提出稀疏模式DMD，区分局部与全局动态结构。
Sparse-mode Dynamic Mode Decomposition for Disambiguating Local and Global Structures
- 引入稀疏正则化，使DMD模态聚焦局部空间特征。
- 可无监督分离离散谱与连续谱对应模式。
- 适用于光波导、量子系统和海温数据等场景。
动态模态分解（DMD）是一种从时空数据中提取主导特征的数据驱动方法。本文提出稀疏模式DMD，作为优化DMD框架的新变体，通过引入促进稀疏性的正则化，逼近具有局部空间结构的DMD模态。该算法在保持优化DMD抗噪能力的同时，有效区分了空间局部与全局性质的模态。在许多应用中，此类模态分别对应离散谱与连续谱，因此该方法能无监督地显式构建频谱的不同部分。我们通过合成数据和真实系统（包括光波导、量子力学及海面温度数据）验证了其有效性。
原文摘要 · Abstract (English)
The dynamic mode decomposition (DMD) is a data-driven approach that extracts the dominant features from spatiotemporal data. In this work, we introduce sparse-mode DMD, a new variant of the optimized DMD framework that specifically leverages sparsity-promoting regularization in order to approximate DMD modes which have localized spatial structure. The algorithm maintains the noise-robust properties of optimized DMD while disambiguating between modes which are spatially local versus global in nature. In many applications, such modes are associated with discrete and continuous spectra respectively, thus allowing the algorithm to explicitly construct, in an unsupervised manner, the distinct portions of the spectrum. We demonstrate this by analyzing synthetic and real-world systems, including examples from optical waveguides, quantum mechanics, and sea surface temperature data.
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