  Domain switching pathways in ferroelectric materials visualized by dynamic
Piezoresponse Force Microscopy (PFM) are explored via variational autoencoder
(VAE), which simplifies the elements of the observed domain structure,
crucially allowing for rotational invariance, thereby reducing the variability
of local polarization distributions to a small number of latent variables. For
small sampling window sizes the latent space is degenerate, and variability is
observed only in the direction of a single latent variable that can be
identified with the presence of domain wall. For larger window sizes, the
latent space is 2D, and the disentangled latent variables can be generally
interpreted as the degree of switching and complexity of domain structure.
Applied to multiple consecutive PFM images acquired while monitoring domain
switching, the polarization switching mechanism can thus be visualized in the
latent space, providing insight into domain evolution mechanisms and their
correlation with the microstructure.
