Context. Open clusters are key targets for studies of Galaxy structure and evolution, and stellar physics. Since the Gaia data release 2 (DR2), the discovery of undetected clusters has shown that previous surveys were incomplete. Aims. Our aim is to exploit the Big Data capabilities of machine learning to detect new open clusters in Gaia DR2, and to complete the open cluster sample to enable further studies of the Galactic disc. Methods. We use a machine-learning based methodology to systematically search the Galactic disc for overdensities in the astrometric space and identify the open clusters using photometric information. First, we used an unsupervised clustering algorithm, DBSCAN, to blindly search for these overdensities in Gaia DR2 (l, b, ϖ, μα*, μδ), and then we used a deep learning artificial neural network trained on colour–magnitude diagrams to identify isochrone patterns in these overdensities, and to confirm them as open clusters. Results. We find 582 new open clusters distributed along the Galactic disc in the region |b| < 20°. We detect substructure in complex regions, and identify the tidal tails of a disrupting cluster UBC 274 of ∼3 Gyr located at ∼2 kpc. Conclusions. Adapting the mentioned methodology to a Big Data environment allows us to target the search using the physical properties of open clusters instead of being driven by computational limitations. This blind search for open clusters in the Galactic disc increases the number of known open clusters by 45%.