  A physics-informed neural network (PINN) that combines deep learning with
physics is studied to solve the nonlinear Schr\"odinger equation for learning
nonlinear dynamics in fiber optics. We carry out a systematic investigation and
comprehensive verification on PINN for multiple physical effects in optical
fibers, including dispersion, self-phase modulation, and higher-order nonlinear
effects. Moreover, both special case (soliton propagation) and general case
(multi-pulse propagation) are investigated and realized with PINN. In the
previous studies, the PINN was mainly effective for single scenario. To
overcome this problem, the physical parameters (pulse peak power and amplitudes
of sub-pulses) are hereby embedded as additional input parameter controllers,
which allow PINN to learn the physical constraints of different scenarios and
perform good generalizability. Furthermore, PINN exhibits better performance
than the data-driven neural network using much less data, and its computational
complexity (in terms of number of multiplications) is much lower than that of
the split-step Fourier method. The results report here show that the PINN is
not only an effective partial differential equation solver, but also a
prospective technique to advance the scientific computing and automatic
modeling in fiber optics.
