  Two-dimensionally extended amorphous carbon ("amorphous graphene") is a
prototype system for disorder in 2D, showing a rich and complex configurational
space that is yet to be fully understood. Here we explore the nature of
amorphous graphene with an atomistic machine-learning (ML) model. We create
structural models by introducing defects into ordered graphene through
Monte-Carlo bond switching, defining acceptance criteria using the
machine-learned local, atomic energies associated with a defect, as well as the
nearest-neighbor (NN) environments. We find that physically meaningful
structural models arise from ML atomic energies in this way, ranging from
continuous random networks to paracrystalline structures. Our results show that
ML atomic energies can be used to guide Monte-Carlo structural searches in
principle, and that their predictions of local stability can be linked to
short- and medium-range order in amorphous graphene. We expect that the former
point will be relevant more generally to the study of amorphous materials, and
that the latter has wider implications for the interpretation of ML potential
models.
