Context. The publication of the Gaia Data Release 2 (Gaia DR2) opens a new era in astronomy. It includes precise astrometric data (positions, proper motions, and parallaxes) for more than 1.3 billion sources, mostly stars. To analyse such a vast amount of new data, the use of data-mining techniques and machine-learning algorithms is mandatory. Aims. A great example of the application of such techniques and algorithms is the search for open clusters (OCs), groups of stars that were born and move together, located in the disc. Our aim is to develop a method to automatically explore the data space, requiring minimal manual intervention. Methods. We explore the performance of a density-based clustering algorithm, DBSCAN, to find clusters in the data together with a supervised learning method such as an artificial neural network (ANN) to automatically distinguish between real OCs and statistical clusters. Results. The development and implementation of this method in a five-dimensional space (l, b, ϖ, μ_α^*, μ_δ) with the Tycho-Gaia Astrometric Solution (TGAS) data, and a posterior validation using Gaia DR2 data, lead to the proposal of a set of new nearby OCs. Conclusions. We have developed a method to find OCs in astrometric data, designed to be applied to the full Gaia DR2 archive.