Normal mode analysis of a relaxation process with Bayesian inference

Abstract

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

Complex Energies of the Coherent Logitudinal Optical Phonon-plasmon Coupled Mode According to Dynamic Mode Decomposition Analysis

“…To apply the DMD to a one-dimensional signal, we constructed a data matrix as shown in Fig. 5, similarly to the previous studies on coherent phonons 31,32 . Now, we can suppose the measurement signal is N points with a constant time interval of δt, and we can denote the time series as (y 0 , ..., y N ).…”

“…DMD has a wide range of applicability in fiels such as neuroscience and nonlinear systems 29,30 . In recent years, DMD has been applied to coherent phonon spectroscopy 31,32 . Thus, DMD is widely used for the analysis of complex time series that include damping.…”

Complex energies of the coherent longitudinal optical phonon–plasmon coupled mode according to dynamic mode decomposition analysis

“…To apply the DMD to a one-dimensional signal, we constructed a data matrix as shown in Fig. 5, similarly to the previous studies on coherent phonons 36,37 . Now, we can suppose the measurement signal is N points with a constant time interval of δt , and we can denote the time series as y 0 , .…”

“…DMD has a wide range of applicability in fields such as neuroscience and nonlinear systems 34,35 . In recent years, DMD has been applied to coherent phonon spectroscopy 36,37 . Thus, DMD is widely used for the analysis of complex time series that include damping.…”

Bayesian estimation of equivalent circuit parameters of photovoltaic cells

“…In recent years, parameter extraction from experimental data via Bayesian estimation has been used in various fields of physics to solve these problems and has yielded significant results. [19][20][21][22][23] In brief, parameter estimations via the leastsquares and Bayesian methods can be considered as hypothesis-driven and data-driven approaches, respectively. Contrary to the least-squares method, Bayesian estimation searches the parameter space according to a pre-specified probability distribution called the prior probability distribution to obtain a probability distribution of the parameter set that can reproduce the experimental data, called the posterior probability distribution.…”