  The dynamic of complex ordering systems with active rotational degrees of
freedom exemplified by protein self-assembly is explored using a machine
learning workflow that combines deep learning-based semantic segmentation and
rotationally invariant variational autoencoder-based analysis of orientation
and shape evolution. The latter allows for disentanglement of the particle
orientation from other degrees of freedom and compensates for shifts. The
disentangled representations in the latent space encode the rich spectrum of
local transitions that can now be visualized and explored via continuous
variables. The time dependence of ensemble averages allows insight into the
time dynamics of the system, and in particular, illustrates the presence of the
potential ordering transition. Finally, analysis of the latent variables along
the single-particle trajectory allows tracing these parameters on a single
particle level. The proposed approach is expected to be universally applicable
for the description of the imaging data in optical, scanning probe, and
electron microscopy seeking to understand the dynamics of complex systems where
rotations are a significant part of the process.
