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

Author

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  • 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)

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.

Suggested Citation

  • Jiang-Long Shen & Run-Fa Zhang & Jing-Wen Huang & Jing-Bin Liang, 2025. "Neural Network-Based Symbolic Computation Algorithm for Solving (2+1)-Dimensional Yu-Toda-Sasa-Fukuyama Equation," Mathematics, MDPI, vol. 13(18), pages 1-18, September.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:18:p:3006-:d:1751686
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