a promising route for accelerating high-fidelity simulations of hyperbolic conservation laws. However, many surrogate models attempt to replace the entire solver, making it difficult to maintain conservation, stability, and robustness over complex topography and wet-dry fronts. This work presents RimNet, a deep learning framework that embeds a neural Riemann flux estimator inside a Godunov-type finite-volume framework for solving the shallow-water equations. Acting as a plug-in surrogate for an HLL approximate Riemann solver, RimNet estimates intercell numerical fluxes from locally reconstructed Riemann states while preserving the conservative update structure and time-stepping of the original finite-volume scheme. A dual-branch neural architecture predicts mass and momentum fluxes separately and is trained under online dynamic supervision, where a reference HLL solver provides on-the-fly targets. Physics-guided loss terms, including scale-aware relative errors and symmetry constraints, reinforce well-balanced property and numerical consistency. Benchmark tests demonstrate that RimNet closely reproduces the reference solutions while reducing flux computation cost by up to ~30%, offering a conservative and resolution-agnostic path for AI-enhanced shallow flow modelling.

DOI:

Year: 2026