Learning spatio-temporal patterns with Neural Cellular Automata
This work provides a data-driven modeling framework for biological pattern formation, representing an incremental advance over prior NCA methods focused on stationary structures.
The authors tackled the problem of learning complex spatio-temporal dynamics from image time series and PDE trajectories using Neural Cellular Automata (NCA), extending previous work to capture both transient and stable structures and Turing pattern formation, with results showing good generalization beyond training data and the ability to respect symmetries.
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.