A "Neural" Riemann solver for Relativistic Hydrodynamics

Abstract

In this paper, we present an approach to solving the Riemann problem in one-dimensional relativistic hydrodynamics, where the most computationally expensive steps of the exact solver are replaced by compact, highly specialized neural networks. The resulting "neural" Riemann solver is integrated into a high-resolution shock-capturing scheme and tested on a range of canonical problems, demonstrating both robustness and efficiency. By constraining the learned components to the root-finding of single-valued functions, the method retains physical interpretability while significantly accelerating the computation. The solver is shown to achieve accuracies comparable to the exact algorithm at a fraction of the cost, suggesting that this approach may offer a viable path toward more efficient Riemann solvers for use in large-scale numerical relativity simulations of astrophysical systems.