  Plasmon-induced transparency (PIT) in advanced materials has attracted
extensive attention for both theoretical and applied physics. Here, we
considered a scheme that can produce PIT and studied the characteristics of
ultraslow low-power magnetic solitons. The PIT metamaterial is constructed as
an array of unit cells that consist of two coupled varactor-loaded split-ring
resonators. Simulations verified that ultraslow magnetic solitons can be
generated in this type of metamaterial. To solve nonlinear equations, various
types of numerical methods can be applied by virtue of exact solutions, which
are always difficult to acquire. However, the initial conditions and
propagation distance impact the ultimate results. In this article, an
artificial neural network (ANN) was used as a supervised learning model to
predict the evolution and final mathematical expressions through training based
on samples with disparate initial conditions. Specifically, the influences of
the number of hidden layers were discussed. Additionally, the learning results
obtained by employing several training algorithms were analyzed and compared.
Our research opens a route for employing machine learning algorithms to save
time in both physical and engineering applications of Schr\"odinger-type
systems.
