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Physics-Informed Neural Networks with Two Weighted Loss Function Methods for Interactions of Two-Dimensional Oceanic Internal Solitary Waves

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Abstract

The multiple patterns of internal solitary wave interactions (ISWI) are a complex oceanic phenomenon. Satellite remote sensing techniques indirectly detect these ISWI, but do not provide information on their detailed structure and dynamics. Recently, the authors considered a three-layer fluid with shear flow and developed a (2+1) Kadomtsev-Petviashvili (KP) model that is capable of describing five types of oceanic ISWI, including O-type, P-type, TO-type, TP-type, and Y-shaped. Deep learning models, particularly physics-informed neural networks (PINN), are widely used in the field of fluids and internal solitary waves. However, the authors find that the amplitude of internal solitary waves is much smaller than the wavelength and the ISWI occur at relatively large spatial scales, and these characteristics lead to an imbalance in the loss function of the PINN model. To solve this problem, the authors introduce two weighted loss function methods, the fixed weighing and the adaptive weighting methods, to improve the PINN model. This successfully simulated the detailed structure and dynamics of ISWI, with simulation results corresponding to the satellite images. In particular, the adaptive weighting method can automatically update the weights of different terms in the loss function and outperforms the fixed weighting method in terms of generalization ability.

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Acknowledgements

The authors would like to thank Dr. Zhengwu Miao for his kindly support and help.

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Key Laboratory of Mathematics and Engineering Applications (Ministry of Education) & Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, 200241, China

    Junchao Sun, Yong Chen & Xiaoyan Tang

  2. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China

    Yong Chen

Authors
  1. Junchao Sun
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  2. Yong Chen
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  3. Xiaoyan Tang
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Corresponding author

Correspondence to Xiaoyan Tang.

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The authors declare no conflict of interest.

Additional information

This work was supported by the National Natural Science Foundation of China under Grant Nos. 12275085, 12235007, and 12175069, and Science and Technology Commission of Shanghai Municipality under Grant Nos. 21JC1402500 and 22DZ2229014.

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Sun, J., Chen, Y. & Tang, X. Physics-Informed Neural Networks with Two Weighted Loss Function Methods for Interactions of Two-Dimensional Oceanic Internal Solitary Waves. J Syst Sci Complex 37, 545–566 (2024). https://doi.org/10.1007/s11424-024-3500-x

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  • DOI: https://doi.org/10.1007/s11424-024-3500-x

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