  Dynamical mass estimates of simple systems such globular clusters (GCs) still
suffer from up to a factor of 2 uncertainty. This is primarily due to the
oversimplifications of standard dynamical models that often neglect the effects
of the long-term evolution of GCs. Here, we introduce a new approach to measure
the dynamical properties of GCs, based on the combination of a deep-learning
framework and the large amount of data from direct $N$-body simulations. Our
algorithm, $\texttt{$\pi$-DOC}$ ($\textit{Predicting Images for the Dynamics Of
stellar Clusters}$) is composed of two convolutional networks, trained to learn
the non-trivial transformation between an observed GC luminosity map and its
associated mass distribution, age, and distance. The training set is made of
V-band luminosity and mass maps constructed as mock observations from $N$-body
simulations. The tests on $\texttt{$\pi$-DOC}$ demonstrate that we can predict
the mass distribution with a mean error per pixel of 27%, and the age and
distance with an accuracy of 1.5 Gyr and 6 kpc, respectively. In turn, we
recover the shape of the mass-to-light profile and its global value with a mean
error of 12%, which implies that we efficiently trace mass segregation. A
preliminary comparison with observations indicates that our algorithm is able
to predict the dynamical properties of GCs within the limits of the training
set. These encouraging results demonstrate that our deep-learning framework and
its forward modelling approach can offer a rapid and adaptable tool competitive
with standard dynamical models.
