Underwater localization using airborne visible light beams offers a promising alternative to acoustic and radio-frequency methods, yet accurate modeling of light propagation through a dynamic air–water interface remains a major challenge. This paper introduces a physics-informed machine learning framework that combines geometric optics with neural network inference to localize submerged optical nodes under both flat and wavy surface conditions. The approach integrates ray-based light transmission modeling with a third-order Stokes wave formulation, enabling a realistic representation of nonlinear surface slopes and their effect on refraction. A multilayer perceptron (MLP) is trained on synthetic intensity–position datasets generated from this model, learning the complex mapping between received optical power (light intensity) and coordinates of the submerged receiver. The proposed method demonstrates high precision, stability, and adaptability across varying geometries and surface dynamics, offering a computationally efficient solution for optical localization in dynamic underwater environments.
Saif et al. (2026) studied this question.