An Introductory Guide to Koopman Learning
Matthew J. Colbrook, Zlatko Drmač, Andrew Horning
Koopman算子为非线性动力系统的数据驱动分析提供了一个线性框架，但其无限维特性带来了重大的计算挑战。本文提供了Koopman学习的入门指南，重点介绍了用于预测和谱分析的严格收敛数据驱动方法。我们通过残差在有限维和无限维设置中提供了误差控制的统一描述，给出了广义拉普拉斯分析收敛性的基本证明——这是一种适用于具有连续谱且无谱间隙算子的滤波幂迭代变体——并回顾了计算连续谱和谱度量的最先进方法。目标是为新入门者和专家提供一个关于Koopman谱分析可靠数据驱动技术的清晰、结构化概述。
Koopman operators provide a linear framework for data-driven analyses of nonlinear dynamical systems, but their infinite-dimensional nature presents major computational challenges. In this article, we offer an introductory guide to Koopman learning, emphasizing rigorously convergent data-driven methods for forecasting and spectral analysis. We provide a unified account of error control via residuals in both finite- and infinite-dimensional settings, an elementary proof of convergence for general...