https://doi.org/10.1140/epjs/s11734-025-01846-y
Regular Article
Data-driven solutions of a Burgers-type equation via physics-informed neural networks and Bäcklund transformation
1
School of Mathematics and Information Science, Zhengzhou University of Light Industry, 450002, Zhengzhou, Henan, China
2
Department of Basic Education, Zhengzhou University of Science and Technology, 450064, Zhengzhou, Henan, China
a
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Received:
10
March
2025
Accepted:
4
August
2025
Published online:
12
August
2025
Abstract
This paper investigates the data-driven solutions of a Burgers-type equation, whose solutions can be related to the ones of Burgers equation in view of the Bäcklund transformation. By means of the physics-informed neural networks (PINN), the numerical solutions of Burgers and Burgers-type equations are simulated at the same network with the help of the Bäcklund transformation and the initial and boundary value of Burgers equation. Under diverse initial and boundary conditions, the comparisons between the exact and predicted solutions of Burgers equations are demonstrated through the graphics, and the corresponding solutions of Burgers-type equation are simulated in the same network. Physics-informed neural networks show the ability to predict the solutions of two systems based on the physical laws and their connection via a small amount of initial data.
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© 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.
