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Control of chaotic systems by Deep Reinforcement Learning

arXiv 1906.07672 ↗First posted 16 Jun 2019math.OC nlin.CD physics.flu-dyncited by 29

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Abstract (arXiv)

Deep Reinforcement Learning (DRL) is applied to control a nonlinear, chaotic system governed by the one-dimensional Kuramoto-Sivashinsky (KS) equation. DRL uses reinforcement learning principles for the determination of optimal control solutions and deep Neural Networks for approximating the value function and the control policy. Recent applications have shown that DRL may achieve superhuman performance in complex cognitive tasks. In this work, we show that using restricted, localized actuations, partial knowledge of the state based on limited sensor measurements, and model-free DRL controllers, it is possible to stabilize the dynamics of the KS system around its unstable fixed solutions, here considered as target states. The robustness of the controllers is tested by considering several trajectories in the phase-space emanating from different initial conditions; we show that the DRL is always capable of driving and stabilizing the dynamics around the target states. The complexity of the KS system, the possibility of defining the DRL control policies by solely relying on the local measurements of the system, and their efficiency in controlling its nonlinear dynamics pave the way for the application of RL methods in control of complex fluid systems such as turbulent boundary layers, turbulent mixers or multiphase flows.

Key facts. Cited by 29 papers in the map (data through 14 Oct 2026). First posted on arXiv 16 Jun 2019.

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Citing papers per year: 2021: 3; 2022: 5; 2023: 4; 2024: 6; 2025: 6; 2026: 5.

29 papers.

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  1. 2023Effective control of two-dimensional Rayleigh--B'enard convection: invariant multi-agent reinforcement learning is all you needcited by 27
  2. 2023Distributed Control of Partial Differential Equations Using Convolutional Reinforcement Learningcited by 24
  3. 2021Physics-informed Dyna-Style Model-Based Deep Reinforcement Learning for Dynamic Controlcited by 23
  4. 2022Data-driven control of spatiotemporal chaos with reduced-order neural ODE-based models and reinforcement learningcited by 17
  5. 2021Hybrid analysis and modeling, eclecticism, and multifidelity computing toward digital twin revolutioncited by 14
  6. 2021Symmetry reduction for deep reinforcement learning active control of chaotic spatiotemporal dynamicscited by 11
  7. 2022Multi-fidelity reinforcement learning framework for shape optimizationcited by 9
  8. 2022A Thermodynamics-informed Active Learning Approach to Perception and Reasoning about Fluidscited by 9
  9. 2024Multi-agent reinforcement learning for the control of three-dimensional Rayleigh-B'enard convectioncited by 8
  10. 2024Stability analysis of chaotic systems in latent spacescited by 7
  11. 2022Comparative analysis of machine learning methods for active flow controlcited by 6
  12. 2023Learning a model is paramount for sample efficiency in reinforcement learning control of PDEscited by 6
17 more
  1. 2023Controlgym: Large-Scale Control Environments for Benchmarking Reinforcement Learning Algorithmscited by 6
  2. 2024Real-time optimal control of high-dimensional parametrized systems by deep learning-based reduced order modelscited by 4
  3. 2025HypeRL: Hypernetwork-Based Reinforcement Learning for Control of Parametrized Dynamical Systemscited by 3
  4. 2025Evidence on the Regularisation Properties of Maximum-Entropy Reinforcement Learningcited by 3
  5. 2025Data-Assimilated Model-Based Reinforcement Learning for Partially Observed Chaotic Flowscited by 3
  6. 2025Multi-fidelity Reinforcement Learning Control for Complex Dynamical Systemscited by 2
  7. 2024Asynchronous Parallel Reinforcement Learning for Optimizing Propulsive Performance in Fin Ray Controlcited by 1
  8. 2025Data-assimilated model-informed reinforcement learningcited by 1
  9. 2022Dynamic Noises of Multi-Agent Environments Can Improve Generalization: Agent-based Models meets Reinforcement Learningcited by 0
  10. 2024Suppressing Modulation Instability with Reinforcement Learningcited by 0
  11. 2024Latent feedback control of distributed systems in multiple scenarios through deep learning-based reduced order modelscited by 0
  12. 2025OGF: An Online Gradient Flow Method for Optimizing the Statistical Steady-State Time Averages of Unsteady Turbulent Flowscited by 0
  13. 2026Koopman-based surrogate modeling for reinforcement-learning-control of Rayleigh-Benard convectioncited by 0
  14. 2026Hyperfastrl: Hypernetwork-based reinforcement learning for unified control of parametric chaotic PDEscited by 0
  15. 2026Physics-enhanced reinforcement learning for real-time optimal control of dynamical systemscited by 0
  16. 2026HypEMBER: Hypernetwork-based Ensemble for Robust Policy Learning of Parametrized Dynamical Systemscited by 0
  17. 2026Toward Goal-Agnostic Joint-Embedding Predictive Control of Partial Differential Equationscited by 0