  Inferring the properties of black holes and neutron stars is a key science
goal of gravitational-wave (GW) astronomy. To extract as much information as
possible from GW observations we must develop methods to reduce the cost of
Bayesian inference. In this paper, we use artificial neural networks (ANNs) and
the parallelisation power of graphics processing units (GPUs) to improve the
surrogate modelling method, which can produce accelerated versions of existing
models. As a first application of our method, ANN-Sur, we build a time-domain
surrogate model of the spin-aligned binary black hole (BBH) waveform model
SEOBNRv4. We achieve median mismatches of 2e-5 and mismatches no worse than
2e-3. For a typical BBH waveform generated from 12 Hz with a total mass of $60
M_\odot$ the original SEOBNRv4 model takes 1812 ms. Existing bespoke code
optimisations (SEOBNRv4opt) reduced this to 91.6 ms and the interpolation
based, frequency-domain surrogate SEOBNRv4ROM can generate this waveform in 6.9
ms. Our ANN-Sur model, when run on a CPU takes 2.7 ms and just 0.4 ms when run
on a GPU. ANN-Sur can also generate large batches of waveforms simultaneously.
We find that batches of up to 10^4 waveforms can be evaluated on a GPU in just
163 ms, corresponding to a time per waveform of 0.016 ms. This method is a
promising way to utilise the parallelisation power of GPUs to drastically
increase the computational efficiency of Bayesian parameter estimation.
