A tomographic spherical mass map emulator of the KiDS-1000 survey using conditional generative adversarial networks

Abstract

Large sets of matter density simulations are becoming increasingly important in large-scale structure cosmology. Matter power spectra emulators, such as the Euclid Emulator and CosmicEmu, are trained on simulations to correct the non-linear part of the power spectrum. Map-based analyses retrieve additional non-Gaussian information from the density field, whether through human-designed statistics such as peak counts, or via machine learning methods such as convolutional neural networks. The simulations required for these methods are very resource-intensive, both in terms of computing time and storage. This creates a computational bottleneck for future cosmological analyses, as well as an entry barrier for testing new, innovative ideas in the area of cosmological information retrieval. Map-level density field emulators, based on deep generative models, have recently been proposed to address these challenges. In this work, we present a novel mass map emulator of the KiDS-1000 survey footprint, which generates noise-free spherical maps in a fraction of a second. It takes a set of cosmological parameters (Ω M , σ 8) as input and produces a consistent set of 5 maps, corresponding to the KiDS-1000 tomographic redshift bins. To construct the emulator, we use a conditional generative adversarial network architecture and the spherical convolutional neural network DeepSphere, and train it on N-body-simulated mass maps. We compare its performance using an array of quantitative comparison metrics: angular power spectra Cℓ , pixel/peaks distributions, Cℓ correlation matrices, and Structural Similarity Index. Overall, the average agreement on these summary statistics is <10% for the cosmologies at the centre of the simulation grid, and degrades slightly on grid edges. However, the quality of the generated maps is worse at high negative κ values or large scale, which can significantly affect summaries sensitive to such observables. Finally, we perform a mock cosmological parameter estimation using the emulator and the original simulation set. We find good agreement in these constraints, for both likelihood and likelihood-free approaches. The emulator is available at tfhub.dev/cosmo-group-ethz/models/kids-cgan.