Emulation of Cosmological Mass Maps with Conditional Generative Adversarial Networks

Abstract

Weak gravitational lensing mass maps play a crucial role in understanding the evolution of structures in the Universe and our ability to constrain cosmological models. The prediction of these mass maps is based on expensive N-body simulations, which can create a computational bottleneck for cosmological analyses. Simulation-based emulators of map summary statistics, such as the matter power spectrum and its covariance, are starting to play increasingly important role, as the analytical predictions are expected to reach their precision limits for upcoming experiments. Creating an emulator of the cosmological mass maps themselves, rather than their summary statistics, is a more challenging task. Modern deep generative models, such as Generative Adversarial Networks (GAN), have demonstrated their potential to achieve this goal. Most existing GAN approaches produce simulations for a fixed value of the cosmological parameters, which limits their practical applicability. We propose a novel conditional GAN model that is able to generate mass maps for any pair of matter density Ωm and matter clustering strength σ8, parameters which have the largest impact on the evolution of structures in the Universe, for a given source galaxy redshift distribution n(z). Our results show that our conditional GAN can interpolate efficiently within the space of simulated cosmologies, and generate maps anywhere inside this space with good visual quality high statistical accuracy. We perform an extensive quantitative comparison of the N-body and GAN -generated maps using a range of metrics: the pixel histograms, peak counts, power spectra, bispectra, Minkowski functionals, correlation matrices of the power spectra, the Multi-Scale Structural Similarity Index (MS-SSIM) and our equivalent of the Fréchet Inception Distance. We find a very good agreement on these metrics, with typical differences are <5% at the center of the simulation grid, and slightly worse for cosmologies at the grid edges. The agreement for the bispectrum is slightly worse, on the <20% level. This contribution is a step toward building emulators of mass maps directly, capturing both the cosmological signal and its variability. We make the code1 and the data2 publicly available.

Large-scale dark matter simulations

“…This architecture has shown to produce 2D and 3D fields quantitatively very similar to those obtained by direct numerical simulation (Rodrı ´guez et al 2018;Perraudin et al 2019;Tamosiunas et al 2021;Ullmo et al 2020;Feder et al 2020), even in previously unseen cosmologies (see Fig. 28 and Perraudin et al 2021). The architectures used to create fake data can also be combined with existing data from, for instance, low resolution simulations to artificially increase their resolution.…”

“…In this case, the GAN was trained with 46 different combinations of cosmological parameters (X m and r 8 ), and we can see it is able to generate data that correctly captures the cosmological dependence of such maps. Image adapted from Perraudin et al (2021), copyright by the authors uncertainty in the data analysis, for which it will be very important to accurately quantify the emulator uncertainty in the first place. This will be a challenge per se since these are typically empirically measured with a small number of simulations.…”

The Dawes Review 10: The impact of deep learning for the analysis of galaxy surveys

“…The GAN model proposed in Feder et al (2020) was for instance made conditional on redshift by simple concatenation of the conditional variable to the latent vector of the GAN, allowing the authors to generate volumes at intermediate redshifts, which would be useful to create lightcones. Perraudin et al (2020) proposed a conditional GANs to produce 2D weak-lensing mass-maps conditioned on (σ 8 , m ) through a remapping of the latent vector of the GAN by a function that rescales the norm of that vector based on the conditional variable. More recently, Wing Hei Yiu, Fluri, & Kacprzak (2021) extended that work to the sphere, using a DeepSphere (Perraudin et al 2019b) graph convolutional architecture, to emulate the KiDS-1000 survey footprint as a function of (σ 8 , m ).…”

Designing quantum many-body matter with conditional generative adversarial networks

“…image-to-image translation [12] or image editing [8,32,38,39]. The computational power of (conditional) GANs has already found its way to physics, starting in high energy physics for the simulation of 2D particle jet images [40] and 3D particle showers [41], cosmology for emulations of cosmological maps [42], and in selected problems of quantum and condensed matter physics including the simulation of correlated Quantum Walk [28] and to simulate 2D Ising model near the critical temperature [29]. Recently, conditional GANs have also been successfully applied for quantum state tomography and the reconstruction of density matrices [30].…”