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Implicit energy regularization of neural ordinary-differential-equation control

arXiv 2103.06525 ↗First posted 11 Mar 2021cs.LG physics.soc-phcited by 29

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Abstract (arXiv)

Although optimal control problems of dynamical systems can be formulated within the framework of variational calculus, their solution for complex systems is often analytically and computationally intractable. In this Letter we present a versatile neural ordinary-differential-equation control (NODEC) framework with implicit energy regularization and use it to obtain neural-network-generated control signals that can steer dynamical systems towards a desired target state within a predefined amount of time. We demonstrate the ability of NODEC to learn control signals that closely resemble those found by corresponding optimal control frameworks in terms of control energy and deviation from the desired target state. Our results suggest that NODEC is capable to solve a wide range of control and optimization problems, including those that are analytically intractable.

Key facts. Cited by 29 papers in the map (data through 14 Oct 2026). Builds on 13 of its 64 references that are in the map. First posted on arXiv 11 Mar 2021.

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13 of 64 references.

References · 13

  1. 2015Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classificationcited by 3,611
  2. 2015Automatic differentiation in machine learning: a surveycited by 855
  3. 2019Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learningcited by 212
  4. 2019Symplectic ODE-Net: Learning Hamiltonian Dynamics with Controlcited by 184
  5. 2019Pontryagin Differentiable Programming: An End-to-End Learning and Control Frameworkcited by 52
  6. 2020Modeling System Dynamics with Physics-Informed Neural Networks Based on Lagrangian Mechanicscited by 32
  7. 2020Neural Ordinary Differential Equation Control of Dynamics on Graphscited by 24
  8. 2013Controllability Metrics, Limitations and Algorithms for Complex Networkscited by 10
  9. 2013Realistic Control of Network Dynamicscited by 5
  10. 2013Minimal Controllability Problemscited by 2
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1 more
  1. 2021Learning Control of Quantum Systemscited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 2; 2022: 8; 2023: 1; 2024: 12; 2025: 3; 2026: 3.

29 papers.

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  3. 2022Near-optimal control of dynamical systems with neural ordinary differential equationscited by 9
  4. 2022On Fast Simulation of Dynamical System with Neural Vector Enhanced Numerical Solvercited by 9
  5. 2023Gradient-free training of neural ODEs for system identification and control using ensemble Kalman inversioncited by 9
  6. 2024A Pontryagin Perspective on Reinforcement Learningcited by 7
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  9. 2024Learning Interpretable Network Dynamics via Universal Neural Symbolic Regressioncited by 4
  10. 2022Offline Supervised Learning V.S. Online Direct Policy Optimization: A Comparative Study and A Unified Training Paradigm for Neural Network-Based Optimal Feedback Controlcited by 3
  11. 2024Control of Medical Digital Twins with Artificial Neural Networkscited by 3
  12. 2024PINNIES: An Efficient Physics-Informed Neural Network Framework to Integral Operator Problemscited by 3
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  4. 2024Reevaluating Meta-Learning Optimization Algorithms Through Contextual Self-Modulationcited by 2
  5. 2021Physics-informed neural networks via stochastic Hamiltonian dynamics learningcited by 1
  6. 2024Systematic construction of continuous-time neural networks for linear dynamical systemscited by 1
  7. 2025High-order expansion of Neural Ordinary Differential Equations flowscited by 1
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  9. 2024Neural Control: Concurrent System Identification and Control Learning with Neural ODEcited by 0
  10. 2024Grey-informed neural network for time-series forecastingcited by 0
  11. 2024Statistical Mechanics and Artificial Neural Networks: Principles, Models, and Applicationscited by 0
  12. 2024Controlling Dynamical Systems into Unseen Target States Using Machine Learningcited by 0
  13. 2025Control of dynamical systems with neural networkscited by 0
  14. 2025Towards agent-based-model informed neural networkscited by 0
  15. 2026A Pontryagin Method of Model-based Reinforcement Learning via Hamiltonian Actor-Criticcited by 0
  16. 2026Physics-enhanced reinforcement learning for real-time optimal control of dynamical systemscited by 0
  17. 2026Gaussian process learning with flow map refinement for parameter estimation in dynamical systemscited by 0