Neural Ordinary Differential Equation Control of Dynamics on Graphs

TL;DR

This paper introduces NODEC, a neural ODE-based framework for controlling complex graph dynamical systems, demonstrating its effectiveness in driving large-scale non-linear systems to desired states with low energy signals.

Contribution

The paper presents a novel neural ODE control framework capable of managing large-scale graph dynamical systems, outperforming traditional controllers and reinforcement learning in various scenarios.

Findings

NODEC can learn effective feedback control signals.

NODEC produces low energy control signals.

NODEC successfully controls systems with over a thousand coupled ODEs.

Abstract

We study the ability of neural networks to calculate feedback control signals that steer trajectories of continuous time non-linear dynamical systems on graphs, which we represent with neural ordinary differential equations (neural ODEs). To do so, we present a neural-ODE control (NODEC) framework and find that it can learn feedback control signals that drive graph dynamical systems into desired target states. While we use loss functions that do not constrain the control energy, our results show, in accordance with related work, that NODEC produces low energy control signals. Finally, we evaluate the performance and versatility of NODEC against well-known feedback controllers and deep reinforcement learning. We use NODEC to generate feedback controls for systems of more than one thousand coupled, non-linear ODEs that represent epidemic processes and coupled oscillators.