Estimating Cluster Masses from SDSS Multi-band Images with Transfer
  Learning
  The total masses of galaxy clusters characterize many aspects of astrophysics
and the underlying cosmology. It is crucial to obtain reliable and accurate
mass estimates for numerous galaxy clusters over a wide range of redshifts and
mass scales. We present a transfer-learning approach to estimate cluster masses
using the ugriz-band images in the SDSS Data Release 12. The target masses are
derived from X-ray or SZ measurements that are only available for a small
subset of the clusters. We designed a semi-supervised deep learning model
consisting of two convolutional neural networks. In the first network, a
feature extractor is trained to classify the SDSS photometric bands. The second
network takes the previously trained features as inputs to estimate their total
masses. The training and testing processes in this work depend purely on real
observational data. Our algorithm reaches a mean absolute error (MAE) of 0.232
dex on average and 0.214 dex for the best fold. The performance is comparable
to that given by redMaPPer, 0.192 dex. We have further applied a joint
integrated gradient and class activation mapping method to interpret such a
two-step neural network. The performance of our algorithm is likely to improve
as the size of training dataset increases. This proof-of-concept experiment
demonstrates the potential of deep learning in maximizing the scientific return
of the current and future large cluster surveys.
