https://doi.org/10.1140/epjs/s11734-025-01961-w
Regular Article
Data-driven solutions and parameter estimations for the integrable generalized fifth-order nonlinear Schrödinger equation based on physics-informed neural networks
School of Science, Zhejiang University of Science and Technology, 310023, Hangzhou, China
a
This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
7
July
2025
Accepted:
15
September
2025
Published online:
22
September
2025
Abstract
Physics-informed neural networks integrate machine learning with physical laws, providing a powerful tool for solving nonlinear evolution equations. This study investigates data-driven solutions and parameter estimation for the generalized fifth-order nonlinear Schrödinger equation, a complex model with three adjustable parameters. By embedding the governing equations as physical constraints within the neural network, we accurately reconstruct rogue wave solutions from sparse spatio-temporal data and simultaneously estimate the model parameters. A comparative analysis of activation functions shows that the Mexican Hat function outperforms the Tanh function in terms of accuracy and convergence, with the combination of two yielding even better results. This method can be extended to other high-order nonlinear systems, and the findings have potential applications in nonlinear optics and condensed matter physics.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
