The next generation of data-intensive surveys are bound to produce a vast amount of data, which can be dealt with using machine-learning methods to explore possible correlations within the multi-dimensional parameter space. We explore the classification capabilities of convolution neural networks (CNNs) to identify galaxy cluster members (CLMs) by using Hubble Space Telescope (HST) images of 15 galaxy clusters at redshift 0.19<z<0.60, observed as part of the CLASH and Hubble Frontier Field programmes. We used extensive spectroscopic information, based on the CLASH-VLT VIMOS programme combined with MUSE observations, to define the knowledge base. We performed various tests to quantify how well CNNs can identify cluster members on the basis of imaging information only. We investigated the CNN capability to predict source memberships outside the training coverage, by identifying CLMs at the faint end of the magnitude distributions. We find that the CNNs achieve a purity-completeness rate ~90%, demonstrating stable behaviour, along with a remarkable generalisation capability with respect to cluster redshifts. We concluded that if extensive spectroscopic information is available as a training base, the proposed approach is a valid alternative to catalogue-based methods because it has the advantage of avoiding photometric measurements, which are particularly challenging and time-consuming in crowded cluster cores. As a byproduct, we identified 372 photometric CLMs, with mag(F814)<25, to complete the sample of 812 spectroscopic CLMs in four galaxy clusters RX~J2248-4431, MACS~J0416-2403, MACS~J1206-0847 and MACS~J1149+2223. When this technique is applied to the data that are expected to become available from forthcoming surveys, it will be an efficient tool for a variety of studies requiring CLM selection, such as galaxy number densities, luminosity functions, and lensing mass reconstruction.
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