Deep learning prediction of fractional dissipative optical solitons via the improved quasi-residual physical-informed neural networks

In addressing the challenges of complex fractional derivative calculations and error accumulation in asymmetric soliton evolution during the prediction of soliton dynamics governed by the nonlinear fractional Schrödinger equation (NLFSE), this study improves upon the earlier quasi-residual physics-informed neural network (QR_PINN) by innovatively proposing a quasi-residual physics-informed neural network with a pseudo-initial boundary strategy (QR_PINN_PB). This strategy dynamically generates prediction results from the previous stage as prior constraints for the subsequent stage, enabling error accumulation suppression without manual subdomain division. It effectively overcomes the limitation of insufficient accuracy in traditional QR_PINN for dynamic evolution scenarios. Experimental validation demonstrates that QR_PINN_PB exhibits high accuracy and robustness in predicting symmetric, asymmetric, and antisymmetric solitons, with superior performance particularly in forecasting fractional dissipative soliton dynamics. It also shows stronger adaptability across different data scenarios, providing a novel approach for dynamic modeling of fractional complex systems.