Nonlinear internal ocean waves are important in stratified marine environments because they are linked to energy transport, momentum transfer, and mixing processes. In this study, the (3 + 1)-dimensional potential Yu–Toda–Sasa–Fukuyama (pYTSF) equation is used as an idealized mathematical model to study wave propagation, energy localization, and nonlinear interactions in multidimensional dispersive media. A multivariate bilinear neural network method (mBNNM), which serves as a hybrid neural-symbolic framework, is applied to obtain exact solutions of the governing equation. The developed [4 2 2 1] neural architecture is used to derive lump wave (LW), one-wave (OW), new lump wave (NLW), and triangular periodic wave (TPW) solutions. The [4 3 2 1] architecture is then used to obtain lump-kink wave (LKW), lump-periodic-kink interaction wave (INT3-W), and lump-periodic interaction wave (INT2-W) solutions. These solutions show localization, nonlinear deformation, periodic behavior, and multidimensional wave interactions. Their main features are illustrated using three-dimensional surface and contour plots. The results provide exact analytical benchmarks for multidimensional nonlinear-wave studies and for validating numerical and physics-informed models. The derived solutions provide qualitative benchmark structures that may be incorporated into future studies of ocean mixing, climate variability, sea-surface roughness, and electromagnetic scattering when combined with realistic physical data and coupled models.
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