Accelerating cosmological inference with Gaussian processes and neural
  networks -- an application to LSST Y1 weak lensing and galaxy clustering
  Studying the impact of systematic effects, optimizing survey strategies,
assessing tensions between different probes and exploring synergies of
different data sets require a large number of simulated likelihood analyses,
each of which cost thousands of CPU hours. In this paper, we present a method
to accelerate cosmological inference using emulators based on Gaussian process
regression and neural networks. We iteratively acquire training samples in
regions of high posterior probability which enables accurate emulation of data
vectors even in high dimensional parameter spaces. We showcase the performance
of our emulator with a simulated 3x2 point analysis of LSST-Y1 with realistic
theoretical and systematics modelling. We show that our emulator leads to
high-fidelity posterior contours, with an order of magnitude speed-up. Most
importantly, the trained emulator can be re-used for extremely fast impact and
optimization studies. We demonstrate this feature by studying baryonic physics
effects in LSST-Y1 3x2 point analyses where each one of our MCMC runs takes
approximately 5 minutes. This technique enables future cosmological analyses to
map out the science return as a function of analysis choices and survey
strategy.
