  We present SPECULATOR - a fast, accurate, and flexible framework for
emulating stellar population synthesis (SPS) models for predicting galaxy
spectra and photometry. For emulating spectra, we use principal component
analysis to construct a set of basis functions, and neural networks to learn
the basis coefficients as a function of the SPS model parameters. For
photometry, we parameterize the magnitudes (for the filters of interest) as a
function of SPS parameters by a neural network. The resulting emulators are
able to predict spectra and photometry under both simple and complicated SPS
model parameterizations to percent-level accuracy, giving a factor of
$10^3$-$10^4$ speed up over direct SPS computation. They have
readily-computable derivatives, making them amenable to gradient-based
inference and optimization methods. The emulators are also straightforward to
call from a GPU, giving an additional order-of-magnitude speed-up. Rapid SPS
computations delivered by emulation offers a massive reduction in the
computational resources required to infer the physical properties of galaxies
from observed spectra or photometry and simulate galaxy populations under SPS
models, whilst maintaining the accuracy required for a range of applications.
