MF-Box: Multi-fidelity and multi-scale emulation for the matter power spectrum (2023)

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

Abstract: We introduce MF-Box, an extended version of MFEmulator, designed as a fast surrogate for power spectra, trained using N-body simulation suites from various box sizes and particle loads. To demonstrate MF-Box's effectiveness, we design simulation suites that include low-fidelity suites (L1 and L2) at 256  Mpc h^-1 and 100  Mpc h^-1, each with 128³ particles, and a high-fidelity suite (HF) with 512³ particles at 256  Mpc h^-1, representing a higher particle load compared to the low-fidelity suites. MF-Box acts as a probabilistic resolution correction function, learning most of the cosmological dependencies from L1 and L2 simulations and rectifying resolution differences with just 3 HF simulations using a Gaussian process. MF-Box successfully emulates power spectra from our HF testing set with a relative error of < 3% up to k ≃ 7  hMpc{^-1} at z in [0, 3], while maintaining a cost similar to our previous multi-fidelity approach, which was accurate only up to z = 1. The addition of an extra low-fidelity node in a smaller box significantly improves emulation accuracy for MF-Box at k > 2  hMpc{^-1}, increasing it by a factor of 10. We conduct an error analysis of MF-Box based on computational budget, providing guidance for optimizing budget allocation per fidelity node. Our proposed MF-Box enables future surveys to efficiently combine simulation suites of varying quality, effectively expanding the range of emulation capabilities while ensuring cost efficiency.

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Ming-Feng Ho, Simeon Bird, Martin A. Fernandez, and Christian R. Shelton (2023). "MF-Box: Multi-fidelity and multi-scale emulation for the matter power spectrum." Monthly Notices of the Royal Astronomical Society, 526(2), 2903-2919.

Bibtex citation

@article{Hoetal23,
   author = "Ming-Feng Ho and Simeon Bird and Martin A. Fernandez and Christian R. Shelton",
   title = "{MF-Box}: Multi-fidelity and multi-scale emulation for the matter power spectrum",
   journal = "Monthly Notices of the Royal Astronomical Society",
   journalabbr = "MNRAS",
   year = 2023,
   volume = 526,
   number = 2,
   month = dec,
   pages = "2903--2919",
   doi = "10.0193/mnras/stad2901",
}