MF-Box: multifidelity and multiscale emulation for the matter power spectrum

Abstract

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 (LF) suites (L1 and L2) at 256 and $100 \, \rm {Mpc\, ~}h^{-1}$, each with 1283 particles, and a high-fidelity (HF) suite with 5123 particles at $256 \, \rm {Mpc\, ~}h^{-1}$, representing a higher particle load compared to the LF 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 three HF simulations using a Gaussian process. MF-Box successfully emulates power spectra from our HF testing set with a relative error of $\lt 3~{{\ \rm per\ cent}}$ up to $k \simeq 7 \, h\rm {Mpc}{^{-1}}$ at z ∈ [0, 3], while maintaining a cost similar to our previous multifidelity approach, which was accurate only up to z = 1. The addition of an extra LF node in a smaller box significantly improves emulation accuracy for MF-Box at $k \gt 2 \, h\rm {Mpc}{^{-1}}$, 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.