A Multi-Fidelity Emulator for the Matter Power Spectrum using Gaussian Processes (2022)

by Ming-Feng Ho, Simeon Bird, and Christian R. Shelton


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 ≃ 100 times better than a single-fidelity emulator at k ≤ 2 hMpc-1, and ≃ 20 times better at 3 ≤ k < 6.4 hMpc-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.

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Ming-Feng Ho, Simeon Bird, and Christian R. Shelton (2022). "A Multi-Fidelity Emulator for the Matter Power Spectrum using Gaussian Processes." Monthly Notices of the Royal Astronomical Society, 509(2), 2551-2565.       code   arxivext

Bibtex citation

@article{HoBirShe22,
   author = "Ming-Feng Ho and Simeon Bird and Christian R. Shelton",
   title = "A Multi-Fidelity Emulator for the Matter Power Spectrum using {G}aussian Processes",
   journal = "Monthly Notices of the Royal Astronomical Society",
   journalabbr = "MNRAS",
   year = 2022,
   month = jan,
   pages = "2551-2565",
   volume = 509,
   number = 2,
   doi = {10.1093/mnras/stab3114},
}