Latent Neural Phase Model for Synchronization Analysis

This study proposes the latent neural phase model (LNPM), a deep generative model that can estimate the phase of coupled oscillators and parameters of the phase equation simultaneously from irregularly sampled noisy observation data. LNPM can handle a wide range of phase equations e.g., equations with time-dependent parameters. Inheriting the property of the classical phase model, we can use LNPM to quantify the degree of collective synchronization of rhythms. We develop a parameter estimation algorithm that minimizes the evidence lower bound (ELBO) by using the reparametrization trick. The effectiveness of LNPM is confirmed by challenges that include Huygens's clock problem.