Anisotropic Machine Learning Representations for Multiscale Systems*

Machine learning methods, particularly machine learned potentials, have increased our ability to perform atomistic simulations with greater accuracy while maintaining lower computational overhead. Many of these methods start by first representing each atom through information-rich, physics-motivated numerical features, then feeding these features into supervised (or, at times, unsupervised) models. However, atom-centered methods, such as the Smooth Overlap of Atomic Positions (SOAP), are limited in their ability to describe or characterize macromolecular systems, where we are more likely wanting to represent groups of atoms, either from a scientific or efficiency standpoint. Here, we present AniSOAP, an anisotropic generalization of SOAP that can incorporate the molecular geometry of groups of atoms, yet retains its compatibility with the original SOAP framework. From this, we can derive fundamental insights on how molecular shape influences mesoscale behavior, as well as understand and incorporate where individual atom-atom interactions remain important, as demonstrated via analysis of benzene interactions determined by first principles. Moving forward, we present AniSOAP as a powerful and flexible coarse-graining framework to systematically reduce molecular degrees of freedom in complex, multiscale simulation.