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.

翻译：我们提出了一种灵活的数据驱动方法用于动力系统分析，该方法无需显式的模型发现。该方法的理论基础源于从数据近似Koopman算子的成熟技术，并通过可数值求解的半定规划实现。此外，该方法对数据生成过程是否具有确定性或随机性保持无关性，因此用户无需根据不同场景预先调整其实现方式。严格的收敛性结果证明了该方法的适用性，同时扩展并统一了文献中类似的研究成果。通过发现Lyapunov函数、执行遍历优化以及约束确定性及随机动力学吸引子极值等实例，本文验证了这些收敛性结果并展示了方法的性能。