  We implement a sample-efficient method for rapid and accurate emulation of
semi-analytical galaxy formation models over a wide range of model outputs. We
use ensembled deep learning algorithms to produce a fast emulator of an updated
version of the GALFORM model from a small number of training examples. We use
the emulator to explore the model's parameter space, and apply sensitivity
analysis techniques to better understand the relative importance of the model
parameters. We uncover key tensions between observational datasets by applying
a heuristic weighting scheme in a Markov chain Monte Carlo framework and
exploring the effects of requiring improved fits to certain datasets relative
to others. Furthermore, we demonstrate that this method can be used to
successfully calibrate the model parameters to a comprehensive list of
observational constraints. In doing so, we re-discover previous GALFORM fits in
an automatic and transparent way, and discover an improved fit by applying a
heavier weighting to the fit to the metallicities of early-type galaxies. The
deep learning emulator requires a fraction of the model evaluations needed in
similar emulation approaches, achieving an out-of-sample mean absolute error at
the knee of the K-band luminosity function of 0.06 dex with less than 1000
model evaluations. We demonstrate that this is an extremely efficient,
inexpensive and transparent way to explore multi-dimensional parameter spaces,
and can be applied more widely beyond semi-analytical galaxy formation models.
