标题： 基于贝叶斯学习和卡尔曼平滑的Koopman谱分析从噪声测量中 显示英文标题

标题： Koopman Spectral Analysis from Noisy Measurements based on Bayesian Learning and Kalman Smoothing

摘要： Koopman谱分析在理解和建模非线性动力系统中起着至关重要的作用，因为它揭示了系统的各种关键行为和长期动力学。 然而，测量噪声的存在对准确提取光谱特性提出了重大挑战。 在这项工作中，我们提出了一种在嘈杂环境中识别Koopman算子并提取其光谱特性的鲁棒方法。 为了应对噪声的影响，我们的方法解决了一个识别问题，该问题同时考虑了有限维近似引起的系统误差和数据中的测量噪声。 通过结合贝叶斯学习和卡尔曼平滑，该方法能够同时识别Koopman算子并估计系统状态，从而有效地将这两种误差源解耦。 通过广泛的实验展示了该方法的效率和鲁棒性，并展示了其在不同噪声水平下的准确性。 显示英文摘要

摘要： Koopman spectral analysis plays a crucial role in understanding and modeling nonlinear dynamical systems as it reveals key system behaviors and long-term dynamics. However, the presence of measurement noise poses a significant challenge to accurately extracting spectral properties. In this work, we propose a robust method for identifying the Koopman operator and extracting its spectral characteristics in noisy environments. To address the impact of noise, our approach tackles an identification problem that accounts for both systematic errors from finite-dimensional approximations and measurement noise in the data. By incorporating Bayesian learning and Kalman smoothing, the method simultaneously identifies the Koopman operator and estimates system states, effectively decoupling these two error sources. The method's efficiency and robustness are demonstrated through extensive experiments, showcasing its accuracy across varying noise levels.