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

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 $k \simeq 7 \,h/\mathrm{Mpc}$ 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 $k > 2 \,h/\mathrm{Mpc}$, 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.