Towards a Universal Field-level Cosmological Emulator

We train convolutional neural networks to correct the output of fast and approximate N-body simulations at the field level. Our model, Neural Enhanced COLA, –NECOLA–, takes as input a snapshot generated by the computationally efficient COLA code and corrects the positions of the cold dark matter particles to match the results of full N-body Quijote simulations. We quantify the accuracy of the network using several summary statistics, and find that NECOLA can reproduce the results of the full N-body simulations with sub-percent accuracy down to k ≃ 1 hMpc-1. Furthermore, the model, that was trained on simulations with a fixed value of the cosmological parameters, is also able to correct the output of COLA simulations with different values of Ωm, Ωb, h, ns, σ8, w, and Mν with very high accuracy: the power spectrum and the cross-correlation coefficients are within ≃ 1% down to k = 1 hMpc-1. Our results indicate that the correction to the power spectrum from fast/approximate simulations or field-level perturbation theory is rather universal. Our model represents a first step towards the development of a fast field-level emulator to sample not only primordial mode amplitudes and phases, but also the parameter space defined by the values of the cosmological parameters.