Neural ordinary differential equation control of dynamics on graphs

Abstract

We study the ability of neural networks to calculate feedback control signals that steer trajectories of continuous-time nonlinear 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 toward 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 more than one thousand coupled, nonlinear ODEs that represent epidemic processes and coupled oscillators.