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Herein, we present a deep-learning technique for reconstructing thedark-matter density field from the redshift-space distribution of dark-matterhalos. We built a UNet-architecture neural network and trained it using theCOmoving Lagrangian Acceleration fast simulation, which is an approximation ofthe N-body simulation with $512^3$ particles in a box size of 500 Mpc $h^{-1}$.Further, we tested the resulting UNet model not only with training-like testsamples but also with standard N-body simulations, such as the Jiutiansimulation with $6144^3$ particles in a box size of 1000 Mpc $h^{-1}$ and theELUCID simulation, which has a different cosmology. The real-space dark-matterdensity fields in the three simulations can be reconstructed reliably with onlya small reduction of the cross-correlation power spectrum at 1% and 10% levelsat $k=0.1$ and $0.3~h\mathrm{Mpc^{-1}}$, respectively. The reconstructionclearly helps to correct for redshift-space distortions and is unaffected bythe different cosmologies between the training (Planck2018) and test samples(WMAP5). Furthermore, we tested the application of the UNet-reconstructeddensity field to obtain the velocity \& tidal field and found that thisapproach provides better results compared to the traditional approach based onthe linear bias model, showing a 12.2% improvement in the correlation slope anda 21.1% reduction in the scatter between the predicted and true velocities.Thus, our method is highly efficient and has excellent extrapolationreliability beyond the training set. This provides an ideal solution fordetermining the three-dimensional underlying density field from the plentifulgalaxy survey data.

(DarkAI) Mapping the large-scale density field of dark matter using artificial intelligence