  We introduce a novel method for reconstructing the projected matter
distributions of galaxy clusters with weak-lensing (WL) data based on
convolutional neural network (CNN). Training datasets are generated with
ray-tracing through cosmological simulations. We control the noise level of the
galaxy shear catalog such that it mimics the typical properties of the existing
ground-based WL observations of galaxy clusters. We find that the mass
reconstruction by our multi-layered CNN with the architecture of alternating
convolution and trans-convolution filters significantly outperforms the
traditional reconstruction methods. The CNN method provides better
pixel-to-pixel correlations with the truth, restores more accurate positions of
the mass peaks, and more efficiently suppresses artifacts near the field edges.
In addition, the CNN mass reconstruction lifts the mass-sheet degeneracy when
applied to sufficiently large fields. This implies that this CNN algorithm can
be used to measure cluster masses in a model independent way for future
wide-field WL surveys.
