A "Neural" Riemann solver for Relativistic Hydrodynamics

TL;DR

This paper introduces a neural network-based Riemann solver for relativistic hydrodynamics that significantly speeds up computations while maintaining accuracy, enabling more efficient large-scale astrophysical simulations.

Contribution

The paper presents a novel neural Riemann solver that replaces expensive root-finding steps, improving efficiency without sacrificing accuracy in relativistic hydrodynamics simulations.

Findings

Achieves accuracy comparable to exact solvers

Demonstrates robustness across canonical problems

Offers significant computational speedup

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.