Machine Learning for Conservative-to-Primitive in Relativistic Hydrodynamics

TL;DR

This paper demonstrates that neural networks can significantly accelerate the conservative-to-primitive variable recovery in relativistic hydrodynamics, maintaining accuracy while improving computational efficiency, especially for complex microphysics models.

Contribution

The study introduces neural network-based methods to replace traditional root-finding algorithms in relativistic hydrodynamics, enhancing speed and robustness.

Findings

Neural networks outperform traditional root finders in benchmark tests.

The conservative-to-primitive map neural network accelerates recovery by over ten times.

Methods maintain accuracy comparable to standard approaches.

Abstract

The numerical solution of relativistic hydrodynamics equations in conservative form requires root-finding algorithms that invert the conservative-to-primitive variables map. These algorithms employ the equation of state of the fluid and can be computationally demanding for applications involving sophisticated microphysics models, such as those required to calculate accurate gravitational wave signals in numerical relativity simulations of binary neutron stars. This work explores the use of machine learning methods to speed up the recovery of primitives in relativistic hydrodynamics. Artificial neural networks are trained to replace either the interpolations of a tabulated equation of state or directly the conservative-to-primitive map. The application of these neural networks to simple benchmark problems shows that both approaches improve over traditional root finders with tabular equation-of-state and multi-dimensional interpolations. In particular, the neural networks for the conservative-to-primitive map accelerate the variable recovery by more than an order of magnitude over standard methods while maintaining accuracy. Neural networks are thus an interesting option to improve the speed and robustness of relativistic hydrodynamics algorithms.