# Learning Stable Deep Dynamics Models

arXiv: https://arxiv.org/abs/2001.06116 · HTML: https://mlsanity.com/paper/2001.06116/

## Key facts

- Cited by 111 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jan 2020.

## Built on by (most cited first, 30 of 111)

- [Approximately Equivariant Networks for Imperfectly Symmetric Dynamics](https://mlsanity.com/paper/2201.11969/) (2022)
- [On the difficulty of learning chaotic dynamics with RNNs](https://mlsanity.com/paper/2110.07238/) (2021)
- [Recurrent Equilibrium Networks: Flexible Dynamic Models with Guaranteed Stability and Robustness](https://mlsanity.com/paper/2104.05942/) (2021)
- [LyaNet: A Lyapunov Framework for Training Neural ODEs](https://mlsanity.com/paper/2202.02526/) (2022)
- [On the Sample Complexity of Stability Constrained Imitation Learning](https://mlsanity.com/paper/2102.09161/) (2021)
- [Meta-Learning Dynamics Forecasting Using Task Inference](https://mlsanity.com/paper/2102.10271/) (2021)
- [HardNet: Hard-Constrained Neural Networks with Universal Approximation Guarantees](https://mlsanity.com/paper/2410.10807/) (2024)
- [Offline Reinforcement Learning for Autonomous Driving with Safety and Exploration Enhancement](https://mlsanity.com/paper/2110.07067/) (2021)
- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [Stability Verification in Stochastic Control Systems via Neural Network Supermartingales](https://mlsanity.com/paper/2112.09495/) (2021)
- [Neural Lyapunov Control for Discrete-Time Systems](https://mlsanity.com/paper/2305.06547/) (2023)
- [Learning Modular Robot Control Policies](https://mlsanity.com/paper/2105.10049/) (2021)
- [Efficient Preference-Based Reinforcement Learning Using Learned Dynamics Models](https://mlsanity.com/paper/2301.04741/) (2023)
- [Causal Modeling with Stationary Diffusions](https://mlsanity.com/paper/2310.17405/) (2023)
- [Value Iteration in Continuous Actions, States and Time](https://mlsanity.com/paper/2105.04682/) (2021)
- [Learning Stable Deep Dynamics Models for Partially Observed or Delayed Dynamical Systems](https://mlsanity.com/paper/2110.14296/) (2021)
- [ENFORCE: Nonlinear Constrained Learning with Adaptive-depth Neural Projection](https://mlsanity.com/paper/2502.06774/) (2025)
- [Almost Surely Stable Deep Dynamics](https://mlsanity.com/paper/2103.14722/) (2021)
- [Joint inference and input optimization in equilibrium networks](https://mlsanity.com/paper/2111.13236/) (2021)
- [Scalable Learning of Safety Guarantees for Autonomous Systems using Hamilton-Jacobi Reachability](https://mlsanity.com/paper/2101.05916/) (2021)
- [Model Error Propagation via Learned Contraction Metrics for Safe Feedback Motion Planning of Unknown Systems](https://mlsanity.com/paper/2104.08695/) (2021)
- [Stable Port-Hamiltonian Neural Networks](https://mlsanity.com/paper/2502.02480/) (2025)
- [Convergent Graph Solvers](https://mlsanity.com/paper/2106.01680/) (2021)
- [Continual Learning from Demonstration of Robotics Skills](https://mlsanity.com/paper/2202.06843/) (2022)
- [FINDE: Neural Differential Equations for Finding and Preserving Invariant Quantities](https://mlsanity.com/paper/2210.00272/) (2022)
- [Statistical Safety and Robustness Guarantees for Feedback Motion Planning of Unknown Underactuated Stochastic Systems](https://mlsanity.com/paper/2212.06874/) (2022)
- [Learning Neural Contracting Dynamics: Extended Linearization and Global Guarantees](https://mlsanity.com/paper/2402.08090/) (2024)
- [Lyapunov-Stable Deep Equilibrium Models](https://mlsanity.com/paper/2304.12707/) (2023)
- [Physics-informed linear regression is competitive with two Machine Learning methods in residential building MPC](https://mlsanity.com/paper/2110.15911/) (2021)
- [Weak Form Generalized Hamiltonian Learning](https://mlsanity.com/paper/2104.05096/) (2021)

## 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.