  In this paper, we introduce a numerical method based on Artificial Neural
Networks (ANNs) for the analysis of black hole solutions to the
Einstein-axion-dilaton system in a high dimensional parabolic class. Leveraging
a profile root-finding technique based on General Relativity we describe an ANN
solver to directly tackle the system of ordinary differential equations.
Through our extensive numerical analysis, we demonstrate, for the first time,
that there is no self-similar critical solution for the parabolic class in the
high dimensions of space-time. Specifically, we develop $95\%$ ANN-based
confidence intervals for all the solutions in their domains. At the $95\%$
confidence level, our ANN estimators confirm that there is no black hole
solution in higher dimensions, hence the gravitational collapse does not occur.
Results provide some doubts about the universality of the Choptuik phenomena.
Therefore, we conclude that the fastest-growing mode of the perturbations that
determine the critical exponent does not exist for the parabolic class in the
high dimensions.
