Estimation of HII Bubble Size Distribution from 21cm Power Spectrum with
  Artificial Neural Networks
  The bubble size distribution of ionized hydrogen regions probes the
information about the morphology of \HII\ bubbles during the reionization.
Conventionally, the \HII\ bubble size distribution can be derived from the
tomographic imaging data of the redshifted 21~cm signal from the epoch of
reionization, which, however, is observationally challenging even for the
upcoming large radio interferometer arrays. Given that these interferometers
promise to measure the 21~cm power spectrum accurately, we propose a new
method, which is based on the artificial neural networks (ANN), to reconstruct
the \HII\ bubble size distribution from the 21~cm power spectrum. We
demonstrate that the reconstruction from the 21~cm power spectrum can be almost
as accurate as directly measured from the imaging data with the fractional
error $\lesssim 10\%$, even with thermal noise at the sensitivity level of the
Square Kilometre Array. Nevertheless, the reconstruction implicitly exploits
the modelling in reionization simulations, and hence the recovered \HII\ bubble
size distribution is not an independent summary statistic from the power
spectrum, and should be used only as the indicator for understanding \HII\
bubble morphology and its evolution.
