Learning spatio-temporal patterns with Neural Cellular Automata

• Published in: PLoS computational biology 2024-04, Vol.20 (4), p.e1011589-e1011589
• Main Authors: Richardson, Alex D, Antal, Tibor, Blythe, Richard A, Schumacher, Linus J
• Format: Article
• Language: English
• Subjects: Artificial intelligence; Biology and Life Sciences; Cellular automata; Computer and Information Sciences; Inverse problems; Machine learning; Methods; Modelling; Neural networks; Nonlinear differential equations; Parabolic differential equations; Partial differential equations; Pattern formation; Physical Sciences; Research and Analysis Methods; Social Sciences; Testing
• ISSN: 1553-7358; 1553-734X; 1553-7358
• DOI: 10.1371/journal.pcbi.1011589

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 Partial Differential Equation (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 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.