This paper presents a novel \(\left( G^{\prime }/G^2\right) \) -expansion neural networks method for deriving exact analytical solutions of nonlinear partial differential equations (PDEs). The approach integrates trial functions within multi-layer neural networks, where each neuron in the first hidden layer is constructed using the Riccati equation. The symbolical outputs obtained from neural network computations are used as trial functions for nonlinear PDEs. This hybrid framework unifies symbolic neural networks with classical symbolic computation, enabling the direct derivation of exact analytical solutions of nonlinear PDEs without reducing them to ordinary differential equations or bilinear forms, thereby improving computational efficiency and preserving structural integrity. The proposed method is applied to three distinct nonlinear models: the Double-Chain Deoxyribonucleic Acid model, the classical FitzHugh–Nagumo equation, and the (4+1)-dimensional Davey–Stewartson–Kadomtsev–Petviashvili equation. These models represent complex phenomena in biological and physical systems, highlighting the versatility of the method in capturing dynamic behaviors. Exact analytical solutions are derived in terms of hyperbolic, trigonometric, and rational functions. The study presents a diverse range of novel solution types, including kink solitons, kink-periodic, kink-bright, singular kink, shock wave, V-shaped, and dark solitons. The dynamic behaviors of these solutions are visualized through 3D with density surface, contour, and 2D plots, providing insight into their physical significance. The findings emphasize the effectiveness and flexibility of the method in describing complex nonlinear phenomena and indicate its potential applications in nonlinear wave propagation across optical communications, fluid dynamics, plasma physics and biological systems.
