Prediction of soliton evolution and parameters evaluation for a high-order nonlinear Schrödinger–Maxwell–Bloch equation in the optical fiber

Abstract

Physics-Informed Neural Networks (PINNs) have established a strong track record in addressing partial differential equations, catering to both predictive (forward) and analytical (inverse) challenges. Building upon the PINN framework, parallel hard-constraint physics-informed neural networks (phPINN) have been effectively utilized to tackle the forward and inverse issues associated with the generalized nonlinear Schrödinger–Maxwell–Bloch (GNLS-MB) equations within the context of optical fibers in this work. In the realm of forward problems, the phPINN model has adeptly forecasted three distinct soliton dynamic scenarios, each shaped by its unique set of initial and boundary conditions. Shifting focus to inverse problems, the method evaluates the parameters of the GNLS-MB equation by leveraging training datasets that encompass varying levels of noise, initial conditions, and solution configurations. The findings demonstrate the phPINN method's capability to effectively handle both forward and inverse problems related to the three-component coupled high-order generalized nonlinear Schrödinger equations.