Predicting large scale cosmological structure evolution with generative adversarial network-based autoencoders

Predicting the nonlinear evolution of cosmic structure from initial conditions is typically approached using Lagrangian, particle-based methods. These techniques excel in terms of tracking individual trajectories, but they might not be suitable for applications where point-based information is unavailable or impractical. In this work, we explore an alternative, field-based approach using Eulerian inputs. Specifically, we developed an autoencoder architecture based on a generative adversarial network (GAN) and trained it to evolve density fields drawn from dark matter N-body simulations. We tested this method on both 2D and 3D data. We find that while predictions on 2D density maps perform well based on density alone, accurate 3D predictions require the inclusion of associated velocity fields. Our results demonstrate the potential of field-based representations to model cosmic structure evolution, offering a complementary path to Lagrangian methods in contexts where field-level data is more accessible.