论文标题
部分可观测时空混沌系统的无模型预测
A Short Introduction to the Koopman Representation of Dynamical Systems
论文作者
论文摘要
Koopman表示是线性或非线性动力学系统的无限尺寸线性表示。它代表输出图的动力学（又称可观测值），该动力学在状态空间上的函数被解释为输出。从概念上讲，对Koopman表示形式进行了简单的派生和评论。我们强调了原始系统的初始条件和输出图与Koopman表示形式的重要双重性。当该表示形式用于数据驱动的应用程序（例如动态模式分解（DMD）及其变体）时，这种双重性是一个重要的考虑因素。还显示了Koopman代表与大众传输的转移操作员之间的伴随关系。
The Koopman representation is an infinite dimensional linear representation of linear or nonlinear dynamical systems. It represents the dynamics of output maps (aka observables), which are functions on the state space whose evaluation is interpreted as an output. Conceptually simple derivations and commentary on the Koopman representation are given. We emphasize an important duality between initial conditions and output maps of the original system, and those of the Koopman representation. This duality is an important consideration when this representation is used in data-driven applications such as the Dynamic Mode Decomposition (DMD) and its variants. The adjoint relation between the Koopman representation and the transfer operator of mass transport is also shown.
