A "Neural" Riemann solver for Relativistic Hydrodynamics

2025/05/25 by Carlo Musolino, Musolino, Carlo
Computer Science · Engineering · Physics and Astronomy · #Advanced Numerical Analysis Techniques #Computer Graphics and Visualization Techniques #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Model Reduction and Neural Networks

paper · pdf · doi:10.48550/arxiv.2505.18914

openalex publication_date 2025/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Employing deep-learning techniques for the conservative-to-primitive recovery in binary neutron star simulations
• GoRINNs: Godunov-Riemann Informed Neural Networks for Learning Hyperbolic Conservation Laws
• GRaM-X: A new GPU-accelerated dynamical spacetime GRMHD code for Exascale computing with the Einstein Toolkit
• AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity
• Gradient Surgery for Multi-Task Learning
• Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators
• AI Feynman: a Physics-Inspired Method for Symbolic Regression
• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer
• High-Order Numerical-Relativity Simulations of Binary Neutron Stars
• Adam: A Method for Stochastic Optimization
• On the difficulty of training Recurrent Neural Networks
• Practical recommendations for gradient-based training of deep architectures
• On Godunov-Type Methods for Gas Dynamics

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