This article introduces an advanced Koopman mode decomposition (KMD) technique -- coined Featurized Koopman Mode Decomposition (FKMD) -- that uses delay embedding and a learned Mahalanobis distance to enhance analysis and prediction of high dimensional dynamical systems. The delay embedding expands the observation space to better capture underlying manifold structure, while the Mahalanobis distance 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 FKMD improves predictions for a high-dimensional linear oscillator, a high-dimensional Lorenz attractor that is partially observed, and a cell signaling problem from cancer research.

翻译：本文提出一种先进的Koopman模态分解(KMD)技术——特征化Koopman模态分解(FKMD)——该方法利用延迟嵌入和学习的马氏距离来增强高维动力系统的分析与预测能力。延迟嵌入通过扩展观测空间以更好地捕捉底层流形结构，而马氏距离则根据系统动力学特性调整观测数据。这种方法可在良好特征未知的情况下实现KMD的特征化构建。我们通过高维线性振荡器、部分观测的高维Lorenz吸引子以及癌症研究中的细胞信号传导问题，验证了FKMD在预测性能上的提升。