  We test the convergence of fast simulations based on the COmoving Lagrangian
Acceleration (COLA) method for predictions of the matter power spectrum,
specialising our analysis in the redshift range $1 \le z \le 1.65$, relevant to
high-redshift spectroscopic galaxy surveys. We then focus on the enhancement of
the matter power spectrum in modified gravity (MG), the boost factor, using the
Dvali-Gabadadze-Porrati (DGP) theory as a test case but developing a general
approach that can be applied to other MG theories. After identifying the
minimal simulation requirements for accurate DGP boost factors, we design and
produce a COLA simulation suite that we use to train a neural network emulator
for the DGP boost factor. Using MG-AREPO simulations as a reference, we
estimate the emulator accuracy to be of $\sim 3\%$ up to $k=5 \, h {\rm
Mpc}^{-1}$ at $0 \leq z \leq 2$. We make the emulator publicly available at:
https://github.com/BartolomeoF/nDGPemu.
