2025/08/14 by Yutaro Tanaka, Hiroya Nakao, Tanaka, Yutaro +1
Engineering · Physics and Astronomy · #Airfoil #Computational Fluid Dynamics and Aerodynamics #Control theory (sociology) #Curse of dimensionality #Dynamic mode decomposition #Fluid Dynamics and Turbulent Flows #Matrix decomposition #Modal #Modal analysis #Model Reduction and Neural Networks #Representation (politics) #Smoothness #Transient (computer programming)
paper · pdf · doi:10.1063/5.0295767
published in Chaos An Interdisciplinary Journal of Nonlinear Science 36(7) (American Institute of Physics)
openalex publication_date 2026/07/01 · openalex created_date 2026/07/14 · openalex updated_date 2026/08/05
Dynamic mode decomposition (DMD) is a data-driven modal decomposition technique that extracts coherent spatiotemporal 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 that facilitates extraction of oscillatory transient activity by introducing time-varying amplitudes for the DMD modes based on sparsity and smoothness regularization. This approach enables the identification of dynamically significant modes and extraction of their transient activities, providing a more interpretable representation of non-steady dynamics. We illustrate the validity of the proposed method using a simple example and then apply it to fluid flow data of a laminar airfoil wake exhibiting transient behavior. We demonstrate that it can capture the temporal structure of mode activations that are not accessible with the standard DMD method.