Learning Graph Cellular Automata
This work addresses the challenge of modeling complex dynamics on irregular structures for researchers in computational modeling and graph-based AI, but it is incremental as it extends existing neural network methods to a generalized CA framework.
The authors tackled the problem of learning transition rules for graph cellular automata (GCA), a generalized version of cellular automata on arbitrary graphs, by using graph neural networks. They demonstrated their approach on tasks such as learning rules for Voronoi tessellations, flocking agents, and convergence to target states, achieving accurate imitation and convergence in experiments.
Cellular automata (CA) are a class of computational models that exhibit rich dynamics emerging from the local interaction of cells arranged in a regular lattice. In this work we focus on a generalised version of typical CA, called graph cellular automata (GCA), in which the lattice structure is replaced by an arbitrary graph. In particular, we extend previous work that used convolutional neural networks to learn the transition rule of conventional CA and we use graph neural networks to learn a variety of transition rules for GCA. First, we present a general-purpose architecture for learning GCA, and we show that it can represent any arbitrary GCA with finite and discrete state space. Then, we test our approach on three different tasks: 1) learning the transition rule of a GCA on a Voronoi tessellation; 2) imitating the behaviour of a group of flocking agents; 3) learning a rule that converges to a desired target state.