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