Machine Learning for Conservative-to-Primitive in Relativistic Hydrodynamics

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 sop...

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Autores principales:	Tobias Dieselhorst, William Cook, Sebastiano Bernuzzi, David Radice
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	relativistic hydrodynamics machine learning conservative-to-primitive Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/4610711e64c94f5eaf8c22d88fb09f53
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id	oai:doaj.org-article:4610711e64c94f5eaf8c22d88fb09f53
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spelling	oai:doaj.org-article:4610711e64c94f5eaf8c22d88fb09f532021-11-25T19:07:12ZMachine Learning for Conservative-to-Primitive in Relativistic Hydrodynamics10.3390/sym131121572073-8994https://doaj.org/article/4610711e64c94f5eaf8c22d88fb09f532021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2157https://doaj.org/toc/2073-8994The 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.Tobias DieselhorstWilliam CookSebastiano BernuzziDavid RadiceMDPI AGarticlerelativistic hydrodynamicsmachine learningconservative-to-primitiveMathematicsQA1-939ENSymmetry, Vol 13, Iss 2157, p 2157 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	relativistic hydrodynamics machine learning conservative-to-primitive Mathematics QA1-939
spellingShingle	relativistic hydrodynamics machine learning conservative-to-primitive Mathematics QA1-939 Tobias Dieselhorst William Cook Sebastiano Bernuzzi David Radice Machine Learning for Conservative-to-Primitive in Relativistic Hydrodynamics
description	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.
format	article
author	Tobias Dieselhorst William Cook Sebastiano Bernuzzi David Radice
author_facet	Tobias Dieselhorst William Cook Sebastiano Bernuzzi David Radice
author_sort	Tobias Dieselhorst
title	Machine Learning for Conservative-to-Primitive in Relativistic Hydrodynamics
title_short	Machine Learning for Conservative-to-Primitive in Relativistic Hydrodynamics
title_full	Machine Learning for Conservative-to-Primitive in Relativistic Hydrodynamics
title_fullStr	Machine Learning for Conservative-to-Primitive in Relativistic Hydrodynamics
title_full_unstemmed	Machine Learning for Conservative-to-Primitive in Relativistic Hydrodynamics
title_sort	machine learning for conservative-to-primitive in relativistic hydrodynamics
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/4610711e64c94f5eaf8c22d88fb09f53
work_keys_str_mv	AT tobiasdieselhorst machinelearningforconservativetoprimitiveinrelativistichydrodynamics AT williamcook machinelearningforconservativetoprimitiveinrelativistichydrodynamics AT sebastianobernuzzi machinelearningforconservativetoprimitiveinrelativistichydrodynamics AT davidradice machinelearningforconservativetoprimitiveinrelativistichydrodynamics
_version_	1718410274016329728

Machine Learning for Conservative-to-Primitive in Relativistic Hydrodynamics

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