Neural Network-Based Symbolic Computation Algorithm for Solving (2+1)-Dimensional Yu-Toda-Sasa-Fukuyama Equation
Jianglong Shen, Runfa Zhang, Jingwen Huang, Jing-Bin Liang
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.
Topics & Concepts
Artificial neural networkComputationSymbolic-numeric computationSymbolic computationComputer scienceAlgorithmAlgebraic numberNonlinear systemSymbolic trajectory evaluationThe SymbolicModels of neural computationArtificial intelligenceMathematicsSymbolic data analysisTheoretical computer scienceAlgebra over a fieldAlgebraic equationNonlinear Waves and SolitonsModel Reduction and Neural NetworksFractional Differential Equations Solutions