We explore the possibility of inferring the properties of the Galactic neutron star population through machine learning. In particular, in this paper we focus on their dynamical characteristics and show that an artificial neural network is able to estimate with high accuracy the parameters which control the current positions of a mock population of pulsars. For this purpose, we implement a simplified population-synthesis framework (where selection biases are neglected at this stage) and concentrate on the natal kick-velocity distribution and the distribution of birth distances from the Galactic plane. By varying these and evolving the pulsar trajectories in time, we generate a series of simulations that are used to train and validate a suitably structured convolutional neural network. We demonstrate that our network is able to recover the parameters governing the kick-velocity and Galactic height distribution with a mean relative error of about $10^{-2}$. We discuss the limitations of our idealized approach and study a toy problem to introduce selection effects in a phenomenological way by incorporating the observed proper motions of 216 isolated pulsars. Our analysis highlights that increasing the sample of pulsars with accurate proper motion measurements by a factor of $sim$10, one of the future breakthroughs of the Square Kilometer Array, we might succeed in constraining the birth spatial and kick-velocity distribution of the neutron stars in the Milky Way with high precision through machine learning.
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