Mapping mesoscopic phase evolution during E-beam induced transformations via deep learning of atomically resolved images

Understanding transformations under electron beam irradiation requires mapping the structural phases and their evolution in real time. To date, this has mostly been a manual endeavor comprising difficult frame-by-frame analysis that is simultaneously tedious and prone to error. Here, we turn toward the use of deep convolutional neural networks (DCNN) to automatically determine the Bravais lattice symmetry present in atomically resolved images. A DCNN is trained to identify the Bravais lattice class given a 2D fast Fourier transform of the input image. Monte-Carlo dropout is used for determining the prediction probability, and results are shown for both simulated and real atomically resolved images from scanning tunneling microscopy and scanning transmission electron microscopy. A reduced representation of the final layer output allows to visualize the separation of classes in the DCNN and agrees with physical intuition. We then apply the trained network to electron beam-induced transformations in WS₂, which allows tracking and determination of growth rate of voids. We highlight two key aspects of these results: (1) it shows that DCNNs can be trained to recognize diffraction patterns, which is markedly different from the typical "real image" cases and (2) it provides a method with in-built uncertainty quantification, allowing the real-time analysis of phases present in atomically resolved images.