  Electron and scanning probe microscopy produce vast amounts of data in the
form of images or hyperspectral data, such as EELS or 4D STEM, that contain
information on a wide range of structural, physical, and chemical properties of
materials. To extract valuable insights from these data, it is crucial to
identify physically separate regions in the data, such as phases, ferroic
variants, and boundaries between them. In order to derive an easily
interpretable feature analysis, combining with well-defined boundaries in a
principled and unsupervised manner, here we present a physics augmented machine
learning method which combines the capability of Variational Autoencoders to
disentangle factors of variability within the data and the physics driven loss
function that seeks to minimize the total length of the discontinuities in
images corresponding to latent representations. Our method is applied to
various materials, including NiO-LSMO, BiFeO3, and graphene. The results
demonstrate the effectiveness of our approach in extracting meaningful
information from large volumes of imaging data. The fully notebook containing
implementation of the code and analysis workflow is available at
https://github.com/arpanbiswas52/PaperNotebooks
