Optica Open
Browse
- No file added yet -

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

Download (5.58 kB)
preprint
posted on 2023-01-12, 13:54 authored by Gang-Zhou Wu, Yin Fang, Yue-Yue Wang, Chao-Qing Dai
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 Schr\"odinger 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 Schr\"odinger equation. Compared with the traditional physics-informed neural network method, the modified method can significantly improve the calculation accuracy.

History

Disclaimer

This arXiv metadata record was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv.

Usage metrics

    Licence

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC