Learning Graph Cellular Automata

TL;DR

This paper introduces a neural network-based framework for learning and representing graph cellular automata (GCA), extending traditional CA models to arbitrary graph structures and demonstrating its effectiveness on various complex tasks.

Contribution

It presents a general architecture using graph neural networks capable of learning any finite-state GCA transition rule, advancing the modeling of complex systems on arbitrary graphs.

Findings

Successfully learned GCA rules on Voronoi tessellations

Imitated flocking agent behaviors with GCA

Achieved convergence to target states using learned rules

Abstract

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.