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Data-driven vector degenerate and nondegenerate solitons of coupled nonlocal nonlinear Schrödinger equation via improved PINN algorithm

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Abstract

In recent years, the Physics-Informed Neural Networks have demonstrated significant potential in solving nonlinear evolution equations, and exhibited high stability and applicability. However, it does not fully adapt to nonlocal nonlinear evolution equations. In this paper, we improve the traditional Physics-Informed Neural Network by incorporating prior information as a supplementary term in the loss function to effectively capture the amplitude distribution at the target location, thereby enhancing the predictive accuracy of the neural network. Additionally, we address the problem of multiple competing objectives in the loss function through stepwise training, leveraging adaptive weights and adaptive activation functions to optimize predictions. We apply these improved strategies of physical information neural networks to predict soliton solution of the coupled nonlocal nonlinear Schrödinger equation, including two kinds of nondegenerate one-soliton, and two kinds of degenerate double-soliton. Moreover, we also discuss the impact of Gaussian noise on data-driven parameter discovery of the coupled nonlocal nonlinear Schrödinger equation.

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Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Funding

National Natural Science Foundation of China(Grant Nos. 12075210 and 12261131495); the Scientific Research and Developed Fund of Zhejiang A&F University(Grant No. 2021FR0009).

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Authors and Affiliations

  1. College of Optical, Mechanical and Electrical Engineering, Zhejiang A&F University, Lin’an, 311300, China

    Wei-Xin Qiu, Zhi-Zeng Si, Da-Sheng Mou, Chao-Qing Dai & Wei Liu

  2. School of Physics and Telecommunications Engineering, Zhoukou Normal University, Zhoukou, 466001, China

    Ji-Tao Li

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  1. Wei-Xin Qiu
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  2. Zhi-Zeng Si
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  3. Da-Sheng Mou
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  4. Chao-Qing Dai
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  6. Wei Liu
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Contributions

Wei-Xin Qiu: Software, Investigation, Writing-Original draft preparation. Zhi-Zeng Si: Software, Investigation. Da-Sheng Mou: Software, Investigation. Dai-Chao Qing: Conceptualization, Methodology, Writing-Reviewing and Editing, Supervision. Ji-Tao Li: Conceptualization, Writing-Reviewing and Editing, Supervision. Wei Liu: Conceptualization, Writing-Reviewing and Editing, Supervision.

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Correspondence to Chao-Qing Dai, Ji-Tao Li or Wei Liu.

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Qiu, WX., Si, ZZ., Mou, DS. et al. Data-driven vector degenerate and nondegenerate solitons of coupled nonlocal nonlinear Schrödinger equation via improved PINN algorithm. Nonlinear Dyn (2024). https://doi.org/10.1007/s11071-024-09648-y

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