We propose the two-subnet physical information neural network with the weighted loss function (WL-tsPINN) to study the higher-order effects of ultra-short pulses in birefringence fiber transmission and analyze the formation mechanism of vector solitons. We predict the dynamical process of mixed-type single/double soliton and soliton molecules based on the higher-order coupled nonlinear Schrödinger equation (CNLSE) by this WL-tsPINN method. Moreover, we deduce the physical coefficients of the higher-order CNLSE from the mixed single soliton solution. Deep learning based on neural network is a powerful tool for further study of higher-order CNLSE and has potential significance for further study of soliton dynamics.

我们提出了具有加权损失函数的双子网物理信息神经网络（WL-tsPINN）来研究超短脉冲在双折射光纤传输中的高阶效应，并分析矢量孤子的形成机制。我们通过这种WL-tsPINN方法基于高阶耦合非线性薛定谔方程（CNLSE）预测混合型单/双孤子和孤子分子的动力学过程。此外，我们从混合单孤子解中推导出高阶 CNLSE 的物理系数。基于神经网络的深度学习是进一步研究高阶CNLSE的有力工具，对进一步研究孤子动力学具有潜在意义。