  We introduce a novel neural network structure called Strongly Constrained
Theory-Guided Neural Network (SCTgNN), to investigate the behaviours of the
localized solutions of the generalized nonlinear Schr\"{o}dinger (NLS)
equation. This equation comprises four physically significant nonlinear
evolution equations, namely, (i) NLS equation, Hirota equation
Lakshmanan-Porsezian-Daniel (LPD) equation and fifth-order NLS equation. The
generalized NLS equation demonstrates nonlinear effects up to quintic order,
indicating rich and complex dynamics in various fields of physics. By combining
concepts from the Physics-Informed Neural Network (PINN) and Theory-Guided
Neural Network (TgNN) models, SCTgNN aims to enhance our understanding of
complex phenomena, particularly within nonlinear systems that defy conventional
patterns. To begin, we employ the TgNN method to predict the behaviours of
localized waves, including solitons, rogue waves, and breathers, within the
generalized NLS equation. We then use SCTgNN to predict the aforementioned
localized solutions and calculate the mean square errors in both SCTgNN and
TgNN in predicting these three localized solutions. Our findings reveal that
both models excel in understanding complex behaviours and provide predictions
across a wide variety of situations.
