When Flat Beats Deep: Accelerated Prediction of Peregrine Soliton Evolution via an Improved Broad Learning System

Peregrine solitons have significant application value in fields such as ultrafast pulse control in optical fibers and turbulence detection. Accurate prediction of their evolution process is crucial for experimental design and control optimization. However, neural network prediction models based on deep extension inevitably face the problems of huge parameters and long training time. To this end, this paper proposes an Improved Broad Learning System (IBLS) for rapid and accurate prediction of Peregrine soliton dynamics. IBLS features a flat network structure to allow feature nodes and enhancement nodes wide expansion and uses the ridge regression algorithm to quickly solve the pseudoinverse. IBLS uses improved incremental learning to update the model structure dynamically during training while preserving earlier training results, which is not possible with deep neural networks. In peregrine solitons' case, the normalized root mean square error of the temporal domain prediction results of IBLS is reduced by 44.6%, and the training speed is increased by a factor of 3 compared to the neural network reference model. Proposed model not only can be extended to fast prediction of other optical nonlinear evolutionary processes but also provides new ideas for broad learning system in physical field modeling.