  Time series prediction (TSP) has been widely used in various fields, such as
life sciences and finance, to forecast future trends based on historical data.
However, to date, there has been relatively little research conducted on the
TSP for quantum physics. In this paper, we explore the potential application of
TSP in forecasting the dynamical evolution of open quantum systems. We employ
deep learning techniques to train a TSP model and evaluate its performance by
comparison with exact solution. We use the ratio of the prediction step length
and the sequence length to define short and long-term forecasting. Our results
show that the trained model has the ability to effectively capture the inherent
characteristics of time series for both short-term and long-term forecasting.
Accurate predictions for different coupling intensities and initial states are
obtained. Furthermore, we use our method to train another model and find that
it can successfully predict the steady state of the system. These findings
suggests that TSP is a valuable tool for the prediction of the dynamics in open
quantum systems.
