An Optimized Dynamic Mode Decomposition Model Robust to Multiplicative Noise

Abstract

Dynamic mode decomposition (DMD) is an efficient tool for decomposing spatio-temporal data into a set of low-dimensional modes, yielding the oscillation frequencies and the growth rates of physically significant modes. In this paper, we propose a novel DMD model that can be used for dynamical systems affected by multiplicative noise. We first derive a maximum a posteriori (MAP) estimator for the data-based model decomposition of a linear dynamical system corrupted by certain multiplicative noise. Applying penalty relaxation to the MAP estimator, we obtain the proposed DMD model whose epigraphical limits are the MAP estimator and the conventional optimized DMD model. We also propose an efficient alternating gradient descent method for solving the proposed DMD model, and analyze its convergence behavior. The proposed model is demonstrated on both the synthetic data and the numerically generated one-dimensional combustor data, and is shown to have superior reconstruction properties compared to state-of-the-art DMD models. Considering that multiplicative noise is ubiquitous in numerous dynamical systems, the proposed DMD model opens up new possibilities for accurate data-based modal decomposition.

arXiv comment35 pages, 10 figures

References in corpus (9)

• On Dynamic Mode Decomposition: Theory and Applications
• Extracting spatial-temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition
• The Complex Gradient Operator and the CR-Calculus
• De-Biasing the Dynamic Mode Decomposition for Applied Koopman Spectral Analysis
• Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition
• Modeling of Transitional Channel Flow Using Balanced Proper Orthogonal Decomposition
• A Finite Element Approach for the Dual Rudin--Osher--Fatemi Model and Its Nonoverlapping Domain Decomposition Methods
• On the proper treatment of improper distributions
• Fast Gradient Methods for Uniformly Convex and Weakly Smooth Problems

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