Predicting certain vector optical solitons via the conservation-law deep-learning method

Abstract

The energy conservation law is introduced into a loss function of the physics-informed neural network (PINN), and an energy-conservation deep-learning (ECDL) method is constructed to study a coupled nonlinear Schrödinger equation (CNLSE). Using the ECDL method, we analyze the formation mechanism of vector solitons in birefringent fibers, and predict the dynamic behaviors of vector solitons, including one-soliton, two-soliton interaction, soliton molecule, rogue wave, and nondegenerate soliton. The related physical processes such as the energy conversion and power conservation along the propagation of soliton are studied. The results show that the nonlinear and dispersive effects separately cause the pulse broadening in time and frequency domains. The energy, shape and velocity of pulse in the transmission process remain unchanged when the two effects are balanced. Compared with the PINN method, the ECDL has higher accuracy and good generalization ability for a variety of soliton pulse propagation scenarios in optical fiber. Therefore, the deep learning method based on the prior knowledge of energy conservation is an effective tool to promote the research of nonlinear optics.