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Boussinesq equation solved by the physics-informed neural networks

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Abstract

Physics-informed neural networks (PINNs) model is utilized to achieve the first- and second-order rogue wave solvers of the Boussinesq equation with different initial and boundary conditions. A new generalized loss term handling the initial first-order derivate is included in the simulations to guarantee the high prediction accuracies in the adaptive PINNs (APINNs) and the gradient-optimized PINNs (GPINNs) models, with a new regularization parameter being considered in the latter case. Learned results with high precision are fulfilled in the large domain simulations by applying more collocation points and more weight parameters in the neural network architecture. The APINNs model currently can be made use of in more situations with high prediction accuracies, while the GPINNs model is more robust in the current research where the initial condition is distributed in the localized sharp areas. Parallel computing is carried out to get the mean relative \(L_2\)-norm errors efficiently in the GPINNs model due to the random choosing of the simulation points during the training iterations.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Funding

This work was supported by the Scientific Research Fund of Zhejiang Provincial Education Department under Grant No. Y202148297 and the National Natural Science Foundation of China under Grant No. 11975008.

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  1. College of Engineering, Lishui University, Lishui, 323000, China

    Ruozhou Gao, Wei Hu, Jinxi Fei & Hongyu Wu

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  1. Ruozhou Gao
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  4. Hongyu Wu
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Correspondence to Wei Hu.

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Gao, R., Hu, W., Fei, J. et al. Boussinesq equation solved by the physics-informed neural networks. Nonlinear Dyn 111, 15279–15291 (2023). https://doi.org/10.1007/s11071-023-08614-4

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