We present in this paper one of the largest galaxy morphological classification catalogues to date, including over 20 million of galaxies, using the Dark Energy Survey (DES) Year 3 data based on Convolutional Neural Networks (CNN). Monochromatic $i$-band DES images with linear, logarithmic, and gradient scales, matched with debiased visual classifications from the Galaxy Zoo 1 (GZ1) catalogue, are used to train our CNN models. With a training set including bright galaxies ($16le{i}<18$) at low redshift ($z<0.25$), we furthermore investigate the limit of the accuracy of our predictions applied to galaxies at fainter magnitude and at higher redshifts. Our final catalogue covers magnitudes $16le{i}<21$, and redshifts $z<1.0$, and provides predicted probabilities to two galaxy types -- Ellipticals and Spirals (disk galaxies). Our CNN classifications reveal an accuracy of over 99% for bright galaxies when comparing with the GZ1 classifications ($i<18$). For fainter galaxies, the visual classification carried out by three of the co-authors shows that the CNN classifier correctly categorises disky galaxies with rounder and blurred features, which humans often incorrectly visually classify as Ellipticals. As a part of the validation, we carry out one of the largest examination of non-parametric methods, including $sim$100,000 galaxies with the same coverage of magnitude and redshift as the training set from our catalogue. We find that the Gini coefficient is the best single parameter discriminator between Ellipticals and Spirals for this data set.
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