标题： Koopman算子特征对的“良好字典”的自动编码 显示英文标题

标题： Autoencoding for the 'Good Dictionary' of eigen pairs of the Koopman Operator

摘要： 降阶建模依赖于使用简化的模式来表示复杂的动态系统，这可以通过Koopman算子分析来实现。 然而，对于高维观测数据计算Koopman特征对可能效率低下。 本文提出使用深度自编码器，一种深度学习技术，在计算Koopman特征向量之前对原始数据进行非线性几何变换。 深度自编码器生成的编码数据与动态系统的流形微分同胚，并且其维度显著低于原始数据。 为了处理高维时间序列数据，提出了Takens的时间延迟嵌入作为预处理技术。 本文最后展示了这些技术的实际应用示例。 显示英文摘要

摘要： Reduced order modelling relies on representing complex dynamical systems using simplified modes, which can be achieved through Koopman operator analysis. However, computing Koopman eigen pairs for high-dimensional observable data can be inefficient. This paper proposes using deep autoencoders, a type of deep learning technique, to perform non-linear geometric transformations on raw data before computing Koopman eigen vectors. The encoded data produced by the deep autoencoder is diffeomorphic to a manifold of the dynamical system, and has a significantly lower dimension than the raw data. To handle high-dimensional time series data, Takens's time delay embedding is presented as a pre-processing technique. The paper concludes by presenting examples of these techniques in action.