MG-NECOLA: Fast Neural Emulators for Modified Gravity Cosmologies

TL;DR

MG-NECOLA addresses the high cost of modified gravity N-body simulations by learning a CNN to upgrade fast MG-PICOLA runs to near-QUIJOTE-MG fidelity. It trains a V-Net–based CNN to predict residual displacements that correct MG-PICOLA outputs, achieving better than $1\%$ accuracy in the power spectrum $P(k)$ and bispectrum $B(k)$ down to non-linear scales ($k \simeq 1~h~\mathrm{Mpc}^{-1}$) and generalizing to scenarios with massive neutrinos. The method yields orders-of-magnitude speedups (≈$180$ s per realization on a GPU) and enables large ensembles for exploring MG and beyond-$\Lambda$CDM cosmologies, with robust transfer to unseen $M_\nu$ and $f_{R_0}$ values. This practical emulator thus facilitates efficient interpretation of upcoming large-scale structure surveys where non-linear MG effects are most pronounced.

Abstract

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-$Λ$CDM cosmologies in upcoming surveys.

Figures (1)

• Figure 1: Performance of MG-NECOLA (NN) compared to MG-PICOLA (input benchmark) and QUIJOTE-MG (truth). Top left: power spectrum (top) and transfer function (bottom). Top right: bispectrum. Bottom left: ablation study comparing our loss function (Eq. \ref{['Eq: Loss Function']}, blue) with NECOLA loss variants, demonstrating improved accuracy on non-linear scales. Bottom right: transfer function for the generalization to massive neutrinos after training on $M_\nu=0$. MG-NECOLA (red dashed) substantially improves upon MG-PICOLA (blue dotted), recovering results in much closer agreement with the QUIJOTE-MG reference (black solid).