Neural Network-Based Symbolic Computation Algorithm for Solving (2+1)-Dimensional Yu-Toda-Sasa-Fukuyama Equation
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.
Authors
- Jinghong Liang (ORCID: https://orcid.org/0000-0001-9237-7291)
- Jianglong Shen (ORCID: https://orcid.org/0000-0001-8729-1469)
- Jingwen Huang (ORCID: https://orcid.org/0000-0001-8412-7890)
- Runfa Zhang (ORCID: https://orcid.org/0000-0002-7436-2915)
Institutions
- Shanxi University (CN)
- Yibin University (CN)
Publication Details
- Journal
- Mathematics
- Published
- 2025-09-17
- DOI
- https://doi.org/10.3390/math13183006
- Citations
- 4
- Primary Topic
- Nonlinear Waves and Solitons
- Type
- article
- Field-Weighted Citation Impact
- 5.29
Funders
- National Natural Science Foundation of China
- Shanxi University
- Yibin University
- Hubei University