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. 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 and on performing ergodic optimization for both deterministic and stochastic dynamics exemplify these convergence results and demonstrate the performance of the method.

翻译：我们提出一种灵活的数据驱动方法用于动力系统分析，该方法无需进行显式模型发现。该方法根植于从数据中近似库普曼算子的成熟技术，并以可数值求解的半定规划形式实现。该方法对数据生成过程是确定性还是随机性不具有依赖性，因此用户实现时无需根据这些不同场景进行预先调整。严格的收敛性结果验证了该方法的适用性，同时扩展并统一了文献中相关研究成果。通过发现李雅普诺夫函数以及对确定性和随机动力学进行遍历优化的实例，不仅体现了这些收敛性结果，也展示了该方法的性能。