Neural Network-Based Symbolic Computation Algorithm for Solving (2+1)-Dimensional Yu-Toda-Sasa-Fukuyama Equation

Jiang-Long Shen, Run-Fa Zhang (), Jing-Wen Huang and Jing-Bin Liang
Additional contact information
Jiang-Long Shen: School of Mathematics and Physics, Yibin University, Yibin 644001, China
Run-Fa Zhang: School of Automation and Software Engineering, Shanxi University, Taiyuan 030006, China
Jing-Wen Huang: School of Mathematics and Physics, Yibin University, Yibin 644001, China
Jing-Bin Liang: School of Mathematics and Physics, Yibin University, Yibin 644001, China

Mathematics, 2025, vol. 13, issue 18, 1-18

Abstract: This paper presents a Neural Network-Based Symbolic Computation Algorithm (NNSCA) for solving the (2+1)-dimensional Yu-Toda-Sasa-Fukuyama (YTSF) equation. By combining neural networks with symbolic computation, NNSCA bypasses traditional method limitations, deriving and visualizing exact solutions. It designs neural network architectures, converts the PDE into algebraic constraints via Maple, and forms a closed-loop solution process. NNSCA provides a general paradigm for high-dimensional nonlinear PDEs, showing great application potential.

Keywords: neural network-based symbolic computation; (2+1)-dimensional YTSF equation; exact solutions; nonlinear partial differential equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/18/3006/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/18/3006/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:18:p:3006-:d:1751686

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().