Multi-Fidelity Emulation for the Matter Power Spectrum using Gaussian Processes

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 multi-fidelity 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 multi-fidelity emulator predicts high-fidelity counterparts to percent-level relative accuracy when using only $3$ high-fidelity 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 high-fidelity training simulations, we show that our multi-fidelity emulator is $\simeq 100$ times better than a single-fidelity emulator at $k\le 2h{\mathrm{Mpc}}^{-1}$, and $\simeq 20$ times better at $3\le k<6.4h{\mathrm{Mpc}}^{-1}$. Multi-fidelity 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.

arXiv comment17 pages, 16 figures, 1 table. Matches version accepted to MNRAS. Code available in https://github.com/jibanCat/matter_multi_fidelity_emu

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