mlsanityData to 7 Oct 2026

Lyapunov-Net: A Deep Neural Network Architecture for Lyapunov Function Approximation

arXiv 2109.13359 ↗First posted 27 Sep 2021cs.LG math.OCcited by 16

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Abstract (arXiv)

We develop a versatile deep neural network architecture, called Lyapunov-Net, to approximate Lyapunov functions of dynamical systems in high dimensions. Lyapunov-Net guarantees positive definiteness, and thus it can be easily trained to satisfy the negative orbital derivative condition, which only renders a single term in the empirical risk function in practice. This significantly reduces the number of hyper-parameters compared to existing methods. We also provide theoretical justifications on the approximation power of Lyapunov-Net and its complexity bounds. We demonstrate the efficiency of the proposed method on nonlinear dynamical systems involving up to 30-dimensional state spaces, and show that the proposed approach significantly outperforms the state-of-the-art methods.

Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). Builds on 20 of its 44 references that are in the map. First posted on arXiv 27 Sep 2021.

Builds on

20 of 44 references.

References · 20

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8 more
  1. 2020Neural Network Approximation: Three Hidden Layers Are Enoughcited by 63
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  3. 2018Exponential Convergence of the Deep Neural Network Approximation for Analytic Functionscited by 38
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 3; 2024: 7; 2025: 3; 2026: 1.

16 papers.

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  1. 2022Neural Lyapunov Control of Unknown Nonlinear Systems with Stability Guaranteescited by 39
  2. 2023Physics-Informed Neural Network Lyapunov Functions: PDE Characterization, Learning, and Verificationcited by 20
  3. 2024LyZNet: A Lightweight Python Tool for Learning and Verifying Neural Lyapunov Functions and Regions of Attractioncited by 10
  4. 2024Verification-Aided Learning of Neural Network Barrier Functions with Termination Guaranteescited by 7
  5. 2024Actor-Critic Physics-informed Neural Lyapunov Controlcited by 6
  6. 2023Value Functions are Control Barrier Functions: Verification of Safe Policies using Control Theorycited by 5
  7. 2024Formally Verified Physics-Informed Neural Control Lyapunov Functionscited by 4
  8. 2022Gaussian Control Barrier Functions : A Non-Parametric Paradigm to Safetycited by 2
  9. 2024Distributionally Robust Policy and Lyapunov-Certificate Learningcited by 2
  10. 2023A Policy Optimization Method Towards Optimal-time Stabilitycited by 0
  11. 2024Structured Deep Neural Network-Based Backstepping Trajectory Tracking Control for Lagrangian Systemscited by 0
  12. 2024(Un)supervised Learning of Maximal Lyapunov Functionscited by 0
4 more
  1. 2025Neural Lyapunov Function Approximation with Self-Supervised Reinforcement Learningcited by 0
  2. 2025Certifying Stability of Reinforcement Learning Policies using Generalized Lyapunov Functionscited by 0
  3. 2025Lyapunov Stability Learning with Nonlinear Control via Inductive Biasescited by 0
  4. 2026Verifiable Error Bounds for Physics-Informed Neural Network Solutions of Lyapunov and Hamilton-Jacobi-Bellman Equationscited by 0