Physics-Informed Deep Learning-Based Inversion of Marine Atmospheric Boundary-Layer Optical Duct Parameters from Free-Space Optical Link Measurements

Marine boundary-layer temperature inversions—warm air advecting over a cold sea surface—can bend near-horizontal light rays back toward the sea surface, forming an optical duct that dramatically alters the propagation of free-space optical (FSO) links over the ocean: ducted rays yield anomalous low-loss, over-the-horizon reception alongside strong multipath interference and scintillation. Although extensive inversion techniques exist for microwave evaporation ducts, no study to date has inverted optical duct parameters directly from optical channel observations. This paper presents, for the first time, a physics-informed deep learning framework that reconstructs the inversion-layer gradient and layer-top height from multi-wavelength FSO channel measurements, while the surface air temperature—shown to be unidentifiable from link observations alone—is supplied by a co-located meteorological station. A forward model based on Bouguer ray tracing in a spherically stratified atmosphere (validated by a scaled-wavelength split-step Fourier parabolic-equation analysis of ducted propagation) generates the training dataset: thousands of inversion profiles sampled by Latin hypercube design, propagated at 850/1550 nm over 5–50 km maritime links, yielding receiver arrival angles, multipath structures, and chromatic dispersion separations. A physics-guided neural network—the refractivity-gradient constraint embedded in the loss—was revised on the basis of a confusion-matrix validation over all 25,000 samples: any arrival in excess of the two-ray (direct plus surface-reflection) baseline unambiguously indicates trapping, P(ducting|n_paths ≥ 3) = 1.00. The revised constraint reduces false ducting detections (from 102 to 57 at the reference seed) and improves balanced classification accuracy. Numerical experiments demonstrate high-accuracy inversion of the inversion gradient, the parameter governing ducting (R2 = 0.835, MAE = 0.033 K/m), with robustness characterized jointly in regression and classification terms. A systematic identifiability analysis further reveals that the layer-top height is weakly identifiable (R2 = 0.21), whereas the surface air temperature is unidentifiable under the observables, profile model, and link geometry considered here—ray bending is effectively invariant under a uniform profile offset—and is thus supplied by a ground meteorological station, as in deployed FSO systems; a two-output network experiment quantifies the (modest) benefit of this strategy. The proposed framework establishes a new sensing dimension for maritime FSO channel prediction; its engineering recommendations are established in the demonstrated synthetic setting and remain gated on field validation.