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：本文提出了一种先进的Koopman模式分解（KMD）技术——特征化Koopman模式分解（FKMD），该方法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。这在优质特征未知的情况下有助于实现KMD的特征化。我们证明，该方法能够改进高维洛伦兹吸引子以及癌症研究中细胞信号传导问题的KMD预测性能。