MG-NECOLA: Fast Neural Emulators for Modified Gravity Cosmologies

Observations of the large-scale structure (LSS) provide a powerful test of gravity on cosmological scales, but high-resolution N-body simulations of modified gravity (MG) are prohibitively expensive. We present MG-NECOLA, a convolutional neural network that enhances fast MG-PICOLA simulations to near-N-body fidelity at a fraction of the cost. MG-NECOLA reproduces QUIJOTE-MG N-body results in the power spectrum and bispectrum with better than 1% accuracy down to non-linear scales ($k \simeq 1~h~\mathrm{Mpc}^{-1}$), while reducing computational time by several orders of magnitude. Importantly, although trained only on $f(R)$ models with massless neutrinos, the network generalizes robustly to scenarios with massive neutrinos, preserving accuracy to within 5% at non-linear scales. This combination of precision and robustness establishes MG-NECOLA as a practical emulator for producing large ensembles of high-fidelity simulations, enabling efficient exploration of modified gravity and beyond-$\Lambda$CDM cosmologies in upcoming surveys.