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Solution of the Hirota equation using a physics-informed neural network method with embedded conservation laws

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Abstract

The solution of the integrable Hirota equation has attracted considerable attention in the applications of nonlinear optics, electromagnetics, and many other natural sciences. In this paper, we propose an improved physics-informed neural network (IPINN) method to study numerical solutions of the Hirota equation, which embeds energy conservation laws into a traditional neural network through the Lax pair formulation. Our simulation results show that the proposed method can predict the solutions and parameters of the Hirota equation more accurately than the traditional physics-informed neural network method. In addition, the influence on the rogue wave solution for the Hirota equation of the three factors of the IPINN method that are, number of network layers and hidden layer neurons, sampling points, and noises, is also analyzed in detail. In our study, it is worth noting that the presented method can achieve good prediction with fewer training data and iterations.

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Acknowledgements

The work was supported by the National Natural Science Foundation of China (Grant No. 11601411), the Natural Science Basic Research Plan in Shaanxi Province of China (Program No. 2021JM-448), and the Natural Science Basic Research Plan in Shaanxi Province of China (Program No. 2023-JC-YB-063).

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  1. School of Science, Xi’an Polytechnic University, Xi’an, 710048, Shaanxi, China

    Ruibo Zhang, Jin Su & Jinqian Feng

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  1. Ruibo Zhang
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Correspondence to Jin Su.

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Zhang, R., Su, J. & Feng, J. Solution of the Hirota equation using a physics-informed neural network method with embedded conservation laws. Nonlinear Dyn 111, 13399–13414 (2023). https://doi.org/10.1007/s11071-023-08557-w

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