  Plasmon-induced transparency (PIT) displays complex nonlinear dynamics that
find critical phenomena in areas such as nonlinear waves. However, such a
nonlinear solution depends sensitively on the selection of parameters and
different potentials in the Schr\"odinger equation. Despite this complexity,
the machine learning community has developed remarkable efficiencies in
predicting complicated datasets by regression. Here, we consider a recurrent
neural network (RNN) approach to predict the complex propagation of nonlinear
solitons in plasmon-induced transparency metamaterial systems with applied
potentials bypassing the need for analytical and numerical approaches of a
guiding model. We demonstrate the success of this scheme on the prediction of
the propagation of the nonlinear solitons solely from a given initial condition
and potential. We prove the prominent agreement of results in simulation and
prediction by long short-term memory (LSTM) artificial neural networks. The
framework presented in this work opens up a new perspective for the application
of RNN in quantum systems and nonlinear waves using Schr\"odinger-type
equations, for example, the nonlinear dynamics in cold-atom systems and
nonlinear fiber optics.
