  In situ scanning transmission electron microscopy enables observation of the
domain dynamics in ferroelectric materials as a function of externally applied
bias and temperature. The resultant data sets contain a wealth of information
on polarization switching and phase transition mechanisms. However,
identification of these mechanisms from observational data sets has remained a
problem due to a large variety of possible configurations, many of which are
degenerate. Here, we introduce an approach based on rotationally invariant
variational autoencoder (VAE), which enables learning a latent space
representation of the data with multiple real-space rotationally equivalent
variants mapped to the same latent space descriptors. By varying the size of
training sub-images in the VAE, we tune the degree of complexity in the
structural descriptors from simple domain wall detection to the identification
of switching pathways. This yields a powerful tool for the exploration of the
dynamic data in mesoscopic electron, scanning probe, optical, and chemical
imaging. Moreover, this work adds to the growing body of knowledge of
incorporating physical constraints into the machine and deep-learning methods
to improve learned descriptors of physical phenomena.
