Advances in experimental techniques and the ever-increasing fidelity of numerical simulations have led to an abundance of data describing fluid flows. This review discusses a range of techniques for analyzing such data, with the aim of extracting simplified models that capture the essential features of these flows, in order to gain insight into the flow physics, and potentially identify mechanisms for controlling these flows. We review well-developed techniques, such as proper orthogonal decomposition and Galerkin projection, and discuss more recent techniques developed for linear systems, such as balanced truncation and dynamic mode decomposition (DMD). We then discuss some of the methods available for nonlinear systems, with particular attention to the Koopman operator, an infinite-dimensional linear operator that completely characterizes the dynamics of a nonlinear system and provides an extension of DMD to nonlinear systems.

中文翻译：

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流量分析和控制的模型简化

实验技术的进步和数值模拟的不断提高的保真度导致了描述流体流动的大量数据。本综述讨论了一系列分析此类数据的技术，目的是提取捕获这些流动基本特征的简化模型，以便深入了解流动物理学，并可能确定控制这些流动的机制。我们回顾了成熟的技术，例如适当的正交分解和伽辽金投影，并讨论了为线性系统开发的最新技术，例如平衡截断和动态模式分解 (DMD)。然后我们讨论一些可用于非线性系统的方法，特别关注 Koopman 算子，