Exploring order parameters and dynamic processes in disordered systems via variational autoencoders.

We suggest and implement an approach for the bottom-up description of systems undergoing large-scale structural changes and chemical transformations from dynamic atomically resolved imaging data, where only partial or uncertain data on atomic positions are available. This approach is predicated on the synergy of two concepts, the parsimony of physical descriptors and general rotational invariance of noncrystalline solids, and is implemented using a rotationally invariant extension of the variational autoencoder applied to semantically segmented atom-resolved data seeking the most effective reduced representation for the system that still contains the maximum amount of original information. This approach allowed us to explore the dynamic evolution of electron beam-induced processes in a silicon-doped graphene system, but it can be also applied for a much broader range of atomic scale and mesoscopic phenomena to introduce the bottom-up order parameters and explore their dynamics with time and in response to external stimuli.