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 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.

Fifth version improves and clears notation

References in corpus (12)

• Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift
• PyTorch: An Imperative Style, High-Performance Deep Learning Library
• Critical phenomena in complex networks
• Effective containment explains sub-exponential growth in confirmed cases of recent COVID-19 outbreak in Mainland China
• Kronecker Graphs: An Approach to Modeling Networks
• Thresholds for epidemic spreading in networks
• Neural Controlled Differential Equations for Irregular Time Series
• Identification of Patient Zero in Static and Temporal Networks - Robustness and Limitations
• Implicit energy regularization of neural ordinary-differential-equation control
• Learning to Control PDEs with Differentiable Physics
• Universal Approximation Property of Neural Ordinary Differential Equations
• Targeted Recovery as an Effective Strategy against Epidemic Spreading

Cited by in corpus (12)

• Controlling epidemics through optimal allocation of test kits and vaccine doses across networks
• Explainable Tensorized Neural Ordinary Differential Equations forArbitrary-step Time Series Prediction
• Near-optimal control of dynamical systems with neural ordinary differential equations
• Surrogate Modeling and Control of Medical Digital Twins
• Control of Dual-Sourcing Inventory Systems using Recurrent Neural Networks
• Spectrally Adapted Physics-Informed Neural Networks for Solving Unbounded Domain Problems
• Structural Inference of Networked Dynamical Systems with Universal Differential Equations
• Visualizing high-dimensional loss landscapes with Hessian directions
• Incentivizing Narrow-Spectrum Antibiotic Development with Refunding
• Control of dynamical systems with neural networks
• Reconstructing Noisy Gene Regulation Dynamics Using Extrinsic-Noise-Driven Neural Stochastic Differential Equations
• Controlling Complex Systems