Machine Learning for ConservativetoPrimitive in Relativistic Hydrodynamics
Abstract
The numerical solution of relativistic hydrodynamics equations in conservative form requires rootfinding algorithms that invert the conservativetoprimitive 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 conservativetoprimitive map. The application of these neural networks to simple benchmark problems shows that both approaches improve over traditional root finders with tabular equationofstate and multidimensional interpolations. In particular, the neural networks for the conservativetoprimitive 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.
 Publication:

Symmetry
 Pub Date:
 November 2021
 DOI:
 10.3390/sym13112157
 arXiv:
 arXiv:2109.02679
 Bibcode:
 2021Symm...13.2157D
 Keywords:

 Astrophysics  Instrumentation and Methods for Astrophysics;
 Physics  Computational Physics;
 Physics  Fluid Dynamics
 EPrint:
 17 pages, 12 figures, 2 tables