Normal mode analysis of a relaxation process with Bayesian inference

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.