Decomposing heterogeneous dynamical systems with graph neural networks

Cedric Allier, Magdalena C. Schneider, Michael Innerberger, Larissa Heinrich, John A. Bogovic, Stephan Saalfeld

Keywords: graph neural networks, gnn, dynamic system, latent parameter discovery

TL;DR: We use graph neural networks to decompose heterogeneous dynamic systems and reveal the underlying interactions.

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.

Primary Area: learning on time series and dynamical systems

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Submission Number: 12051