Decomposing heterogeneous dynamical systems with graph neural networks

TL;DR

This paper introduces a method using graph neural networks to learn and decompose complex heterogeneous dynamical systems, enabling better understanding and modeling of their underlying rules from observable data.

Contribution

It presents a novel approach to jointly learn interaction rules and heterogeneity in complex systems using graph neural networks, facilitating their decomposition and analysis.

Findings

Successfully applied to simulated particle interactions, vector fields, and signaling networks.

Able to infer underlying governing equations from observable dynamics.

Demonstrates potential as a general tool for analyzing complex natural systems.

Abstract

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.