  We introduce a de novo elastography method to learn the elasticity of solids
from measured strains. The deep neural network in our new method is supervised
by the theory of elasticity and does not require labeled data for training.
Results show that the proposed method can learn the hidden elasticity of solids
accurately and is robust when it comes to noisy and missing measurements. A
probable elasticity distribution for areas without measurements may also be
reconstructed by the neural network based on the elasticity distribution in
nearby regions. The neural network learns the hidden elasticity of solids as a
function of positions and thus it can generate elasticity images with an
arbitrary resolution. This feature is applied to create super-resolution
elasticity images in this study. We demonstrate that the neural network can
also learn the hidden physics when strain and elasticity distributions are both
given. The proposed method has various unique features and can be applied to a
broad range of elastography applications.
