mlsanityData to 7 Oct 2026

Auxiliary Functions as Koopman Observables: Data-Driven Analysis of Dynamical Systems via Polynomial Optimization

arXiv 2303.01483 ↗First posted 2 Mar 2023math.DS cs.LG math.OCcited by 2

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Abstract (arXiv)

We present a flexible data-driven method for dynamical system analysis that does not require explicit model discovery. The method is rooted in well-established techniques for approximating the Koopman operator from data and is implemented as a semidefinite program that can be solved numerically. Furthermore, the method is agnostic of whether data is generated through a deterministic or stochastic process, so its implementation requires no prior adjustments by the user to accommodate these different scenarios. Rigorous convergence results justify the applicability of the method, while also extending and uniting similar results from across the literature. Examples on discovering Lyapunov functions, performing ergodic optimization, and bounding extrema over attractors for both deterministic and stochastic dynamics exemplify these convergence results and demonstrate the performance of the method.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 32 of its 92 references that are in the map. First posted on arXiv 2 Mar 2023.

Builds on

32 of 92 references.

References · 32

  1. 2021Modern Koopman Theory for Dynamical Systemscited by 269
  2. 2020Weak SINDy For Partial Differential Equationscited by 154
  3. 2016Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive controlcited by 134
  4. 2020SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamicscited by 125
  5. 2019Data-driven approximation of the Koopman generator: Model reduction, system identification, and controlcited by 85
  6. 2017On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operatorcited by 70
  7. 2017Data-driven discovery of Koopman eigenfunctions for controlcited by 64
  8. 2017Koopman operator-based model reduction for switched-system control of PDEscited by 31
  9. 2019Active Learning of Dynamics for Data-Driven Control Using Koopman Operatorscited by 31
  10. 2020Learning Dynamical Systems with Side Informationcited by 19
  11. 2022Koopman-Based Neural Lyapunov Functions for General Attractorscited by 7
  12. 2013Convex computation of the maximum controlled invariant set for polynomial control systemscited by 5
20 more
  1. 2016Region of Attraction Estimation Using Invariant Sets and Rational Lyapunov Functionscited by 3
  2. 2019Computing controlled invariant sets from data using convex optimizationcited by 2
  3. 2020Converging outer approximations to global attractors using semidefinite programmingcited by 2
  4. 2013Estimation of consistent parameter sets for continuous-time nonlinear systems using occupation measures and LMI relaxationscited by 1
  5. 2013Probabilistic and Set-based Model Invalidation and Estimation using LMIscited by 1
  6. 2015Bounds for deterministic and stochastic dynamical systems using sum-of-squares optimizationcited by 1
  7. 2016Bounding stationary averages of polynomial diffusions via semidefinite programmingcited by 1
  8. 2016Bounding averages rigorously using semidefinite programming: mean moments of the Lorenz systemcited by 1
  9. 2017Rigorous bounds on the stationary distributions of the chemical master equation via mathematical programmingcited by 1
  10. 2017Semidefinite Approximations of Reachable Sets for Discrete-time Polynomial Systemscited by 1
  11. 2017Optimal bounds and extremal trajectories for time averages in nonlinear dynamical systemscited by 1
  12. 2018Semidefinite Approximations of Invariant Measures for Polynomial Systemscited by 1
  13. 2018Convex computation of extremal invariant measures of nonlinear dynamical systems and Markov processescited by 1
  14. 2019Bounding extreme events in nonlinear dynamics using convex optimizationcited by 1
  15. 2020Minimum wave speeds in monostable reaction-diffusion equations: sharp bounds by polynomial optimizationcited by 1
  16. 2020Peak Estimation and Recovery with Occupation Measurescited by 1
  17. 2021Peak Estimation for Uncertain and Switched Systemscited by 1
  18. 2022Data-Driven Optimal Control via Linear Transfer Operators: A Convex Approachcited by 1
  19. 2022Converging approximations of attractors via almost Lyapunov functions and semidefinite programmingcited by 1
  20. 2022Uncertainty propagation for nonlinear dynamics: A polynomial optimization approachcited by 1

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Citing papers per year: 2025: 2.

2 papers.

  1. 2025Learning graphons from data: Random walks, transfer operators, and spectral clusteringcited by 2
  2. 2025Weighted Birkhoff Averages Accelerate Data-Driven Methodscited by 1