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Mix-training physics-informed neural networks for the rogue waves of nonlinear Schrödinger equation

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  • Li, Jiaheng
  • Li, Biao

Abstract

In this paper, we propose mix-training physics-informed neural networks (PINNs). This is a deep learning model with more approximation ability based on PINNs, combined with mixed training and prior information. We demonstrate the advantages of this model by exploring rogue waves with rich dynamic behavior in the nonlinear Schrödinger (NLS) equation. Compared with the original PINNs, numerical results show that this model can not only quickly recover the dynamical behavior of the rogue waves of NLS equation, but also improve its approximation ability and absolute error accuracy significantly, and the prediction accuracy has been improved by two to three orders of magnitude. In particular, when the space–time domain of the solution expands, or the solution has a local sharp region, the proposed model still has high prediction accuracy.

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  • Li, Jiaheng & Li, Biao, 2022. "Mix-training physics-informed neural networks for the rogue waves of nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008918
    DOI: 10.1016/j.chaos.2022.112712
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    References listed on IDEAS

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    1. Justin Sirignano & Konstantinos Spiliopoulos, 2017. "DGM: A deep learning algorithm for solving partial differential equations," Papers 1708.07469, arXiv.org, revised Sep 2018.
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    Cited by:

    1. Li, Wentao & Li, Biao, 2024. "Construction of degenerate lump solutions for (2+1)-dimensional Yu-Toda-Sasa-Fukuyama equation," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    2. Chen, Chaodong, 2024. "PGNM: Using Physics-Informed Gated Recurrent Units Network Method to capture the dynamic data feature propagation process of PDEs," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    3. Jiang, Jun-Hang & Si, Zhi-Zeng & Kudryashov, Nikolay A. & Dai, Chao-Qing & Liu, Wei, 2024. "Prediction of symmetric and asymmetric solitons and model parameters for nonlinear Schrödinger equations with competing nonlinearities," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    4. Liu, Yindi & Zhao, Zhonglong, 2024. "Periodic line wave, rogue waves and the interaction solutions of the (2+1)-dimensional integrable Kadomtsev–Petviashvili-based system," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    5. Chen, Junchao & Song, Jin & Zhou, Zijian & Yan, Zhenya, 2023. "Data-driven localized waves and parameter discovery in the massive Thirring model via extended physics-informed neural networks with interface zones," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    6. Yin, Yu-Hang & Lü, Xing, 2024. "Multi-parallelized PINNs for the inverse problem study of NLS typed equations in optical fiber communications: Discovery on diverse high-order terms and variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    7. Wang, Haotian & Li, Xin & Zhou, Qin & Liu, Wenjun, 2023. "Dynamics and spectral analysis of optical rogue waves for a coupled nonlinear Schrödinger equation applicable to pulse propagation in isotropic media," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).

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