arXiv subjects

Gang-Zhou Wu

Publications and source records attributed to Gang-Zhou Wu.

4 recordsLinked to original sources

arXiv2022

Data-driven soliton solutions and model parameters of nonlinear wave models via the conservation-law constrained neural network method

In the process of the deep learning, we integrate more integrable information of nonlinear wave models, such as the conservation law obtained from the integrable theory, into the neural network structure, and propose a conservation-law constrained neural network method with the flexible learning rate to predict solutions and parameters of nonlinear wave models. As some examples, we study real and complex typical nonlinear wave models, including nonlinear Schrödinger equation, Korteweg-de Vries and modified Korteweg-de Vries equations. Compared with the traditional physics-informed neural network method, this new method can more accurately predict solutions and parameters of some specific nonlinear wave models even when less information is needed, for example, in the absence of the boundary conditions. This provides a reference to further study solutions of nonlinear wave models by combining the deep learning and the integrable theory.

nlin.PS↗

arXiv2021

Predicting the dynamic process and model parameters of the vector optical solitons in birefringent fibers via the modified PINN

A modified physics-informed neural network is used to predict the dynamics of optical pulses including one-soliton, two-soliton, and rogue wave based on the coupled nonlinear Schrödinger equation in birefringent fibers. At the same time, the elastic collision process of the mixed bright-dark soliton is predicted. Compared the predicted results with the exact solution, the modified physics-informed neural network method is proven to be effective to solve the coupled nonlinear Schrödinger equation. Moreover, the dispersion coefficients and nonlinearity coefficients of the coupled nonlinear Schrodinger equation can be learned by modified physics-informed neural network. This provides a reference for us to use deep learning methods to study the dynamic characteristics of solitons in optical fibers.

nlin.PS↗

arXiv2021

Modified physics-informed neural network method based on the conservation law constraint and its prediction of optical solitons

Based on conservation laws as one of the important integrable properties of nonlinear physical models, we design a modified physics-informed neural network method based on the conservation law constraint. From a global perspective, this method imposes physical constraints on the solution of nonlinear physical models by introducing the conservation law into the mean square error of the loss function to train the neural network. Using this method, we mainly study the standard nonlinear Schrödinger equation and predict various data-driven optical soliton solutions, including one-soliton, soliton molecules, two-soliton interaction, and rogue wave. In addition, based on various exact solutions, we use the modified physics-informed neural network method based on the conservation law constraint to predict the dispersion and nonlinear coefficients of the standard nonlinear Schrödinger equation. Compared with the traditional physics-informed neural network method, the modified method can significantly improve the calculation accuracy.

nlin.PS↗

arXiv2021

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 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.

nlin.PS↗