Challenges in dynamic mode decomposition

Area of Science:

• Data analysis
• Dynamical systems theory
• Robotics

Background:

• Dynamic mode decomposition (DMD) extracts spatio-temporal patterns from time series data.
• Key challenges in DMD include noise sensitivity and modeling nonlinearities.
• Existing DMD methods face difficulties with systems exhibiting both noise and nonlinearity.

Purpose of the Study:

• Investigate the combined effects of noise and nonlinearity on DMD performance.
• Analyze DMD's ability to recover spectral information and predict system behavior.
• Understand limitations of DMD in mildly nonlinear systems, particularly in robotics applications.

Main Methods:

• Studied systems with linear latent dynamics observed via multinomial observables.
• Incorporated both system and measurement noise into numerical models.
• Explored influences of dataset metrics, latent dynamics spectrum, system matrix normality, and dynamics geometry.

Main Results:

• DMD methods frequently fail to recover the true spectrum under combined noise and mild nonlinearity.
• Predictive accuracy of DMD degrades significantly in these conditions.
• Observed poor performance even when latent dynamics are linear and nonlinearity is minimal.

Conclusions:

• Standard DMD approaches are unreliable for systems with combined noise and nonlinearity.
• The findings highlight critical limitations for DMD in complex real-world applications like robotics.
• Further research is needed to develop robust DMD variants for noisy, nonlinear data.