  Collective behaviors are typically hard to model. The scale of the swarm, the
large number of interactions, and the richness and complexity of the behaviors
are factors that make it difficult to distill a collective behavior into simple
symbolic expressions. In this paper, we propose a novel approach to symbolic
regression designed to facilitate such modeling. Using raw and post-processed
data as an input, our approach produces viable symbolic expressions that
closely model the target behavior. Our approach is composed of two phases. In
the first, a graph neural network (GNN) is trained to extract an approximation
of the target behavior. In the second phase, the GNN is used to produce data
for a nested evolutionary algorithm called macro-micro evolution (MME). The
macro layer of this algorithm selects candidate symbolic expressions, while the
micro layer tunes its parameters. Experimental evaluation shows that our
approach outperforms competing solutions for symbolic regression, making it
possible to extract compact expressions for complex swarm behaviors.
