  The supervised machine learning (ML) approach is applied to realize the
trajectory-based nonadiabatic dynamics within the framework of the symmetrical
quasi-classical dynamics method based on the Meyer-Miller mapping Hamiltonian
(MM-SQC). After the construction of the long short-term memory recurrent neural
network (LSTM-RNN) model, it is used to perform the entire trajectory
evolutions from initial sampling conditions. The proposed idea is proven to be
reliable and accurate in the simulations of the dynamics of several
site-exciton electron-phonon coupling models, which cover two-site and
three-site systems with biased and unbiased energy levels, as well as include a
few or many phonon modes. The LSTM-RNN approach also shows the powerful ability
to obtain the accurate and stable results for the long-time evolutions. It
indicates that the LSTM-RNN model perfectly captures of dynamical correction
information in the trajectory evolution in the MM-SQC dynamics. Our work
provides the possibility to employ the ML methods in the simulation of the
trajectory-based nonadiabatic dynamic of complex systems with a large number of
degrees of freedoms.
