Learning spatio-temporal patterns with Neural Cellular Automata
Alex D. Richardson Tibor Antal Richard A. Blythe Linus J. Schumacher
Neural Cellular Automata (NCA) are a powerful combination of machine learning
and mechanistic modelling. We train NCA to learn complex dynamics from time
series of images and PDE trajectories. Our method is designed to identify
underlying local rules that govern large scale dynamic emergent behaviours.
Previous work on NCA focuses on learning rules that give stationary emergent
structures. We extend NCA to capture both transient and stable structures
within the same system, as well as learning rules that capture the dynamics of
Turing pattern formation in nonlinear Partial Differential Equations (PDEs). We
demonstrate that NCA can generalise very well beyond their PDE training data,
we show how to constrain NCA to respect given symmetries, and we explore the
effects of associated hyperparameters on model performance and stability. Being
able to learn arbitrary dynamics gives NCA great potential as a data driven
modelling framework, especially for modelling biological pattern formation.