Extracting the 21-cm Power Spectrum and the reionization parameters from
  mock datasets using Artificial Neural Networks
  Detection of the \hi~ 21-cm power spectrum is one of the key science drivers
of several ongoing and upcoming low-frequency radio interferometers. However,
the major challenge in such observations come from bright foregrounds, whose
accurate removal or avoidance is key to the success of these experiments. In
this work, we demonstrate the use of artificial neural networks (ANNs) to
extract the \hi~ 21-cm power spectrum from synthetic datasets and extract the
reionization parameters from the \hi~ 21-cm power spectrum. For the first time,
using a suite of simulations, we present an ANN based framework capable of
extracting the \hi~ signal power spectrum directly from the total observed sky
power spectrum (which contains the 21-cm signal, along with the foregrounds and
effects of the instrument). To achieve this, we have used a combination of two
separate neural networks sequentially. As the first step, \texttt{ANN1}
predicts the 21-cm power spectrum directly from foreground corrupted synthetic
datasets. In the second step, \texttt{ANN2} predicts the reionization
parameters from the predicted \hi~ power spectra from \texttt{ANN1}. Our
ANN-based framework is trained at a redshift of $9.01$, and for \kk-modes in
the range, $\rm{0.17<\kk<0.37~Mpc^{-1}}$. We have tested the network's
performance with mock datasets that include foregrounds and are corrupted with
thermal noise, corresponding to $1080$ hrs of observations of the \textsc{ska-1
low} and \textsc{hera}. Using our ANN framework, we are able to recover the
\hi~ power spectra with an accuracy of $\approx95-99\%$ for the different test
sets. For the predicted astrophysical parameters, we have achieved an accuracy
of $\approx~81-90\%$ and $\approx~50-60\%$ for the test sets corrupted with
thermal noise corresponding to the \textsc{ska-1 low} and \textsc{hera},
respectively.
