  Phase retrieval, the problem of recovering lost phase information from
measured intensity alone, is an inverse problem that is widely faced in various
imaging modalities ranging from astronomy to nanoscale imaging. The current
process of phase recovery is iterative in nature. As a result, the image
formation is time-consuming and computationally expensive, precluding real-time
imaging. Here, we use 3D nanoscale X-ray imaging as a representative example to
develop a deep learning model to address this phase retrieval problem. We
introduce 3D-CDI-NN, a deep convolutional neural network and differential
programming framework trained to predict 3D structure and strain solely from
input 3D X-ray coherent scattering data. Our networks are designed to be
"physics-aware" in multiple aspects; in that the physics of x-ray scattering
process is explicitly enforced in the training of the network, and the training
data are drawn from atomistic simulations that are representative of the
physics of the material. We further refine the neural network prediction
through a physics-based optimization procedure to enable maximum accuracy at
lowest computational cost. 3D-CDI-NN can invert a 3D coherent diffraction
pattern to real-space structure and strain hundreds of times faster than
traditional iterative phase retrieval methods, with negligible loss in
accuracy. Our integrated machine learning and differential programming solution
to the phase retrieval problem is broadly applicable across inverse problems in
other application areas.

Image and Video Processing;Materials Science;Machine Learning;Applied Physics