Predicting Ultrafast Nonlinear Dynamics in Fiber Optics by Enhanced Physics-Informed Neural Network

Ultrafast nonlinear dynamics plays a crucial role in ultrafast optics, necessitating accurate solutions to the generalized nonlinear Schrödinger equation (GNLSE) for understanding its underlying mathematical mechanisms. However, the GNLSE exhibits intricate physical interactions with highly nonlinear effects, leading to the complexity bottleneck in numerical methods and physical inconsistency in data-driven methods. Physics-informed neural networks (PINNs) can address these challenges by learning prior physical knowledge during the network optimization. However, the pathologies in the structure and learning mode of the vanilla PINN hinders its ability to learn high-nonlinear dynamics and high-frequency features. In this study, an enhanced PINN is proposed for ultrafast nonlinear dynamics in fiber optics, which strictly follows the spatial causality while simultaneously learning all frequency components. The model performance and generalization ability are investigated in two typical ultrafast nonlinear scenarios: higher-order soliton compression and supercontinuum generation, and the generated results exhibit remarkable agreement with reference results. Moreover, we also analyze the computational complexity of numerical methods and physical inconsistency of data-driven methods, and propose potential extensions for more complex scenarios. This work demonstrates the promising potential of the enhanced PINN in comprehending, characterizing, and modeling intricate dynamics with high-nonlinearity and high-frequency.