Uncertainty-aware and Data-efficient Cosmological Emulation using Gaussian Processes and PCA

Bayesian parameter inference is one of the key elements for model selection in cosmological research. However, the available inference tools require a large number of calls to simulation codes which can lead to high and sometimes even infeasible computational costs. In this work we propose a new way of emulating simulation codes for Bayesian parameter inference. In particular, this novel approach emphasizes the uncertainty-awareness of the emulator, which allows to state the emulation accuracy and ensures reliable performance. With a focus on data efficiency, we implement an active learning algorithm based on a combination of Gaussian Processes and Principal Component Analysis. We find that for an MCMC analysis of Planck and BAO data on the $\Lambda$CDM model (6 model and 21 nuisance parameters) we can reduce the number of simulation calls by a factor of $\sim$500 and save about $96\%$ of the computational costs.