High-Efficiency Neural-Symbolic Framework for Automated Soliton Solutions in (3+1)dimension Fluid Dynamics

This study introduces a novel neural network-based symbolic computation algorithm (NNSCA) for obtaining exact solutions to the (3+1)dimension Jimbo-Miwa equation. By integrating neural networks with symbolic computation, NNSCA addresses the limitations of conventional approaches, enabling the derivation and visualization of exact solutions. The neural network architecture is meticulously designed, and the partial differential equation is transformed into algebraic constraints via Maple, establishing a closed-loop solution framework. NNSCA offers a generalized paradigm for investigating high-dimensional nonlinear partial differential equations, highlighting its substantial application prospects.