  To investigate gravity in the non-linear regime of cosmic structure using
measurements from Stage-IV surveys, it is imperative to accurately compute
large-scale structure observables, such as non-linear matter power spectra, for
gravity models that extend beyond general relativity. However, the theoretical
predictions of non-linear observables are typically derived from N-body
simulations, which demand substantial computational resources. In this study,
we introduce a novel public emulator, termed FREmu, designed to provide rapid
and precise forecasts of non-linear power spectra specifically for the
Hu-Sawicki $f(R)$ gravity model across scales $0.0089 h \mathrm{Mpc}^{-1}<k<0.5
h \mathrm{Mpc}^{-1}$ and redshifts $0<z<3$. FREmu leverages Principal Component
Analysis and Artificial Neural Networks to establish a mapping from parameters
to power spectra, utilizing training data derived from the Quijote-MG
simulation suite. With a parameter space encompassing 7 dimensions, including
$\Omega_m$, $\Omega_b$, $h$, $n_s$, $\sigma_8$, $M_{\nu}$ and $f_{R_0}$, the
emulator achieves an accuracy exceeding 95% for the majority of cases, thus
proving to be highly efficient for constraining parameters.
