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

Extracting Symbolic Models of Collective Behaviors with Graph Neural Networks and Macro-Micro Evolution