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

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 $256\mathrm{Mpc}/h$ and $100\mathrm{Mpc}/h$, each with $128^3$ particles, and a high-fidelity suite (HF) with $512^3$ particles at $256\mathrm{Mpc}/h$, 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 $k\simeq 7h/\mathrm{Mpc}$ 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 $k>2h/\mathrm{Mpc}$, 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.

arXiv comment19 pages, 16 figures. Match the MNRAS version. Data available at: https://github.com/jibanCat/MFBoxData, Code and tutorials available at: https://github.com/jibanCat/matter_emu_mfbox

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