Data-driven soliton solutions and parameter identification of the nonlocal nonlinear Schrödinger equation using the physics-informed neural network algorithm with parameter regularization

This paper presents a systematic study of data-driven soliton solutions and parameter identification for the nonlocal nonlinear Schrödinger (NLS) equation by employing the physics-informed neural network (PINN) algorithm with parameter regularization. This nonlocal NLS equation is obtained from the classical Manakov system under the special reduction that two components are related by a parity symmetry. Compared with the PINN structure of the local coupled NLS system, a relatively simple neural network with parameter regularization is constructed with fewer physical constraints of governing equations and less objective optimization by introducing the nonlocal connection between two components. Numerous data-driven local wave solutions including one- and two-soliton solutions with four collision patterns are accurately simulated and comparatively analyzed with relative and absolute errors. These numerical results demonstrate that the established PINN is able to predict one- and two-soliton solutions with high precision and accuracy. For the parameter identification of the nonlocal NLS equation, nonlinear coefficients are recognized through the known training data with different noise intensity.