Intelligent Design: On the Emulation of Cosmological Simulations

Abstract: Simulation design is the choice of locations in parameter space at which simulations are to be run and is the first step in building an emulator capable of quickly providing estimates of simulation results for arbitrary locations in the parameter space. We introduce an alteration to the "OALHS" design used by Heitmann et al. (2006) that reduces the number of simulation runs required to achieve a fixed accuracy in our case study by a factor of two. We also compare interpolation procedures for emulators and find that interpolation via Gaussian Process models and via the much-easier-to-implement polynomial interpolation have comparable accuracy. A very simple emulation-building procedure consisting of a design sampled from the parameter prior distribution, combined with interpolation via polynomials also performs well. Although our primary motivation is efficient emulators of non-linear cosmological N-body simulations, in an appendix we describe an emulator for the CMB temperature power spectrum publicly available as computer code.