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The dynamic of complex ordering systems with active rotational degrees offreedom exemplified by protein self-assembly is explored using a machinelearning workflow that combines deep learning-based semantic segmentation androtationally invariant variational autoencoder-based analysis of orientationand shape evolution. The latter allows for disentanglement of the particleorientation from other degrees of freedom and compensates for shifts. Thedisentangled representations in the latent space encode the rich spectrum oflocal transitions that can now be visualized and explored via continuousvariables. The time dependence of ensemble averages allows insight into thetime dynamics of the system, and in particular, illustrates the presence of thepotential ordering transition. Finally, analysis of the latent variables alongthe single-particle trajectory allows tracing these parameters on a singleparticle level. The proposed approach is expected to be universally applicablefor the description of the imaging data in optical, scanning probe, andelectron microscopy seeking to understand the dynamics of complex systems whererotations are a significant part of the process.

Exploring particle dynamics during self-organization processes via rotationally invariant latent representations