Atomic Cluster Expansion Descriptors for Structural Dataset Analysis and Classification

The Atomic Cluster Expansion (ACE) is a general set of rotationally-invariant local structural descriptors that have proven effective for constructing interatomic potentials that reproduce first-principles methods. The ACE representation for functions of atomic configuration, such as the energy, allows for continuous and systematic improvement of interatomic potentials by defining a complete set of n-body descriptors. Additionally, they can be used to characterize the various states (atomic configurations) generated in an molecular dynamics simulation of a material. The ACE descriptors up to rank seven (i.e. involving up to eight atoms) were used to identify energy basins and transition states in Cu systems. Physically meaningful n-body decompositions of reaction events are provided in terms of ACE descriptors, providing much needed interpretability in these machine learned models. In addition to characterizing a single atomic configuration, ACE descriptors were used to characterize whole training sets of machine-learning interatomic potentials. Quantitative measurements of how well a training set spans a descriptor space, up to arbitrary or physically motivated n-body descriptors, are provided. It is shown that these quantities may be used for continuous training set improvement and classification.