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

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  • Fang, Yin
  • Wu, Gang-Zhou
  • Kudryashov, Nikolay A.
  • Wang, Yue-Yue
  • Dai, Chao-Qing

Abstract

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.

Suggested Citation

  • Fang, Yin & Wu, Gang-Zhou & Kudryashov, Nikolay A. & Wang, Yue-Yue & Dai, Chao-Qing, 2022. "Data-driven soliton solutions and model parameters of nonlinear wave models via the conservation-law constrained neural network method," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
  • Handle: RePEc:eee:chsofr:v:158:y:2022:i:c:s0960077922003289
    DOI: 10.1016/j.chaos.2022.112118
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    References listed on IDEAS

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    Cited by:

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    4. Wu, Gang-Zhou & Fang, Yin & Kudryashov, Nikolay A. & Wang, Yue-Yue & Dai, Chao-Qing, 2022. "Prediction of optical solitons using an improved physics-informed neural network method with the conservation law constraint," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    5. Fang, Yin & Bo, Wen-Bo & Wang, Ru-Ru & Wang, Yue-Yue & Dai, Chao-Qing, 2022. "Predicting nonlinear dynamics of optical solitons in optical fiber via the SCPINN," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    6. Chen, Liang-Yuan & Wu, Hong-Yu & Jiang, Li-Hong, 2024. "Partially nonlocal ring-like spatiotemporal superimposed second-order breathers under a harmonic potential," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    7. Fang, Yin & Zhu, Bo-Wei & Bo, Wen-Bo & Wang, Yue-Yue & Dai, Chao-Qing, 2023. "Data-driven prediction of spatial optical solitons in fractional diffraction," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    8. Kudryashov, Nikolay A., 2024. "Solitons of the complex modified Korteweg–de Vries hierarchy," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    9. Chen, Yi-Xiang, 2024. "(3+1)-dimensional partially nonlocal ring-like bright-dark monster waves," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    10. 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).
    11. Zhu, Bo-Wei & Fang, Yin & Liu, Wei & Dai, Chao-Qing, 2022. "Predicting the dynamic process and model parameters of vector optical solitons under coupled higher-order effects via WL-tsPINN," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    12. Zhong, WenYe & Qin, Pei & Zhong, Wei-Ping & Belić, Milivoj, 2022. "Two-dimensional rogue wave clusters in self-focusing Kerr-media," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).

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