  From pedestrians to Kuramoto oscillators, interactions between agents govern
how a multitude of dynamical systems evolve in space and time. Discovering how
these agents relate to each other can improve our understanding of the often
complex dynamics that underlie these systems. Recent works learn to categorize
relationships between agents based on observations of their physical behavior.
These approaches are limited in that the relationship categories are modelled
as independent and mutually exclusive, when in real world systems categories
are often interacting. In this work, we introduce a level of abstraction
between the physical behavior of agents and the categories that define their
behavior. To do this, we learn a mapping from the agents' states to their
affinities for each category in a graph neural network. We integrate the
physical proximity of agents and their affinities in a nonlinear opinion
dynamics model which provides a mechanism to identify mutually exclusive
categories, predict an agent's evolution in time, and control an agent's
behavior. We demonstrate the utility of our model for learning interpretable
categories for mechanical systems, and demonstrate its efficacy on several
long-horizon trajectory prediction benchmarks where we consistently out perform
existing methods.
