Neural Ordinary Differential Equation Control of Dynamics on Graphs

We study the ability of neural networks to steer or control trajectories of continuous time non-linear dynamical systems on graphs, which we represent with neural ordinary differential equations (neural ODEs). To do so, we introduce a neural-ODE control (NODEC) framework and find that it can learn 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 that NODEC produces low energy control signals. Finally, we showcase the performance and versatility of NODEC by using it to control a system of more than one thousand coupled, non-linear ODEs.