Predicting 21cm-line map from Lyman $\alpha$ emitter distribution with
  Generative Adversarial Networks
  The radio observation of 21\,cm-line signal from the Epoch of Reionization
(EoR) enables us to explore the evolution of galaxies and intergalactic medium
in the early universe. However, the detection and imaging of the 21\,cm-line
signal are tough due to the foreground and instrumental systematics. In order
to overcome these obstacles, as a new approach, we propose to take a cross
correlation between observed 21\,cm-line data and 21\,cm-line images generated
from the distribution of the Lyman-$\alpha$ emitters (LAEs) through machine
learning. In order to create 21\,cm-line maps from LAE distribution, we apply
conditional Generative Adversarial Network (cGAN) trained with the results of
our numerical simulations. We find that the 21\,cm-line brightness temperature
maps and the neutral fraction maps can be reproduced with correlation function
of 0.5 at large scales $k<0.1~{\rm Mpc}^{-1}$. Furthermore, we study the
detectability of the the cross correlation assuming the the LAE deep survey of
the Subaru Hyper Suprime Cam, the 21\,cm observation of the MWA Phase II and
the presence of the foreground residuals. We show that the signal is detectable
at $k < 0.1~{\rm Mpc}^{-1}$ with 1000 hours of MWA observation even if the
foreground residuals are 5 times larger than the 21\,cm-line power spectrum.
Our new approach of cross correlation with image construction using the cGAN
can not only boost the detectability of EoR 21\,cm-line signal but also allow
us to estimate the 21\,cm-line auto-power spectrum.
