  We present our results from training and evaluating a convolutional neural
network (CNN) to predict galaxy shapes from wide-field survey images of the
first data release of the Dark Energy Survey (DES DR1). We use conventional
shape measurements as ground truth from an overlapping, deeper survey with less
sky coverage, the Canada-France Hawaii Telescope Lensing Survey (CFHTLenS). We
demonstrate that CNN predictions from single band DES images reproduce the
results of CFHTLenS at bright magnitudes and show higher correlation with
CFHTLenS at fainter magnitudes than maximum likelihood model fitting estimates
in the DES Y1 im3shape catalogue. Prediction of shape parameters with a CNN is
also extremely fast, it takes only 0.2 milliseconds per galaxy, improving more
than 4 orders of magnitudes over forward model fitting. The CNN can also
accurately predict shapes when using multiple images of the same galaxy, even
in different color bands, with no additional computational overhead. The CNN is
again more precise for faint objects, and the advantage of the CNN is more
pronounced for blue galaxies than red ones when compared to the DES Y1
metacalibration catalogue, which fits a single Gaussian profile using riz band
images. We demonstrate that CNN shape predictions within the metacalibration
self-calibrating framework yield shear estimates with negligible multiplicative
bias, $ m < 10^{-3}$, and no significant PSF leakage. Our proposed setup is
applicable to current and next generation weak lensing surveys where higher
quality ground truth shapes can be measured in dedicated deep fields.
