Deriving star cluster parameters with convolutional neural networks. I.
  Age, mass, and size
  Context. Convolutional neural networks (CNNs) have been proven to perform
fast classification and detection on natural images and have potential to infer
astrophysical parameters on the exponentially increasing amount of sky survey
imaging data. The inference pipeline can be trained either from real
human-annotated data or simulated mock observations. Until now star cluster
analysis was based on integral or individual resolved stellar photometry. This
limits the amount of information that can be extracted from cluster images.
  Aims. Develop a CNN-based algorithm aimed to simultaneously derive ages,
masses, and sizes of star clusters directly from multi-band images. Demonstrate
CNN capabilities on low mass semi-resolved star clusters in a low
signal-to-noise ratio regime.
  Methods. A CNN was constructed based on the deep residual network (ResNet)
architecture and trained on simulated images of star clusters with various
ages, masses, and sizes. To provide realistic backgrounds, M31 star fields
taken from the PHAT survey were added to the mock cluster images.
  Results. The proposed CNN was verified on mock images of artificial clusters
and has demonstrated high precision and no significant bias for clusters of
ages $\lesssim$3Gyr and masses between 250 and 4,000 ${\rm M_\odot}$. The
pipeline is end-to-end, starting from input images all the way to the inferred
parameters; no hand-coded steps have to be performed: estimates of parameters
are provided by the neural network in one inferential step from raw images.
