mlsanityData to 7 Oct 2026

Neural Ordinary Differential Equation Control of Dynamics on Graphs

arXiv 2006.09773 ↗First posted 17 Jun 2020cs.LG cs.SI stat.MLcited by 24

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Abstract (arXiv)

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.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). First posted on arXiv 17 Jun 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 9; 2023: 3; 2024: 4; 2025: 4; 2026: 2.

24 papers.

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  1. 2021Implicit energy regularization of neural ordinary-differential-equation controlcited by 29
  2. 2023Physics-Informed Machine Learning for Modeling and Control of Dynamical Systemscited by 28
  3. 2022Challenges and Opportunities in Deep Reinforcement Learning with Graph Neural Networks: A Comprehensive review of Algorithms and Applicationscited by 27
  4. 2022Visualizing high-dimensional loss landscapes with Hessian directionscited by 16
  5. 2025Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networkscited by 14
  6. 2024Hybrid2 Neural ODE Causal Modeling and an Application to Glycemic Responsecited by 13
  7. 2022On the Forward Invariance of Neural ODEscited by 10
  8. 2022Spectrally Adapted Physics-Informed Neural Networks for Solving Unbounded Domain Problemscited by 9
  9. 2022Near-optimal control of dynamical systems with neural ordinary differential equationscited by 9
  10. 2023Gradient-free training of neural ODEs for system identification and control using ensemble Kalman inversioncited by 9
  11. 2022Control of Dual-Sourcing Inventory Systems using Recurrent Neural Networkscited by 6
  12. 2024Control of Medical Digital Twins with Artificial Neural Networkscited by 3
12 more
  1. 2022Structural Inference of Networked Dynamical Systems with Universal Differential Equationscited by 2
  2. 2023Stretched and measured neural predictions of complex network dynamicscited by 1
  3. 2025Robust Moment Identification for Nonlinear PDEs via a Neural ODE Approachcited by 1
  4. 2021Multi-Objective Optimization for Value-Sensitive and Sustainable Basket Recommendationscited by 0
  5. 2022Inverse Boundary Value and Optimal Control Problems on Graphs: A Neural and Numerical Synthesiscited by 0
  6. 2022Domain-aware Control-oriented Neural Models for Autonomous Underwater Vehiclescited by 0
  7. 2024Neural Control: Concurrent System Identification and Control Learning with Neural ODEcited by 0
  8. 2024Statistical Mechanics and Artificial Neural Networks: Principles, Models, and Applicationscited by 0
  9. 2025Community-Aware Temporal Walks: Parameter-Free Representation Learning on Continuous-Time Dynamic Graphscited by 0
  10. 2025Control of dynamical systems with neural networkscited by 0
  11. 2026Power Interpretable Causal ODE Networks: A Unified Model for Explainable Anomaly Detection and Root Cause Analysis in Power Systemscited by 0
  12. 2026Improving Infinitely Deep Bayesian Neural Networks with Nesterov's Accelerated Gradient Methodcited by 0