Searching for strong galaxy-scale lenses in galaxy clusters with deep networks: I. Methodology and network performance

Strong galaxy-scale lenses in galaxy clusters provide a unique tool with which to investigate the inner mass distribution of these clusters and the subhalo density profiles in the low-mass regime, which can be compared with predictions from ΛCDM cosmological simulations. We search for galaxy-galaxy strong-lensing systems in the Hubble Space Telescope (HST) multi-band imaging of galaxy cluster cores by exploring the classification capabilities of deep learning techniques. Convolutional neural networks (CNNs) are trained utilising highly realistic simulations of galaxy-scale strong lenses injected into the HST cluster fields around cluster members (CLMs). To this aim, we take advantage of extensive spectroscopic information available in 16 clusters and accurate knowledge of the deflection fields in half of these from high-precision strong-lensing models. Using observationally based distributions, we sample the magnitudes (down to F814W = 29 AB), redshifts, and sizes of the background galaxy population. By placing these sources within the secondary caustics associated with the cluster galaxies, we build a sample of approximately 3000 strong galaxy-galaxy lenses, which preserve the full complexity of real multi-colour data and produce a wide diversity of strong-lensing configurations. We study two deep learning networks, processing a large sample of image cutouts, in three bands, acquired by HST Advanced Camera for Survey (ACS), and we quantify their classification performance using several standard metrics. We find that both networks achieve a very good trade-off between purity and completeness (85%-95%), as well as a good stability, with fluctuations within 2%-4%. We characterise the limited number of false negatives (FNs) and false positives (FPs) in terms of the physical properties of the background sources (magnitudes, colours, redshifts, and effective radii) and CLMs (Einstein radii and morphology). We also demonstrate the high degree of generalisation of the neural networks by applying our method to HST observations of 12 clusters with previously known galaxy-scale lensing systems.