Analysis of Coherent Phonon Signals by Sparsity-promoting Dynamic Mode Decomposition

Murata, Shigeo; Aihara, Shingo; Tokuda, S.; Iwamitsu, Kazunori; Mizoguchi, K.; Akai, Ichiro; Okada, Masato

doi:10.7566/jpsj.87.054003

Cited by 9 publications

(14 citation statements)

References 19 publications

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“…As shown by the red and green lines in Figure 3(a), the previously proposed method successfully extracted the normal vibration modes A 1g and E g . Moreover, the other selected modes are denoted by the black dotted lines and correspond to a weak background in the experimental data [19]. By using the selected modes, the recovered signals coincide with the experimental data, as shown in the pink filled area and the blue line of Figure 3(a).…”

Section: Background Close To Steady-statementioning

confidence: 67%

“…The previous method determined the optimal number of modes to be nine, where the curve of the MSE curve crosses the estimated noise variance σ 2 est ¼ 4:00 Â 10 À14 , as shown in Figure 3(c). Note that the authors estimated the noise variance from the variance of the negative time signal [19]. On the other hand, the proposed method also succeeded in extracting the normal modes from the experimental data without using speculative noise information, as shown in Figure 3(b).…”

Section: Background Close To Steady-statementioning

confidence: 97%

“…The residual signal between the original signal and the reconstructed signal is close to zero, as shown by the solid bottom lines of Figure 3(a). In Murata et al [19], assuming prior knowledge that the normal modes representing lattice oscillations of the substance of interest were sparse, the authors selected the modes extracted by DMD as explained in Section 2.1. The previous method determined the optimal number of modes to be nine, where the curve of the MSE curve crosses the estimated noise variance σ 2 est ¼ 4:00 Â 10 À14 , as shown in Figure 3(c).…”

Section: Background Close To Steady-statementioning

confidence: 99%

“…To address the aforementioned issue, Murata et al [19] analyzed a CP signal using sparsity-promoting dynamic mode decomposition (SpDMD [20]) based on the fact that CP signals consist of a few damped oscillation modes. SpDMD is a method that decomposes time series data into a sum of damped oscillations and observation noise.…”

Section: Introductionmentioning

confidence: 99%

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Normal mode analysis of a relaxation process with Bayesian inference

Sakata

Nagano

Igarashi

et al. 2020

Science and Technology of Advanced Materials

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Measurements of relaxation processes are essential in many fields, including nonlinear optics. Relaxation processes provide many insights into atomic/molecular structures and the kinetics and mechanisms of chemical reactions. For the analysis of these processes, the extraction of modes that are specific to the phenomenon of interest (normal modes) is unavoidable. In this study we propose a framework to systematically extract normal modes from the viewpoint of model selection with Bayesian inference. Our approach consists of a well-known method called sparsity-promoting dynamic mode decomposition, which decomposes a mixture of damped oscillations, and the Bayesian model selection framework. We numerically verify the performance of our proposed method by using coherent phonon signals of a bismuth polycrystal and virtual data as typical examples of relaxation processes. Our method succeeds in extracting the normal modes even from experimental data with strong backgrounds. Moreover, the selected set of modes is robust to observation noise, and our method can estimate the level of observation noise. From these observations, our method is applicable to normal mode analysis, especially for data with strong backgrounds. ARTICLE HISTORY

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Section: Background Close To Steady-statementioning

confidence: 67%

Section: Background Close To Steady-statementioning

confidence: 97%

Section: Background Close To Steady-statementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Normal mode analysis of a relaxation process with Bayesian inference

Sakata

Nagano

Igarashi

et al. 2020

Science and Technology of Advanced Materials

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“…A reduced-order modeling algorithm that has been effective in creating sparse DMD models is Sparsity-Promoting Dynamic Mode Decomposition (DMDSP) [9][10][11]. DMDSP has also been extended to systems with inputs [12].…”

Section: Introductionmentioning

confidence: 99%

Reduced-order modeling using Dynamic Mode Decomposition and Least Angle Regression

Graff

Lagor

et al. 2019

AIAA Aviation 2019 Forum

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Dynamic Mode Decomposition (DMD) yields a linear, approximate model of a system's dynamics that is built from data. We seek to reduce the order of this model by identifying a reduced set of modes that best fit the output. We adopt a model selection algorithm from statistics and machine learning known as Least Angle Regression (LARS). We modify LARS to be complex-valued and utilize LARS to select DMD modes. We refer to the resulting algorithm as Least Angle Regression for Dynamic Mode Decomposition (LARS4DMD). Sparsity-Promoting Dynamic Mode Decomposition (DMDSP), a popular mode-selection algorithm, serves as a benchmark for comparison. Numerical results from a Poiseuille flow test problem show that LARS4DMD yields reduced-order models that have comparable performance to DMDSP. LARS4DMD has the added benefit that the regularization weighting parameter required for DMDSP is not needed. II. Data-driven, reduced-order modelingThis section presents the techniques necessary for development of LARS4DMD: Section II.A reviews DMD; Section II.B describes DMDSP, a state-of-the-art method for DMD mode selection; and Section II.C introduces the original LARS algorithm. A. Dynamic Mode Decomposition (DMD)The DMD data analysis begins with the collection and proper arrangement of measurements for processing. Although generalized definitions of DMD exist (e.g., see [8,17]), we focus on the case of sequential, constant-interval measurements of a process evolving in time, similar to [9]. Let ψ k be a measurement vector (or snapshot) of the system for time steps k = 0, . . . , N. DMD seeks the best-fit linear operator A that advances each snapshot one time step such that ψ k+1 ≈ Aψ k . By constructing two data matrices, Ψ 0 = [ ψ 0 ψ 1 . . . ψ (N −1) ] and Ψ 1 = [ ψ 1 ψ 2 . . . ψ N ],

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Exploring the Molecular-Scale Structures at Solid/Liquid Interfaces of Li-Ion Battery Materials: A Force Spectroscopy Analysis with Sparse Modeling

Yamagishi,

Ohuchi,

Igaki

et al. 2024

Nano Lett.

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In this study, we clarify the liquid structure formed at the interface between LiCoO2 (LCO), the cathode material of Li-ion batteries, and propylene carbonate (PC), which is used as a solvent in the electrolyte, on a molecular scale. We apply sparse modeling-based modal analysis to force spectroscopy data measured by frequency modulation atomic force microscopy (FM-AFM) and show that each component in the FM-AFM force curve, such as oscillatory solvation force, background, and noise, can be automatically decomposed. Moreover, by combining detailed force curve analysis with solid/liquid interface simulations based on first-principles calculation, we have identified that there are distinct damped vibrational modes in the force curves at the LCO/PC interface with a period of about 0.57 nm and those with shorter periods, which likely correspond to the solvation forces associated with bulk-state PC molecules and those with PC molecules in “lying down” orientations.

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Analysis of Coherent Phonon Signals by Sparsity-promoting Dynamic Mode Decomposition

Cited by 9 publications

References 19 publications

Normal mode analysis of a relaxation process with Bayesian inference

Normal mode analysis of a relaxation process with Bayesian inference

Reduced-order modeling using Dynamic Mode Decomposition and Least Angle Regression

Exploring the Molecular-Scale Structures at Solid/Liquid Interfaces of Li-Ion Battery Materials: A Force Spectroscopy Analysis with Sparse Modeling

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