We use the physics-informed neural network to solve a variety of femtosecond optical soliton solutions of the high-order nonlinear Schrödinger equation, including one-soliton solution, two-soliton solution, rogue wave solution, W-soliton solution and M-soliton solution. The prediction error for one-soliton, W-soliton and M-soliton is smaller. As the prediction distance increases, the prediction error will gradually increase. The unknown physical parameters of the high-order nonlinear Schrödinger equation are studied by using rogue wave solutions as data sets. The neural network is optimized from three aspects including the number of layers of the neural network, the number of neurons, and the sampling points. Compared with previous research, our error is greatly reduced. This is not a replacement for the traditional numerical method, but hopefully to open up new ideas.

我们使用物理信息神经网络求解高阶非线性薛定谔方程的各种飞秒光学孤子解，包括单孤子解、双孤子解、流氓波解、W-孤子解和M-孤子解. 单孤子、W-孤子和M-孤子的预测误差较小。随着预测距离的增加，预测误差会逐渐增加。以流氓波解为数据集，研究了高阶非线性薛定谔方程的未知物理参数。神经网络从神经网络的层数、神经元数量、采样点数三个方面进行优化。与之前的研究相比，我们的错误大大减少了。这不是传统数值方法的替代品，