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

TL;DR

This paper tackles predicting the nonlinear evolution of cosmic structure using Eulerian density fields instead of particle-based methods. It introduces Timewarper (TW), a GAN-based autoencoder that uses a pretrained GAN generator as the decoder and a perceptual loss to map input density fields at $z\ge 0$ to the target $z=0$ field, tested in both 2D and 3D. Results show strong 2D performance with density-only inputs, while 3D predictions degrade without velocity information; incorporating the velocity field substantially improves 3D predictions and stabilizes training. The study demonstrates a viable field-based emulation path that complements Lagrangian approaches, with future improvements including stronger conditional GANs, larger latent spaces, and extensions to inverse evolution and additional auxiliary fields.

Abstract

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.

Figures (11)

• Figure 1: Architecture of the timewarper. A trained GAN's generator is used as a readily built decoder. Only the encoder's weights are changed during training. The same GAN's truncated discriminator is used to compute a perceptual loss (see Eq. \ref{['eq:AEloss']}).
• Figure 2: Example of simulation-issued data: a 2D image from a 2D simulation( left) and a 3D cube ( right) from a 3D simulation. These data are built by dividing an N-body simulation snapshot into pixels (or voxels) and counting the particles within each, creating a discrete density map. The map is then smoothed with a Gaussian filter and log-transformed, allowing cosmic structure to stand out starkly. This process creates data that are compatible with convolutional neural networks, which specialize in feature detection.
• Figure 3: Six images from the 2D simulations at various redshifts ( left), and their equivalent predictions of redshift $z=0$ ( right) inferred by the baseline TW. The true $z=0$ simulation images are shown above the predicted images ( upper right) for comparison.
• Figure 4: Spectra, cross-correlation coefficient and Dice coefficient for baseline timewarper on 2D data. (a) Average power spectra from predictions from input redshifts z = 3 → 0 (blue scale), and average target spectrum at z = 0 (black). (b) Corresponding average cross-correlation coefficient between prediction and target over the same redshift range. (c) Average Dice coefficient between prediction and target (same blue color scale as in a and b).
• Figure 5: Five images from the 3D simulations at various redshifts ( left) and their equivalent predictions of redshift $z=0$ ( right) as inferred by the baseline TW. The true $z=0$ simulation images are shown above the predicted images ( top-right) for comparison.