  Numerically computing physical quantities of time-evolved states in quantum
many-body systems is a challenging task in general. Here, we propose a method
that utilizes reliable short-time data of physical quantities to accurately
forecast long-time behavior. The method is based on the dynamic mode
decomposition (DMD), which is commonly used in fluid dynamics. The
effectiveness and applicability of the DMD in quantum many-body systems such as
the Ising model in the transverse field at the critical point are studied, even
when the input data exhibits complicated features such as multiple oscillatory
components and a power-law decay with long-ranged quantum entanglements unlike
fluid dynamics. It is demonstrated that the present method enables accurate
forecasts at time as long as nearly an order of magnitude longer than that of
the short-time training data. Effects of noise on the accuracy of the forecast
are also investigated, because they are important especially when dealing with
the experimental data. We find that a few percent of noise does not affect the
prediction accuracy destructively.
