mlsanityData to 7 Oct 2026

Computing Lyapunov functions using deep neural networks

arXiv 2005.08965 ↗First posted 18 May 2020math.OC cs.NA math.NAcited by 14

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Abstract (arXiv)

We propose a deep neural network architecture and a training algorithm for computing approximate Lyapunov functions of systems of nonlinear ordinary differential equations. Under the assumption that the system admits a compositional Lyapunov function, we prove that the number of neurons needed for an approximation of a Lyapunov function with fixed accuracy grows only polynomially in the state dimension, i.e., the proposed approach is able to overcome the curse of dimensionality. We show that nonlinear systems satisfying a small-gain condition admit compositional Lyapunov functions. Numerical examples in up to ten space dimensions illustrate the performance of the training scheme.

Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 May 2020.

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Citing papers per year: 2021: 3; 2022: 0; 2023: 2; 2024: 5; 2025: 3; 2026: 1.

14 papers.

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  1. 2023Physics-Informed Machine Learning for Modeling and Control of Dynamical Systemscited by 28
  2. 2023Physics-Informed Neural Network Lyapunov Functions: PDE Characterization, Learning, and Verificationcited by 20
  3. 2021Lyapunov-Net: A Deep Neural Network Architecture for Lyapunov Function Approximationcited by 16
  4. 2024LyZNet: A Lightweight Python Tool for Learning and Verifying Neural Lyapunov Functions and Regions of Attractioncited by 10
  5. 2021Data-Driven Computational Methods for the Domain of Attraction and Zubov's Equationcited by 7
  6. 2024Actor-Critic Physics-informed Neural Lyapunov Controlcited by 6
  7. 2021Total Energy Shaping with Neural Interconnection and Damping Assignment -- Passivity Based Controlcited by 5
  8. 2024Formally Verified Physics-Informed Neural Control Lyapunov Functionscited by 4
  9. 2024Combining Neural Networks and Symbolic Regression for Analytical Lyapunov Function Discoverycited by 1
  10. 2025Analytical Lyapunov Function Discovery: An RL-based Generative Approachcited by 1
  11. 2024(Un)supervised Learning of Maximal Lyapunov Functionscited by 0
  12. 2025Lyapunov Stability Learning with Nonlinear Control via Inductive Biasescited by 0
2 more
  1. 2025Physics-Informed Machine Learning for Characterizing System Stabilitycited by 0
  2. 2026Verifiable Error Bounds for Physics-Informed Neural Network Solutions of Lyapunov and Hamilton-Jacobi-Bellman Equationscited by 0