Variational Autoencoder Toolkit

Variational Autoencoders (VAEs) provide a robust framework for extracting latent structures and revealing physical insights in high-dimensional microscopy data. Although initial clustering with Gaussian Mixture Models (GMM) in the original descriptor space reveals distinct domain configurations and substrate regions, we miss underlying details, such as domain walls associated with unit cell rotations, chemical and mis-tilt effects, and the distinction between positive and negative wall orientations. By combining invariant and conditional VAEs, we capture nuanced features by encoding intrinsic factors of variation, such as orientation and translation, while incorporating cation type. This approach effectively links structural characteristics with physical phenomena. This approach demonstrates how invariant and conditional VAEs can extract both data-driven and physically interpretable features, offering an adaptable toolkit for analyzing ferroic materials, multiphase systems, and similar complex datasets.