Forecasting the Forced van der Pol Equation with Frequent Phase Shifts Using Reservoir Computing

TL;DR

This study demonstrates that reservoir computing can effectively predict the dynamics of a forced van der Pol oscillator with varying phase shifts, with potential applications in circadian rhythm management for shift workers.

Contribution

It shows that reservoir computing trained on complex data can generalize to predict oscillations under different phase shifts in a non-autonomous system.

Findings

Reservoir computing accurately predicts oscillations with different phase shifts.

Training on complex data improves prediction accuracy across phase shifts.

Potential applications in optimizing shift work schedules based on circadian rhythms.

Abstract

We tested the performance of reservoir computing (RC) in predicting the dynamics of a certain non-autonomous dynamical system. Specifically, we considered a van del Pol oscillator subjected to periodic external force with frequent phase shifts. The reservoir computer, which was trained and optimized with simulation data generated for a particular phase shift, was designed to predict the oscillation dynamics under periodic external forces with different phase shifts. The results suggest that if the training data have some complexity, it is possible to quantitatively predict the oscillation dynamics exposed to different phase shifts. The setting of this study was motivated by the problem of predicting the state of the circadian rhythm of shift workers and designing a better shift work schedule for each individual. Our results suggest that RC could be exploited for such applications.