On ab initio-based, free and closed-form expressions for gravitational waves

Abstract We introduce a new approach for finding high accuracy, free and closed-form expressions for the gravitational waves emitted by binary black hole collisions from ab initio models. More precisely, our expressions are built from numerical surrogate models based on supercomputer simulations of...

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Autores principales:	Manuel Tiglio, Aarón Villanueva
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/40fccd16613a4ea5abf39d489843e778
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spelling	oai:doaj.org-article:40fccd16613a4ea5abf39d489843e7782021-12-02T13:15:56ZOn ab initio-based, free and closed-form expressions for gravitational waves10.1038/s41598-021-85102-y2045-2322https://doaj.org/article/40fccd16613a4ea5abf39d489843e7782021-03-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-85102-yhttps://doaj.org/toc/2045-2322Abstract We introduce a new approach for finding high accuracy, free and closed-form expressions for the gravitational waves emitted by binary black hole collisions from ab initio models. More precisely, our expressions are built from numerical surrogate models based on supercomputer simulations of the Einstein equations, which have been shown to be essentially indistinguishable from each other. Distinct aspects of our approach are that: (i) representations of the gravitational waves can be explicitly written in a few lines, (ii) these representations are free-form yet still fast to search for and validate and (iii) there are no underlying physical approximations in the underlying model. The key strategy is combining techniques from Artificial Intelligence and Reduced Order Modeling for parameterized systems. Namely, symbolic regression through genetic programming combined with sparse representations in parameter space and the time domain using Reduced Basis and the Empirical Interpolation Method enabling fast free-form symbolic searches and large-scale a posteriori validations. As a proof of concept we present our results for the collision of two black holes, initially without spin, and with an initial separation corresponding to 25–31 gravitational wave cycles before merger. The minimum overlap, compared to ground truth solutions, is 99%. That is, 1% difference between our closed-form expressions and supercomputer simulations; this is considered for gravitational (GW) science more than the minimum required due to experimental numerical errors which otherwise dominate. This paper aims to contribute to the field of GWs in particular and Artificial Intelligence in general.Manuel TiglioAarón VillanuevaNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-11 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Manuel Tiglio Aarón Villanueva On ab initio-based, free and closed-form expressions for gravitational waves
description	Abstract We introduce a new approach for finding high accuracy, free and closed-form expressions for the gravitational waves emitted by binary black hole collisions from ab initio models. More precisely, our expressions are built from numerical surrogate models based on supercomputer simulations of the Einstein equations, which have been shown to be essentially indistinguishable from each other. Distinct aspects of our approach are that: (i) representations of the gravitational waves can be explicitly written in a few lines, (ii) these representations are free-form yet still fast to search for and validate and (iii) there are no underlying physical approximations in the underlying model. The key strategy is combining techniques from Artificial Intelligence and Reduced Order Modeling for parameterized systems. Namely, symbolic regression through genetic programming combined with sparse representations in parameter space and the time domain using Reduced Basis and the Empirical Interpolation Method enabling fast free-form symbolic searches and large-scale a posteriori validations. As a proof of concept we present our results for the collision of two black holes, initially without spin, and with an initial separation corresponding to 25–31 gravitational wave cycles before merger. The minimum overlap, compared to ground truth solutions, is 99%. That is, 1% difference between our closed-form expressions and supercomputer simulations; this is considered for gravitational (GW) science more than the minimum required due to experimental numerical errors which otherwise dominate. This paper aims to contribute to the field of GWs in particular and Artificial Intelligence in general.
format	article
author	Manuel Tiglio Aarón Villanueva
author_facet	Manuel Tiglio Aarón Villanueva
author_sort	Manuel Tiglio
title	On ab initio-based, free and closed-form expressions for gravitational waves
title_short	On ab initio-based, free and closed-form expressions for gravitational waves
title_full	On ab initio-based, free and closed-form expressions for gravitational waves
title_fullStr	On ab initio-based, free and closed-form expressions for gravitational waves
title_full_unstemmed	On ab initio-based, free and closed-form expressions for gravitational waves
title_sort	on ab initio-based, free and closed-form expressions for gravitational waves
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/40fccd16613a4ea5abf39d489843e778
work_keys_str_mv	AT manueltiglio onabinitiobasedfreeandclosedformexpressionsforgravitationalwaves AT aaronvillanueva onabinitiobasedfreeandclosedformexpressionsforgravitationalwaves
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On ab initio-based, free and closed-form expressions for gravitational waves

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