Physics-Informed Graph Neural Cellular Automata: an Application to Compartmental Modelling

The recent outbreak of COVID-19 has spurred global collaborative research efforts to model and forecast the disease to improve preparation and control. Epidemiological models integrate experimental data and expert opinions to understand infection dynamics and control measures. Classical Machine Learning techniques often face challenges such as high data requirements, lack of interpretability, and difficulty integrating domain knowledge. A potential solution is to leverage Physically-Informed Machine Learning (PIML) models, which enhance models by incorporating known physical properties of viral spread. Additionally, epidemiological datasets are best represented as graphs, facilitating the modelling of interactions between individuals. In this paper, we propose a novel, interpretable graph-based PIML technique called SINDy-Graph to model infectious disease dynamics. Our approach is a Graph Cellular Automata architecture that combines the ability to identify dynamics for discovering the differential equations governing the physical phenomena under study using graphs modelling relationships between nodes (individuals). The experimental results demonstrate that integrating domain knowledge ensures better physical plausibility. In addition, our proposed model is easier to train and achieves a lower generalisation error compared to other baseline methods.