<i>ν</i> GAN: A Deep Learning Emulator for Cosmic Web Simulations with Massive Neutrinos

Abstract Understanding the impact of neutrino masses on the evolution of the Universe is a central goal of modern cosmology. Due to their large free-streaming lengths, neutrinos significantly affect structure formation at nonlinear scales, requiring accurate theoretical predictions to fully exploit current and future galaxy surveys. However, generating such predictions through large ensembles of cosmological simulations is computationally expensive. In this work, we introduce a deep learning-based generative adversarial network, ν GAN, to emulate the Universe across a range of neutrino masses from 0.0 to 1.2 eV. The generated 2D cosmic web maps are statistically independent, show no correlations with the training data, and closely reproduce the matter distribution of true simulations. We validate the model through visual inspection and key cosmological and computer-vision statistics. Our results show that ν GAN achieves ∼5% accuracy in the 2D power spectrum over the range 0.03 ≲ k ≲ 1 h Mpc −1 . Scales k ≳ 0.5 h Mpc −1 , corresponding to the fully nonlinear regime, exhibit increased scatter, reflecting the intrinsic difficulty of modeling highly nonlinear structure formation dominated by strong mode coupling and non-Gaussian features. While ν GAN attains percent-level accuracy across linear and quasi-nonlinear scales and remains reliable up to k ≈ 1 h Mpc −1 , improved fidelity in the deeply nonlinear regime is expected to require more expressive generative approaches, such as diffusion models. This work establishes a proof of concept for fast, scalable emulation of massive neutrino cosmologies, enabling large simulation ensembles and precision cosmological analyses. Future extensions will focus on higher-resolution 3D data and more advanced generative models.