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Data-driven soliton solutions and parameter identification of the nonlocal nonlinear Schrödinger equation using the physics-informed neural network algorithm with parameter regularization

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Abstract

This paper presents a systematic study of data-driven soliton solutions and parameter identification for the nonlocal nonlinear Schrödinger (NLS) equation by employing the physics-informed neural network (PINN) algorithm with parameter regularization. This nonlocal NLS equation is obtained from the classical Manakov system under the special reduction that two components are related by a parity symmetry. Compared with the PINN structure of the local coupled NLS system, a relatively simple neural network with parameter regularization is constructed with fewer physical constraints of governing equations and less objective optimization by introducing the nonlocal connection between two components. Numerous data-driven local wave solutions including one- and two-soliton solutions with four collision patterns are accurately simulated and comparatively analyzed with relative and absolute errors. These numerical results demonstrate that the established PINN is able to predict one- and two-soliton solutions with high precision and accuracy. For the parameter identification of the nonlocal NLS equation, nonlinear coefficients are recognized through the known training data with different noise intensity.

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Funding

The work was supported by the National Natural Science Foundation of China (Grant Nos.12375003 and 12171217), the Zhejiang Province Natural Science Foundation of China (Grant No.2022SJGYZC01) and Zhejiang Sci-Tech University Excellent Postgraduate Dissertation Cultivation Fund Project (Grant No.LW-YP2024015).

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, 310018, China

    Nan Zhao

  2. Department of Mathematics, Lishui University, Lishui, 323000, China

    Yuheng Chen, Li Cheng & Junchao Chen

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  1. Nan Zhao
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  2. Yuheng Chen
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  3. Li Cheng
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Correspondence to Junchao Chen.

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Zhao, N., Chen, Y., Cheng, L. et al. Data-driven soliton solutions and parameter identification of the nonlocal nonlinear Schrödinger equation using the physics-informed neural network algorithm with parameter regularization. Nonlinear Dyn (2024). https://doi.org/10.1007/s11071-024-10562-6

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