  Reservoir computing is a machine learning algorithm that excels at predicting
the evolution of time series, in particular, dynamical systems. Moreover, it
has also shown superb performance at solving partial differential equations. In
this work, we adapt this methodology to integrate the time-dependent
Schr\"odinger equation, propagating an initial wavefunction in time. Since such
wavefunctions are complex-valued high-dimensional arrays the reservoir
computing formalism needs to be extended to cope with complex-valued data.
Furthermore, we propose a multi-step learning strategy that avoids overfitting
the training data. We illustrate the performance of our adapted reservoir
computing method by application to four standard problems in molecular
vibrational dynamics.
