This article introduces an advanced Koopman mode decomposition (KMD) technique -- coined Featurized Koopman Mode Decomposition (FKMD) -- that uses time embedding and Mahalanobis scaling to enhance analysis and prediction of high dimensional dynamical systems. The time embedding expands the observation space to better capture underlying manifold structure, while the Mahalanobis scaling, applied to kernel or random Fourier features, adjusts observations based on the system's dynamics. This aids in featurizing KMD in cases where good features are not a priori known. We show that our method improves KMD predictions for a high dimensional Lorenz attractor and for a cell signaling problem from cancer research.

翻译：本文介绍一种先进的库普曼模态分解（KMD）技术——称为基于特征的库普曼模态分解（FKMD）——该技术利用时间嵌入和马氏距离缩放来增强高维动力系统的分析与预测。时间嵌入扩展了观测空间，以更好地捕捉潜在的流形结构，而应用于核函数或随机傅里叶特征的马氏距离缩放则根据系统动力学调整观测值。这有助于在良好特征并非先验已知的情况下实现KMD的基于特征分析。我们证明，该方法可改进对高维洛伦兹吸引子以及癌症研究中的细胞信号问题的KMD预测。