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Dynamic Digital Biomarkers of Motor and Cognitive Function in Parkinson's Disease

Dynamic Digital Biomarkers of Motor and Cognitive Function in Parkinson's Disease

Published on: July 24, 2019

Dynamic mode decomposition for detecting oscillatory transient activity via sparsity and smoothness regularization.

Yutaro Tanaka¹, Hiroya Nakao^1,2

¹Department of Systems and Control Engineering, Institute of Science Tokyo, Tokyo 152-8552, Japan.

Chaos (Woodbury, N.Y.)

|July 13, 2026

Summary

This study introduces an enhanced Dynamic Mode Decomposition (DMD) method to better interpret transient dynamics. The new approach uses time-varying amplitudes for DMD modes, improving the analysis of complex systems.

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Area of Science:

Fluid dynamics
Data-driven modeling
Time-series analysis

Background:

Dynamic Mode Decomposition (DMD) extracts coherent structures from complex systems.
Standard DMD struggles to interpret transient dynamics, limiting its application.
Understanding non-steady fluid flows requires advanced analytical tools.

Purpose of the Study:

To extend DMD for improved analysis of transient dynamics.
To develop a method for extracting oscillatory transient activity.
To provide a more interpretable representation of non-steady dynamical systems.

Main Methods:

Introduced time-varying amplitudes for DMD modes.
Applied sparsity and smoothness regularization.
Validated the method with a simple example and fluid flow data.

Main Results:

Successfully extracted oscillatory transient activity.
Identified dynamically significant modes and their transient behaviors.
Demonstrated improved interpretability of non-steady dynamics compared to standard DMD.
Captured temporal structures of mode activations in laminar airfoil wake flow.

Conclusions:

The proposed DMD extension effectively captures transient dynamics.
This method enhances the interpretability of complex, non-steady systems.
Offers a powerful tool for analyzing transient phenomena in fluid mechanics and other fields.