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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

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  • Yin, Yu-Hang
  • Lü, Xing

Abstract

In this paper, we focus on the inverse problem study of nonlinear Schrödinger (NLS) typed equations in optical fiber communicaitons. As an extension of the physics-informed neural network (PINN), multi-parallelized PINNs are constructed and trained for the discovery of diverse high-order terms and variable coefficients. We firstly study various constant-coefficient combinations of a generalized high-order NLS typed equation, where the Chen-Lee-Liu equation, the Gerdjikov-Ivanov equation and the Kundu-Eckhaus equation are included. With small amount of exact solutions available to us, we predict the value of multiple coefficients under different cases to deduce the undetermined terms of the generalized equation based on the multi-parallelized PINN. Different categories of NLS typed equations are then inferred. In the meantime, high accuracy numerical solutions on localized regions can be accordingly obtained.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:181:y:2024:i:c:s0960077924001462
    DOI: 10.1016/j.chaos.2024.114595
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    1. Zhang, Zhi-Yong & Zhang, Hui & Liu, Ye & Li, Jie-Ying & Liu, Cheng-Bao, 2023. "Generalized conditional symmetry enhanced physics-informed neural network and application to the forward and inverse problems of nonlinear diffusion equations," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    2. Wu, Gang-Zhou & Fang, Yin & Wang, Yue-Yue & Wu, Guo-Cheng & Dai, Chao-Qing, 2021. "Predicting the dynamic process and model parameters of the vector optical solitons in birefringent fibers via the modified PINN," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. Zhang, Yabin & Wang, Lei & Zhang, Peng & Luo, Haotian & Shi, Wanlin & Wang, Xin, 2022. "The nonlinear wave solutions and parameters discovery of the Lakshmanan-Porsezian-Daniel based on deep learning," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    4. Ma, Wen-Xiu, 2021. "N-soliton solution and the Hirota condition of a (2+1)-dimensional combined equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 270-279.
    5. Djelah, Gabriel & Ndzana, Fabien II & Abdoulkary, Saidou & Mohamadou, Alidou, 2023. "First and second order rogue waves dynamics in a nonlinear electrical transmission line with the next nearest neighbor couplings," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    6. Mohammadi, Reza, 2018. "Smooth Quintic spline approximation for nonlinear Schrödinger equations with variable coefficients in one and two dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 204-215.
    7. 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).
    8. Pu, Jun-Cai & Chen, Yong, 2022. "Data-driven vector localized waves and parameters discovery for Manakov system using deep learning approach," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    9. Han, Haoming & Zhang, Jing & Liu, Yan, 2023. "Stability analysis of hybrid high-order nonlinear multiple time-delayed coupled systems via aperiodically intermittent control," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    10. Tian, Hao & Niu, Yujun & Ghanbari, Behzad & Zhang, Zhao & Cao, Yulei, 2022. "Integrability and high-order localized waves of the (4 + 1)-dimensional nonlinear evolution equation," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    11. Haq, Abdul & Sukavanam, N., 2022. "Existence and partial approximate controllability of nonlinear Riemann–Liouville fractional systems of higher order," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    12. 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).
    13. Yin, Yu-Hang & Lü, Xing & Jiang, Rui & Jia, Bin & Gao, Ziyou, 2024. "Kinetic analysis and numerical tests of an adaptive car-following model for real-time traffic in ITS," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 635(C).
    14. 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).
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