https://doi.org/10.1140/epjs/s11734-025-01963-8
Regular Article
Data-driven soliton dynamics and parameter discovery of longitudinal wave equations in magneto-electro-elastic circular rods based on deep learning
1
School of Mathematical Sciences, Dalian Minzu University, 116600, Dalian, China
2
College of Mathematics and Systems Science, Shandong University of Science and Technology, 266590, Qingdao, China
Received:
31
July
2025
Accepted:
15
September
2025
Published online:
20
September
2025
In recent years, research in the field of solid mechanics has increasingly focused on solitary waves in nonlinear elasticity. With the widespread application of magneto-electro-elastic structures such as sensors and actuators in engineering, the propagation of waves in magneto-electro-elastic media has emerged as a prominent research area. This study employs physics-informed neural networks (PINNs) to systematically investigate data-driven solutions for various solitary waves in magnetoelectric elastic cylindrical rods, including bright solitons, dark solitons, composite bright-dark solitons, kink solitons, periodic singular solitons, and the interaction between a kink soliton and a solitary wave. Additionally, PINNs is applied to explore the inverse problem algorithm for the nonlinear longitudinal wave equation in magnetoelectric elastic cylindrical rods, successfully identifying the parameters of the nonlinear terms in the equation. To address the network’s limitations in capturing the peak characteristics of steep periodic singular waves in magneto-electroelastic cylindrical rods, the residual-based adaptive sampling strategy is introduced, effectively improving this issue and reducing the L2 relative error of periodic singular solitons from 
to 
. Using PINNs, this paper successfully obtained data-driven solutions for various solitary waves in magneto-electro-elastic circular rods, with L2 relative errors all below 
. These data-driven solutions can provide references for studying energy exchange and information transmission in magneto-electro-elastic media, and have certain significance for theoretical research on the design of high-performance sensors and actuators.
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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.
