A derivative-informed, physics-referenced parametric surrogate for uncertainty-aware inversion of mesoscale-eddy acoustic observations

Mesoscale eddies alter long-range acoustic fields, making repeated monitoring and inversion costly. This study develops a derivative-informed parametric neural surrogate (DINO) for a fixed 20-receiver, 12/20-Hz configuration. Its five-parameter eddy model uses the first three empirical orthogonal function modes derived from 368 Kuroshio Extension Argo profiles. On held-out synthetic cases, DINO achieves forward/Jacobian errors of 1.63%/5.11%, compared with 5.41%/14.84% for point-fitting, while its forward call is 1216 times faster than the reference parabolic-equation solver. Split-conformal calibration reaches 97.5% coverage at nominal 95% but inflates region volume 44-fold. Across 250 paired trials, the median scale-normalised parameter root mean square error is 0.075 for DINO versus 0.113 for point-fitting (two-sided Wilcoxon p=3.3×10−11). The comparison does not isolate Jacobian fidelity from forward accuracy or optimisation smoothness. SWellEx-96 validates only a calibration/tracking component, not end-to-end eddy inversion. Results are therefore scoped to the specified fixed array/frequency and synthetic eddy prior.