# Koopman-Based Neural Lyapunov Functions for General Attractors

arXiv: https://arxiv.org/abs/2203.12303 · HTML: https://mlsanity.com/paper/2203.12303/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2022.

## Built on by (most cited first, 7 of 7)

- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [Auxiliary Functions as Koopman Observables: Data-Driven Analysis of Dynamical Systems via Polynomial Optimization](https://mlsanity.com/paper/2303.01483/) (2023)
- [Automated Global Analysis of Experimental Dynamics through Low-Dimensional Linear Embeddings](https://mlsanity.com/paper/2411.00989/) (2024)
- [Learning Koopman-based Stability Certificates for Unknown Nonlinear Systems](https://mlsanity.com/paper/2412.02807/) (2024)
- [Finding separatrices of dynamical flows with Deep Koopman Eigenfunctions](https://mlsanity.com/paper/2505.15231/) (2025)
- [MAKO: Meta-Adaptive Koopman Operators for Learning-based Model Predictive Control of Parametrically Uncertain Nonlinear Systems](https://mlsanity.com/paper/2510.09042/) (2025)
- [Physics-Informed Machine Learning for Characterizing System Stability](https://mlsanity.com/paper/2511.08831/) (2025)

## Abstract (arXiv)

Koopman spectral theory has grown in the past decade as a powerful tool for dynamical systems analysis and control. In this paper, we show how recent data-driven techniques for estimating Koopman-Invariant subspaces with neural networks can be leveraged to extract Lyapunov certificates for the underlying system. In our work, we specifically focus on systems with a limit-cycle, beyond just an isolated equilibrium point, and use Koopman eigenfunctions to efficiently parameterize candidate Lyapunov functions to construct forward-invariant sets under some (unknown) attractor dynamics. Additionally, when the dynamics are polynomial and when neural networks are replaced by polynomials as a choice of function approximators in our approach, one can further leverage Sum-of-Squares programs and/or nonlinear programs to yield provably correct Lyapunov certificates. In such a polynomial case, our Koopman-based approach for constructing Lyapunov functions uses significantly fewer decision variables compared to directly formulating and solving a Sum-of-Squares optimization problem.