Phase reduction of rhythmic phenomena using an autoencoder

Abstract

Spontaneous rhythmic phenomena have been observed in a wide range of fields from biology to engineering, including walking and power systems, and rhythmic phenomena have been widely studied, including synchronization phenomena in which the rhythms of multiple individuals are synchronized. Phase reduction theory has analyzed these phenomena by reducing rhythmic phenomena to a single variable phase. However, data-driven phase reduction has been considered difficult, especially for high-dimensional systems. In this study, the phase-sensitive function of a van der Pol oscillator was estimated using an auto-encoder that takes the trajectory data of rhythmic phenomena as input and enables phase reduction using a loss function that induces a value corresponding to the phase in the latent space, and it was confirmed that this function can be estimated with good accuracy.