  The Lyman-alpha forest provides strong constraints on both cosmological
parameters and intergalactic medium astrophysics, which are forecast to improve
further with the next generation of surveys including eBOSS and DESI. As is
generic in cosmological inference, extracting this information requires a
likelihood to be computed throughout a high-dimensional parameter space.
Evaluating the likelihood requires a robust and accurate mapping between the
parameters and observables, in this case the 1D flux power spectrum.
Cosmological simulations enable such a mapping, but due to computational time
constraints can only be evaluated at a handful of sample points; "emulators"
are designed to interpolate between these. The problem then reduces to placing
the sample points such that an accurate mapping is obtained while minimising
the number of expensive simulations required. To address this, we introduce an
emulation procedure that employs Bayesian optimisation of the training set for
a Gaussian process interpolation scheme. Starting with a Latin hypercube
sampling (other schemes with good space-filling properties can be used), we
iteratively augment the training set with extra simulations at new parameter
positions which balance the need to reduce interpolation error while focussing
on regions of high likelihood. We show that smaller emulator error from the
Bayesian optimisation propagates to smaller widths on the posterior
distribution. Even with fewer simulations than a Latin hypercube, Bayesian
optimisation shrinks the 95% credible volume by 90% and, e.g., the 1 sigma
error on the amplitude of small-scale primordial fluctuations by 38%. This is
the first demonstration of Bayesian optimisation applied to large-scale
structure emulation, and we anticipate the technique will generalise to many
other probes such as galaxy clustering, weak lensing and 21cm.
