Decomposing heterogeneous dynamical systems with graph neural networks
This method addresses the challenge of understanding and modeling complex natural systems, such as physical, chemical, and biological dynamics, by providing a tool to uncover underlying governing rules, though it is currently incremental as it focuses on validation with simulated data.
The authors tackled the problem of decomposing complex dynamical systems with heterogeneous components by designing simple graph neural networks to jointly learn interaction rules and latent heterogeneity from observable dynamics, enabling virtual decomposition for inferring governing equations. They validated the approach using simulation experiments with moving particles, vector fields, and signaling networks.
Natural physical, chemical, and biological dynamical systems are often complex, with heterogeneous components interacting in diverse ways. We show how simple graph neural networks can be designed to jointly learn the interaction rules and the latent heterogeneity from observable dynamics. The learned latent heterogeneity and dynamics can be used to virtually decompose the complex system which is necessary to infer and parameterize the underlying governing equations. We tested the approach with simulation experiments of interacting moving particles, vector fields, and signaling networks. While our current aim is to better understand and validate the approach with simulated data, we anticipate it to become a generally applicable tool to uncover the governing rules underlying complex dynamics observed in nature.