标题： 通过稀疏性和平滑性正则化检测瞬态活动的动力模式分解 显示英文标题

标题： Dynamic mode decomposition for detecting transient activity via sparsity and smoothness regularization

摘要： 动态模式分解（DMD）是一种数据驱动的模态分解技术，可以从高维时间序列数据中提取相干的时空结构。 通过将动力学分解为一组模式，每个模式与一个单一频率和一个增长速率相关联，DMD能够对复杂动力系统进行自然的模态分解和降维。 然而，当DMD应用于瞬态动力学时，即使使用大量模式，也难以解释这些模式如何贡献于瞬态行为。 在本研究中，我们提出了一种DMD的简单扩展方法，通过引入基于稀疏性和平滑性正则化的时变幅度来克服这一限制。 该方法能够识别动态重要的模式并提取其瞬态活动，提供对非稳态动力学更可解释和真实的表示。 我们将所提出的方法应用于表现出瞬态行为的流体流动数据，并证明它能够捕捉标准DMD方法无法获取的模式激活的时间结构。 显示英文摘要

摘要： Dynamic Mode Decomposition (DMD) is a data-driven modal decomposition technique that extracts coherent spatio-temporal structures from high-dimensional time-series data. By decomposing the dynamics into a set of modes, each associated with a single frequency and a growth rate, DMD enables a natural modal decomposition and dimensionality reduction of complex dynamical systems. However, when DMD is applied to transient dynamics, even if a large number of modes are used, it remains difficult to interpret how these modes contribute to the transient behavior. In this study, we propose a simple extension of DMD to overcome this limitation by introducing time-varying amplitudes for the DMD modes based on sparsity and smoothness regularization. This approach enables identification of dynamically significant modes and extraction of their transient activities, providing a more interpretable and faithful representation of non-steady dynamics. We apply the proposed method to fluid flow data exhibiting transient behavior and demonstrate that it can capture the temporal structure of mode activations that are not accessible with the standard DMD method.