Armin Hatefi, Ehsan Hatefi and Roberto J. Lopez-Sastre
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Neural networks assisted Metropolis-Hastings for Bayesian estimation of critical exponent on elliptic black hole solution in 4D using quantum perturbation theory
It is well-known that the critical gravitational collapse produces continuous self-similar solutions characterized by the Choptuik critical exponent, γ. We examine the solutions in the domains of the linear perturbation equations, considering the numerical measurement errors. Specifically, we study quantum perturbation theory for the four-dimensional Einstein-axion-dilaton system of the elliptic class of SL(2,ℝ) transformations. We develop a novel artificial neural network-assisted Metropolis-Hastings algorithm based on quantum perturbation theory to find the distribution of the critical exponent in a Bayesian framework. Unlike existing methods, this new probabilistic approach identifies the available deterministic solution and explores the range of physically distinguishable critical exponents that may arise due to numerical measurement errors.
期刊介绍:
Journal of Cosmology and Astroparticle Physics (JCAP) encompasses theoretical, observational and experimental areas as well as computation and simulation. The journal covers the latest developments in the theory of all fundamental interactions and their cosmological implications (e.g. M-theory and cosmology, brane cosmology). JCAP''s coverage also includes topics such as formation, dynamics and clustering of galaxies, pre-galactic star formation, x-ray astronomy, radio astronomy, gravitational lensing, active galactic nuclei, intergalactic and interstellar matter.