Characterizing the velocity of a wandering black hole and properties of the surrounding medium using convolutional neural networks

We present a method for estimating the velocity of a wandering black hole and the equation of state for the gas around, based on a catalog of numerical simulations. The method uses machine learning methods based on convolutional neural networks applied to the classification of images resulting from numerical simulations. Specifically we focus on the supersonic velocity regime and choose the direction of the black hole to be parallel to its spin. We build a catalog of 900 simulations by numerically solving Euler's equations onto the fixed space-time background of a black hole, for two parameters: the adiabatic index $\Gamma$ with values in the range [1.1, 5/3], and the asymptotic relative velocity of the black hole with respect to the surroundings $v_{\infty}$, with values within $[0.2, 0.8]c$. For each simulation we produce a 2D image of the gas density once the process of accretion has approached a stationary regime. The results obtained show that the implemented Convolutional Neural Networks are capable to classify correctly the adiabatic index $87.78\%$ of the time within an uncertainty of $\pm 0.0284$ while the prediction of the velocity is correct $96.67\%$ of the times within an uncertainty of $\pm 0.03c$. We expect that this combination of a massive number of numerical simulations and machine learning methods will help analyze more complicated scenarios related to future high resolution observations of black holes, like those from the Event Horizon Telescope.