Uncertainty in ocean acoustic field modeling propagates sequentially from stochastic ocean environments to the acoustic field, ultimately degrading the performance of underwater acoustic applications such as communication, target detection, and ocean observation. Polynomial Chaos Expansion (PCE) is widely used for uncertainty quantification (UQ), with intrusive and non-intrusive variants. Intrusive PCE substitutes uncertain parameters and acoustic fields with PCE representations in the Helmholtz equation, deriving coupled deterministic equations for PCE coefficients. However, it requires cumbersome formula derivations and simplifications of complex ocean environments, limiting its applicability. The non-intrusive PCE treats the acoustic model as a black box, but it tends to violates physical laws and suffers from rapidly increasing computational cost as spatial resolution increases. To address these limitations, this paper proposes a hybrid UQ framework that integrates a physics-informed neural network surrogate with PCE to estimate coefficients without intrusive derivations or excessive sampling, while enforcing physical consistency through a coupled Helmholtz equation-based constraint. Experiments in stochastic ocean environments with uncertain parameters show that the proposed method reduces computational cost by a factor of 35 compared to Monte Carlo (MC) simulations. Moreover, it consistently achieves lower RMSE than non-intrusive UQ methods implemented in UQLab, particularly in variance estimation, where errors are reduced by up to 84%, thereby demonstrating superior accuracy relative to MC benchmarks. This work provides a computationally efficient and physically consistent UQ solution for complex ocean acoustic scenarios, advancing the reliability of real-world underwater acoustic systems.
Duan et al. (Fri,) studied this question.