mlsanityData to 7 Oct 2026

Learning Stable Deep Dynamics Models

arXiv 2001.06116 ↗First posted 17 Jan 2020cs.LG math.DS stat.MLcited by 110

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Abstract (arXiv)

Deep networks are commonly used to model dynamical systems, predicting how the state of a system will evolve over time (either autonomously or in response to control inputs). Despite the predictive power of these systems, it has been difficult to make formal claims about the basic properties of the learned systems. In this paper, we propose an approach for learning dynamical systems that are guaranteed to be stable over the entire state space. The approach works by jointly learning a dynamics model and Lyapunov function that guarantees non-expansiveness of the dynamics under the learned Lyapunov function. We show that such learning systems are able to model simple dynamical systems and can be combined with additional deep generative models to learn complex dynamics, such as video textures, in a fully end-to-end fashion.

Key facts. Cited by 110 papers in the map (data through 7 Oct 2026). First posted on arXiv 17 Jan 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 26; 2022: 19; 2023: 16; 2024: 18; 2025: 17; 2026: 14.

110 papers.

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  1. 2022Approximately Equivariant Networks for Imperfectly Symmetric Dynamicscited by 95
  2. 2021On the difficulty of learning chaotic dynamics with RNNscited by 64
  3. 2021Recurrent Equilibrium Networks: Flexible Dynamic Models with Guaranteed Stability and Robustnesscited by 43
  4. 2022LyaNet: A Lyapunov Framework for Training Neural ODEscited by 43
  5. 2021On the Sample Complexity of Stability Constrained Imitation Learningcited by 38
  6. 2021Meta-Learning Dynamics Forecasting Using Task Inferencecited by 37
  7. 2024HardNet: Hard-Constrained Neural Networks with Universal Approximation Guaranteescited by 29
  8. 2021Offline Reinforcement Learning for Autonomous Driving with Safety and Exploration Enhancementcited by 28
  9. 2023Physics-Informed Machine Learning for Modeling and Control of Dynamical Systemscited by 28
  10. 2021Stability Verification in Stochastic Control Systems via Neural Network Supermartingalescited by 24
  11. 2023Neural Lyapunov Control for Discrete-Time Systemscited by 21
  12. 2023Efficient Preference-Based Reinforcement Learning Using Learned Dynamics Modelscited by 20
38 more
  1. 2023Causal Modeling with Stationary Diffusionscited by 19
  2. 2021Learning Modular Robot Control Policiescited by 18
  3. 2021Value Iteration in Continuous Actions, States and Timecited by 17
  4. 2021Learning Stable Deep Dynamics Models for Partially Observed or Delayed Dynamical Systemscited by 17
  5. 2021Almost Surely Stable Deep Dynamicscited by 16
  6. 2021Joint inference and input optimization in equilibrium networkscited by 15
  7. 2025ENFORCE: Nonlinear Constrained Learning with Adaptive-depth Neural Projectioncited by 15
  8. 2021Model Error Propagation via Learned Contraction Metrics for Safe Feedback Motion Planning of Unknown Systemscited by 13
  9. 2025Stable Port-Hamiltonian Neural Networkscited by 13
  10. 2022FINDE: Neural Differential Equations for Finding and Preserving Invariant Quantitiescited by 12
  11. 2021Convergent Graph Solverscited by 11
  12. 2022Continual Learning from Demonstration of Robotics Skillscited by 11
  13. 2022Statistical Safety and Robustness Guarantees for Feedback Motion Planning of Unknown Underactuated Stochastic Systemscited by 11
  14. 2024Learning Neural Contracting Dynamics: Extended Linearization and Global Guaranteescited by 11
  15. 2021Scalable Learning of Safety Guarantees for Autonomous Systems using Hamilton-Jacobi Reachabilitycited by 10
  16. 2023Lyapunov-Stable Deep Equilibrium Modelscited by 10
  17. 2021Weak Form Generalized Hamiltonian Learningcited by 8
  18. 2021Robust Value Iteration for Continuous Control Taskscited by 8
  19. 2021Physics-informed linear regression is competitive with two Machine Learning methods in residential building MPCcited by 8
  20. 2021Training Recurrent Neural Networks by Sequential Least Squares and the Alternating Direction Method of Multiplierscited by 8
  21. 2022Recognition Models to Learn Dynamics from Partial Observations with Neural ODEscited by 8
  22. 2025Predictability Enables Parallelization of Nonlinear State Space Modelscited by 7
  23. 2021Continuous-Time Fitted Value Iteration for Robust Policiescited by 6
  24. 2022No More Pesky Hyperparameters: Offline Hyperparameter Tuning for RLcited by 6
  25. 2022Neural Lyapunov Differentiable Predictive Controlcited by 6
  26. 2022Reachable Polyhedral Marching (RPM): An Exact Analysis Tool for Deep-Learned Control Systemscited by 6
  27. 2023Data-Driven Control with Inherent Lyapunov Stabilitycited by 6
  28. 2023Scalable and Efficient Continual Learning from Demonstration via a Hypernetwork-generated Stable Dynamics Modelcited by 6
  29. 2024Structure-Preserving Physics-Informed Neural Networks With Energy or Lyapunov Structurecited by 6
  30. 2024Adversarially Robust Out-of-Distribution Detection Using Lyapunov-Stabilized Embeddingscited by 6
  31. 2021Koopman Spectrum Nonlinear Regulators and Efficient Online Learningcited by 5
  32. 2022Bounded nonlinear forecasts of partially observed geophysical systems with physics-constrained deep learningcited by 5
  33. 2023Learning Control-Oriented Dynamical Structure from Datacited by 5
  34. 2023ConCerNet: A Contrastive Learning Based Framework for Automated Conservation Law Discovery and Trustworthy Dynamical System Predictioncited by 5
  35. 2023Value Functions are Control Barrier Functions: Verification of Safe Policies using Control Theorycited by 5
  36. 2023MMP++: Motion Manifold Primitives with Parametric Curve Modelscited by 5
  37. 2024Contractive Dynamical Imitation Policies for Efficient Out-of-Sample Recoverycited by 5
  38. 2021On the Stochastic Stability of Deep Markov Modelscited by 4

50 most cited of 110 All 110 (JSON)