3D extinction mapping of the Milky Way using Convolutional Neural
  Networks: Presentation of the method and demonstration in the Carina Arm
  region
  Context. Several methods have been proposed to build 3D extinction maps of
the Milky Way (MW), most often based on Bayesian approaches. Although some
studies employed machine learning (ML) methods in part of their procedure, or
to specific targets, no 3D extinction map of a large volume of the MW solely
based on a Neural Network method has been reported so far. Aims. We aim to
apply deep learning as a solution to build 3D extinction maps of the MW.
Methods. We built a convolutional neural network (CNN) using the CIANNA
framework, and trained it with synthetic 2MASS data. We used the Besan\c{c}on
Galaxy model to generate mock star catalogs, and 1D Gaussian random fields to
simulate the extinction profiles. From these data we computed color-magnitude
diagrams (CMDs) to train the network, using the corresponding extinction
profiles as targets. A forward pass with observed 2MASS CMDs provided
extinction profile estimates for a grid of lines of sight. Results. We trained
our network with data simulating lines of sight in the area of the Carina
spiral arm tangent and obtained a 3D extinction map for a large sector in this
region ($l = 257 - 303$ deg, $|b| \le 5$ deg), with distance and angular
resolutions of $100$ pc and $30$ arcmin, respectively, and reaching up to $\sim
10$ kpc. Although each sightline is computed independently in the forward
phase, the so-called fingers-of-God artifacts are weaker than in many other 3D
extinction maps. We found that our CNN was efficient in taking advantage of
redundancy across lines of sight, enabling us to train it with only 9
sightlines simultaneously to build the whole map. Conclusions. We found deep
learning to be a reliable approach to produce 3D extinction maps from large
surveys. With this methodology, we expect to easily combine heterogeneous
surveys without cross-matching, and therefore to exploit several surveys in a
complementary fashion.
