Physics-Informed Neural Network for Optical Fiber Parameter Estimation From the Nonlinear Schrödinger Equation

For any system that follows rigorous mathematical and physical theories like fiber-optic system, system parameter estimation is crucial for system detection and monitoring. In this paper, a physics-informed neural network (PINN)-based method is proposed for optical fiber parameter estimation by solving the inverse problem of the nonlinear Schrödinger equation (NLSE), i.e., inferring the unknown parameters of NLSE. The proposed method considers both the prior knowledge of physical law and the characteristics of observation data from only the transmitted and received waveforms. In PINN, the NLSE and observation data are set as the loss function, and the typical fiber parameters (attenuation, dispersion, and nonlinear coefficient) are optimized iteratively until they satisfy the inferred NLSE by learning the limited observation data. Three scenarios are validated, including single Gaussian pulse propagation, ultrashort pulse propagation in highly nonlinear fiber, and optical signal transmission in standard single-mode fiber. The launch power of the signal is embedded in PINN as a parametric feature, which makes PINN learn the signal transmissions under different powers simultaneously. The weights of mean square error terms for NLSE and observation data in the loss function are properly adjusted to balance learning difficulties. Moreover, the statistical results of 128 different signals and model performance under different signal-to-noise ratios are analyzed. As an extension, fiber length estimation is also studied, and the error is 0.375% when the launch power is 0 dBm. Our work verifiably shows that the proposed approach performs well and can be further extended to multiple applications in fiber optics.