Hunting for open clusters in Gaia EDR3: $628$ new open clusters found
  with OCfinder
  The improvements in the precision of the published data in \textit{Gaia} EDR3
with respect to \textit{Gaia} DR2, particularly for parallaxes and proper
motions, offer the opportunity to increase the number of known open clusters in
the Milky Way by detecting farther and fainter objects that have so far go
unnoticed. Our aim is to keep completing the open cluster census in the Milky
Way with the detection of new stellar groups in the Galactic disc. We use
\textit{Gaia} EDR3 up to magnitude $G = 18$ mag, increasing in one unit the
magnitude limit and therefore the search volume explored in our previous
studies. We use the \texttt{OCfinder} method to search for new open clusters in
\textit{Gaia} EDR3 using a Big Data environment. As a first step,
\texttt{OCfinder} identifies stellar statistical overdensities in the five
dimensional astrometric space (position, parallax and proper motions) using the
\texttt{DBSCAN} clustering algorithm. Then, these overdensities are classified
into random statistical overdensities or real physical open clusters using a
deep artificial neural network trained on well-characterised $G$, $G_{\rm BP} -
G_{\rm RP}$ colour-magnitude diagrams. We report the discovery of $664$ new
open clusters within the Galactic disc, most of them located beyond $1$ kpc
from the Sun. From the estimation of ages, distances and line-of-sight
extinctions of these open clusters, we see that young clusters align following
the Galactic spiral arms while older ones are dispersed in the Galactic disc.
Furthermore, we find that most open clusters are located at low Galactic
altitudes with the exception of a few groups older than $1$ Gyr. We show the
success of the \texttt{OCfinder} method leading to the discovery of a total of
$1\,310$ open clusters (joining the discoveries here with the previous ones
based on \textit{Gaia} DR2)[abridged]
