Extracting Photometric Redshift from Galaxy Flux and Image Data using
  Neural Networks in the CSST Survey
  The accuracy of galaxy photometric redshift (photo-$z$) can significantly
affect the analysis of weak gravitational lensing measurements, especially for
future high-precision surveys. In this work, we try to extract photo-$z$
information from both galaxy flux and image data expected to be obtained by
China Space Station Telescope (CSST) using neural networks. We generate mock
galaxy images based on the observational images from the Advanced Camera for
Surveys of Hubble Space Telescope (HST-ACS) and COSMOS catalogs, considering
the CSST instrumental effects. Galaxy flux data are then measured directly from
these images by aperture photometry. The Multi-Layer Perceptron (MLP) and
Convolutional Neural Network (CNN) are constructed to predict photo-$z$ from
fluxes and images, respectively. We also propose to use an efficient hybrid
network, which combines MLP and CNN, by employing transfer learning techniques
to investigate the improvement of the result with both flux and image data
included. We find that the photo-$z$ accuracy and outlier fraction can achieve
$\sigma_{\rm NMAD} = 0.023$ and $\eta = 1.43\%$ for the MLP using flux data
only, and $\sigma_{\rm NMAD} = 0.025$ and $\eta = 1.21\%$ for the CNN using
image data only. The result can be further improved in high efficiency as
$\sigma_{\rm NMAD} = 0.020$ and $\eta = 0.90\%$ for the hybrid transfer
network. These approaches result in similar galaxy median and mean redshifts
~0.8 and 0.9, respectively, for the redshift range from 0 to 4. This indicates
that our networks can effectively and properly extract photo-$z$ information
from the CSST galaxy flux and image data.
