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An approach for the analysis of atomically resolved scanning transmissionelectron microscopy data with multiple ferroic variants in the presence ofimaging non-idealities and chemical variabilities based on a rotationallyinvariant variational autoencoder (rVAE) is presented. We show that an optimallocal descriptor for the analysis is a sub-image centered at specific atomicunits, since materials and microscope distortions preclude the use of an ideallattice as a reference point. The applicability of unsupervised clustering anddimensionality reduction methods is explored and are shown to produce clustersdominated by chemical and microscope effects, with a large number of classesrequired to establish the presence of rotational variants. Comparatively, therVAE allows extraction of the angle corresponding to the orientation of ferroicvariants explicitly, enabling straightforward identification of the ferroicvariants as regions with constant or smoothly changing latent variables andsharp orientational changes. This approach allows further exploration of thechemical variability by separating the rotational degrees of freedom via rVAEand searching for remaining variability in the system. The code used in themanuscript is available athttps://github.com/saimani5/ferroelectric_domains_rVAE.

Unsupervised learning of ferroic variants from atomically resolved STEM images