  Physics-based, atom-centered machine learning (ML) representations have been
instrumental to the effective integration of ML within the atomistic simulation
community. Many of these representations build off the idea of atoms as having
spherical, or isotropic, interactions. In many communities, there is often a
need to represent groups of atoms, either to increase the computational
efficiency of simulation via coarse-graining or to understand molecular
influences on system behavior. In such cases, atom-centered representations
will have limited utility, as groups of atoms may not be well-approximated as
spheres. In this work, we extend the popular Smooth Overlap of Atomic Positions
(SOAP) ML representation for systems consisting of non-spherical anisotropic
particles or clusters of atoms. We show the power of this anisotropic extension
of SOAP, which we deem \AniSOAP, in accurately characterizing liquid crystal
systems and predicting the energetics of Gay-Berne ellipsoids and
coarse-grained benzene crystals. With our study of these prototypical
anisotropic systems, we derive fundamental insights into how molecular shape
influences mesoscale behavior and explain how to reincorporate important
atom-atom interactions typically not captured by coarse-grained models. Moving
forward, we propose \AniSOAP as a flexible, unified framework for
coarse-graining in complex, multiscale simulation.
