Learning Dynamics and Structure of Complex Systems Using Graph Neural Networks

TL;DR

This paper demonstrates how graph neural networks can learn the dynamics and structure of complex systems like belief propagation, enabling generalization to new system instances through interpretation of learned representations.

Contribution

It introduces a method to interpret GNNs trained on dynamical systems, revealing a 'graph translator' that links statistical interactions to network parameters for better generalization.

Findings

GNNs can model belief propagation dynamics effectively.

A 'graph translator' links learned models to underlying system structure.

The approach enables structure recovery and network construction from time series.

Abstract

Many complex systems are composed of interacting parts, and the underlying laws are usually simple and universal. While graph neural networks provide a useful relational inductive bias for modeling such systems, generalization to new system instances of the same type is less studied. In this work we trained graph neural networks to fit time series from an example nonlinear dynamical system, the belief propagation algorithm. We found simple interpretations of the learned representation and model components, and they are consistent with core properties of the probabilistic inference algorithm. We successfully identified a 'graph translator' between the statistical interactions in belief propagation and parameters of the corresponding trained network, and showed that it enables two types of novel generalization: to recover the underlying structure of a new system instance based solely on time series observations, or to construct a new network from this structure directly. Our results demonstrated a path towards understanding both dynamics and structure of a complex system and how such understanding can be used for generalization.