This paper proposes a novel roadmap of the bilinear neural network method (BNNM) to derive new classes of exact solutions for the extended sixth-order Benney–Luke (BL) equation. Extended from previous models due to space lower nonlinearities, the extended sixth-order equation incorporates additional dispersive and nonlinear interaction terms, enabling more comprehensive mod elling of wave dynamics in fluid systems and nonlinear phenomena. Using Hi rota’s bilinear operator and a neural network-based framework, we construct a diverse spectrum of analytical solutions, including kink, rogue, lump, and peakon-type solitons. These solutions significantly expand the known solution space of the BL family and offer deeper physical insights into nonlinear wave behaviour such as wave steepening, resonance, and dispersion. The extended equation not only bridges mathematical rigour and physical realism but also improves the computational efficiency and adaptability of neural network-based structures in analysing nonlinear partial differential equations.