Forecasting the forced van der Pol equation with frequent phase shifts using Reservoir Computing

We tested the performance of reservoir computing (RC) in predicting the dynamics of a specific nonautonomous dynamical system. Specifically, we considered a van der Pol oscillator subjected to a periodic external force with frequent phase shifts. The reservoir computer, trained and optimized using simulation data generated for a specific 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 exhibit sufficient complexity, it is possible to quantitatively predict the oscillation dynamics subjected to different phase shifts. This study was motivated by the challenge of predicting the circadian rhythm of shift workers and optimizing their shift schedules individually. Our results suggest that RC could be utilized for such applications.