A tomographic spherical mass map emulator of the KiDS-1000 survey using
  conditional generative adversarial networks
  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. 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 $(\Omega_M, \sigma_8)$ 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 $\texttt{DeepSphere}$, and train it on N-body-simulated mass
maps. We compare its performance using an array of quantitative comparison
metrics: angular power spectra $C_\ell$, pixel/peaks distributions, $C_\ell$
correlation matrices, and Structural Similarity Index. Overall, the agreement
on these summary statistics is $<10\%$ for the cosmologies at the centre of the
simulation grid, and degrades slightly on grid edges. Finally, we perform a
mock cosmological parameter estimation using the emulator and the original
simulation set. We find a good agreement in these constraints, for both
likelihood and likelihood-free approaches. The emulator is available at
https://tfhub.dev/cosmo-group-ethz/models/kids-cgan/1.
