Data-driven femtosecond optical soliton excitations and parameters discovery of the high-order NLSE using the PINN

We use the physics-informed neural network to solve a variety of femtosecond optical soliton solutions of the high-order nonlinear Schrodinger 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 Schrodinger 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.

Automated summary

The researchers utilized a physics-informed neural network to address various femtosecond optical soliton solutions of the high-order nonlinear Schrodinger equation, achieving smaller prediction errors for specific solutions. As the prediction distance increases, the prediction error gradually rises. By optimizing the neural network in terms of layers, neurons, and sampling points, the researchers significantly reduced errors compared to prior research, indicating potential for new methodologies in this field.