  The strongly-constrained physics-informed neural network (SCPINN) is proposed
by adding the information of compound derivative embedded into the
soft-constraint of physics-informed neural network(PINN). It is used to predict
nonlinear dynamics and the formation process of bright and dark picosecond
optical solitons, and femtosecond soliton molecule in the single-mode fiber,
and reveal the variation of physical quantities including the energy,
amplitude, spectrum and phase of pulses during the soliton transmission. The
adaptive weight is introduced to accelerate the convergence of loss function in
this new neural network. Compared with the PINN, the accuracy of SCPINN in
predicting soliton dynamics is improved by 5-11 times. Therefore, the SCPINN is
a forward-looking method to study the modeling and analysis of soliton dynamics
in the fiber.
