Neural Ordinary Differential Equation Control of Dynamics on Graphs
This work addresses control of complex graph-based dynamical systems, such as epidemics and oscillators, but appears incremental as it builds on neural ODEs and related control methods.
The authors tackled the problem of steering trajectories of continuous-time nonlinear dynamical systems on graphs using neural networks, and found that their neural-ODE control (NODEC) framework can learn feedback control signals that drive these systems into desired target states, producing low-energy controls for systems with over a thousand coupled ODEs.
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.