Multifidelity emulation for the matter power spectrum using Gaussian processes

• Published in: Monthly notices of the Royal Astronomical Society 2022-01, Vol.509 (2), p.2551-2565
• Main Authors: Ho, Ming-Feng, Bird, Simeon, Shelton, Christian R
• Format: Article
• Language: English
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1093/mnras/stab3114

ABSTRACT We present methods for emulating the matter power spectrum by combining information from cosmological N-body simulations at different resolutions. An emulator allows estimation of simulation output by interpolating across the parameter space of a limited number of simulations. We present the first implementation in cosmology of multifidelity emulation, where many low-resolution simulations are combined with a few high-resolution simulations to achieve an increased emulation accuracy. The power spectrum’s dependence on cosmology is learned from the low-resolution simulations, which are in turn calibrated using high-resolution simulations. We show that our multifidelity emulator predicts high-fidelity (HF) counterparts to percent-level relative accuracy when using only three HF simulations and outperforms a single-fidelity emulator that uses 11 simulations, although we do not attempt to produce a converged emulator with high absolute accuracy. With a fixed number of HF training simulations, we show that our multifidelity emulator is ≃100 times better than a single-fidelity emulator at $k \le 2 \, h\textrm {Mpc}{^{-1}}$, and ≃20 times better at $3 \le k \lt 6.4 \, h\textrm {Mpc}{^{-1}}$. Multifidelity emulation is fast to train, using only a simple modification to standard Gaussian processes. Our proposed emulator shows a new way to predict non-linear scales by fusing simulations from different fidelities.