Classification of atomic environments via the Gromov–Wasserstein distance

Interpreting molecular dynamics simulations usually involves automated classification of local atomic environments to identify regions interest. Existing approaches are generally limited a small number reference structures and only include information about the chemical composition. This work proposes use variant Gromov-Wasserstein (GW) distance quantify difference between environment set arbitrary in way that is sensitive displacements, missing atoms, differences describing as finite metric measure space, which has additional advantages not requiring be centered on an atom making any assumptions material class. Numerical examples illustrate efficacy versatility algorithm.