We present a data-driven method based on long short-term memory (LSTM) neural networks to analyze spectral time series of Type Ia supernovae (SNe Ia). The data set includes 3091 spectra from 361 individual SNe Ia. The method allows for accurate reconstruction of the spectral sequence of an SN Ia based on a single observed spectrum around maximum light. The precision of the spectral reconstruction increases with more spectral time coverages, but the significant benefit of multiple epoch data at around optical maximum is only evident for observations separated by more than a week. The method shows great power in extracting the spectral information of SNe Ia and suggests that the most critical information of an SN Ia can be derived from a single spectrum around the optical maximum. The algorithm we have developed is important for the planning of spectroscopic follow-up observations of future SN surveys with the LSST/Rubin and WFIRST/Roman telescopes.