Accurate prediction of acoustic eigenrays and travel times is critical for ocean acoustic tomography, but neural modeling is challenging because ray paths are branch-dependent, variable in length, and highly sensitive to small arc-length errors. We develop and compare two neural approaches for learning perturbed eigenrays from mean ray geometry, mean environmental fields, and short-term perturbation fields.
The first approach directly learns ray-path perturbations and travel-time changes, providing strong empirical accuracy and efficient inference. The second approach introduces a solver-consistent formulation in which the network predicts ray geometry, while travel time is computed through a differentiable path-integral operator using accumulated arc length and sound speed along the ray. To preserve physical consistency, variable-length rays are represented on their original grids with padding and masks rather than being forced onto a fixed interpolation grid.
Results show that the direct learning approach achieves the best travel-time accuracy, while the solver-consistent approach provides a physically interpretable path-to-travel-time relationship. Using the original variable-length ray representation substantially reduces numerical travel-time error compared with fixed-grid interpolation. These results suggest that combining neural ray prediction with physically consistent travel-time evaluation is a promising route toward fast and reliable acoustic tomography workflows.

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