mlsanityData to 7 Oct 2026

Almost Surely Stable Deep Dynamics

arXiv 2103.14722 ↗First posted 26 Mar 2021cs.LG cs.SY eess.SYcited by 16

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Abstract (arXiv)

We introduce a method for learning provably stable deep neural network based dynamic models from observed data. Specifically, we consider discrete-time stochastic dynamic models, as they are of particular interest in practical applications such as estimation and control. However, these aspects exacerbate the challenge of guaranteeing stability. Our method works by embedding a Lyapunov neural network into the dynamic model, thereby inherently satisfying the stability criterion. To this end, we propose two approaches and apply them in both the deterministic and stochastic settings: one exploits convexity of the Lyapunov function, while the other enforces stability through an implicit output layer. We demonstrate the utility of each approach through numerical examples.

Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). Builds on 28 of its 43 references that are in the map. First posted on arXiv 26 Mar 2021.

Builds on

28 of 43 references.

References · 28

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16 more
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 5; 2023: 5; 2024: 1; 2025: 3; 2026: 1.

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  1. 2021Stability Verification in Stochastic Control Systems via Neural Network Supermartingalescited by 24
  2. 2022Learning Control Policies for Stochastic Systems with Reach-avoid Guaranteescited by 21
  3. 2025Stable Port-Hamiltonian Neural Networkscited by 13
  4. 2022No More Pesky Hyperparameters: Offline Hyperparameter Tuning for RLcited by 6
  5. 2023Scalable and Efficient Continual Learning from Demonstration via a Hypernetwork-generated Stable Dynamics Modelcited by 6
  6. 2025MPCritic: A plug-and-play MPC architecture for reinforcement learningcited by 3
  7. 2022Learning Stabilizable Deep Dynamics Modelscited by 2
  8. 2022Learning Deep Input-Output Stable Dynamicscited by 2
  9. 2023Stabilizing reinforcement learning control: A modular framework for optimizing over all stable behaviorcited by 2
  10. 2024Stable Autonomous Flow Matchingcited by 2
  11. 2022The Underlying Correlated Dynamics in Neural Trainingcited by 1
  12. 2023A modular framework for stabilizing deep reinforcement learning controlcited by 1
4 more
  1. 2023A Policy Optimization Method Towards Optimal-time Stabilitycited by 0
  2. 2023Efficient Exploration Using Extra Safety Budget in Constrained Policy Optimizationcited by 0
  3. 2025LILAD: Learning In-context Lyapunov-stable Adaptive Dynamics Modelscited by 0
  4. 2026Atoms to Processes: The Role of Artificial Intelligence and Machine Learning in Chemical Engineeringcited by 0