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

We present a multi-fidelity emulation framework, MF-Box, an extended version of our previous MFEmulator, allowing us to emulate the high-fidelity matter power spectrum by combining information from N-body simulations of varying box sizes. We model the cosmological simulations using a graphical Gaussian process, with the particle load as a fidelity variable and the simulation volume as a different fidelity variable. By comparing to a high-fidelity testing suite, MF-Box achieves $< 3\%$ error until $k \simeq 7 h \,\mathrm{Mpc}^{-1}$ at $z \in [0, 3]$ with a similar cost to our previous multi-fidelity method, which was accurate only for $z \leq 1$. With an additional low-fidelity node in a smaller box, our new method MF-Box improves the emulation accuracy at $k > 2 h \,\mathrm{Mpc}^{-1}$ by a factor of $\simeq 10$. We also analyze MF-Box error as a function of computational budget and provide a guideline for optimal budget allocation per fidelity node. Our newly proposed MF-Box opens a new avenue for future surveys to combine simulation suites from different qualities and cheaply increase the dynamic range of emulation.