<p>This paper first presents novel solutions to the sixth-order Benney–Luke equation (BL) using the bilinear neural network method (BNNM). The sixth-order extension of the BL equation enables a comprehensive study of dispersion effects in the propagation of the water wave under uniform conditions and provides more diverse kinds of solutions compared to the original BL equation. By employing Hirota’s bilinear form, BNNM successfully constructs multiple solution types, including one-soliton, two-soliton, hyperbolic, and trigonometric soliton solutions that the original equation has not obtained. These solutions are crucial for modeling wave phenomena, particularly in analyzing stress distributions on water surfaces in high-order structures. Incorporating neural network architectures simplifies the solution process and significantly enhances the computational efficiency of higher-order models. This innovative approach provides a robust framework for solving higher-order nonlinear partial differential equations, offering deeper insights into the dynamics of soliton in complex systems.</p>