Uncovering the rate of the martensitic transformation in superheated shape memory alloy wires

Dynamic mode decomposition (DMD) is a leading tool for equation-free analysis of high-dimensional dynamical systems from observations. In this work, we focus on a combination of DMD and delay-coordinates embedding, which is termed delay-coordinates DMD and is based on augmenting observations from current and past time steps, accommodating the analysis of a broad family of observations. An important utility of DMD is the compact and reduced-order spectral representation of observations in terms of the DMD eigenvalues and modes, where the temporal information is separated from the spatial information. From a spatiotemporal viewpoint, we show that when DMD is applied to delay-coordinates embedding, temporal information is intertwined with spatial information, inducing a particular spectral structure on the DMD components. We formulate and analyze this structure, which we term the spatiotemporal coupling in delay-coordinates DMD. Based on this spatiotemporal coupling, we propose a new method for DMD components selection. When using delay-coordinates DMD that comprises redundant modes, this selection is an essential step for obtaining a compact and reduced-order representation of the observations. We demonstrate our method on noisy simulated signals and various dynamical systems and show superior component selection compared to a commonly used method that relies on the amplitudes of the modes.

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The spatiotemporal coupling in delay-coordinates dynamic mode decomposition

Bronstein

Aviad

Shilo

et al. 2022

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Uncovering the rate of the martensitic transformation in superheated shape memory alloy wires

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The spatiotemporal coupling in delay-coordinates dynamic mode decomposition

The spatiotemporal coupling in delay-coordinates dynamic mode decomposition

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