Multi-Fidelity Emulation for the Matter Power Spectrum using Gaussian Processes

TL;DR

This paper introduces a multi-fidelity Gaussian process emulator for the matter power spectrum that combines low- and high-resolution simulations to achieve high accuracy with fewer high-fidelity runs.

Contribution

It presents the first implementation of multi-fidelity emulation in cosmology, significantly improving prediction accuracy while reducing the need for numerous high-resolution simulations.

Findings

Multi-fidelity emulator achieves percent-level accuracy with only 3 high-res simulations.

Outperforms single-fidelity emulator by up to 100 times at certain scales.

Emulator is fast to train and effectively fuses different fidelity simulations.

Abstract

We present methods for emulating the matter power spectrum by combining information from cosmological $N$-body simulations at different resolutions. An emulator allows estimation of simulation output by interpolating across the parameter space of a limited number of simulations. We present the first implementation in cosmology of multi-fidelity emulation, where many low-resolution simulations are combined with a few high-resolution simulations to achieve an increased emulation accuracy. The power spectrum's dependence on cosmology is learned from the low-resolution simulations, which are in turn calibrated using high-resolution simulations. We show that our multi-fidelity emulator predicts high-fidelity counterparts to percent-level relative accuracy when using only $3$ high-fidelity simulations and outperforms a single-fidelity emulator that uses $11$ simulations, although we do not attempt to produce a converged emulator with high absolute accuracy. With a fixed number of high-fidelity training simulations, we show that our multi-fidelity emulator is $\simeq 100$ times better than a single-fidelity emulator at $k \leq 2 h \mathrm{Mpc}^{-1}$, and $\simeq 20$ times better at $3 \leq k < 6.4 h \mathrm{Mpc}^{-1}$. Multi-fidelity emulation is fast to train, using only a simple modification to standard Gaussian processes. Our proposed emulator shows a new way to predict non-linear scales by fusing simulations from different fidelities.