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

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.