Photometric redshift estimates using Bayesian neural networks in the CSST survey

Galaxy photometric redshift (photo-$z$) is crucial in cosmological studies, such as weak gravitational lensing and galaxy angular clustering measurements. In this work, we try to extract photo-$z$ information and construct its probability distribution function (PDF) using the Bayesian neural networks (BNN) from both galaxy flux and image data expected to be obtained by the China Space Station Telescope (CSST). The mock galaxy images are generated from the Advanced Camera for Surveys of Hubble Space Telescope ($HST$-ACS) and COSMOS catalog, in which the CSST instrumental effects are carefully considered. And the galaxy flux data are measured from galaxy images using aperture photometry. We construct Bayesian multilayer perceptron (B-MLP) and Bayesian convolutional neural network (B-CNN) to predict photo-$z$ along with the PDFs from fluxes and images, respectively. We combine the B-MLP and B-CNN together, and construct a hybrid network and employ the transfer learning techniques to investigate the improvement of including both flux and image data. For galaxy samples with SNR$>$10 in $g$ or $i$ band, we find the accuracy and outlier fraction of photo-$z$ can achieve $\sigma_{\rm NMAD}=0.022$ and $\eta=2.35\%$ for the B-MLP using flux data only, and $\sigma_{\rm NMAD}=0.022$ and $\eta=1.32\%$ for the B-CNN using image data only. The Bayesian hybrid network can achieve $\sigma_{\rm NMAD}=0.021$ and $\eta=1.23\%$, and utilizing transfer learning technique can improve results to $\sigma_{\rm NMAD}=0.019$ and $\eta=1.17\%$, which can provide the most confident predictions with the lowest average uncertainty.