Intelligent Design: On the Emulation of Cosmological Simulations

TL;DR

This paper improves the design of simulation sampling strategies for cosmological emulators, demonstrating that simpler interpolation methods can achieve comparable accuracy with fewer simulations, and provides a publicly available emulator for the CMB spectrum.

Contribution

It introduces an improved simulation design method reducing required runs and compares interpolation techniques, highlighting the effectiveness of polynomial interpolation for cosmological emulators.

Findings

Reduced simulation runs by a factor of two with the new design

Polynomial interpolation performs comparably to Gaussian Process models

Provided a publicly available emulator for the CMB temperature power spectrum

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.