<p>Noise control has always been a critical issue in engineering applications, especially when ground reflection is considered, as it makes the propagation of sound more complex. The innovation of this study lies in the proposal of a novel method to accelerate uncertainty quantification in the acoustic analysis of complex structures. The proposed approach integrates the isogeometric boundary element method based on Loop subdivision surfaces with singular value decomposition (SVD), radial basis functions (RBF), and a Bayesian neural network (BNN) to achieve efficient uncertainty analysis. In this framework, the SVD–RBF module is employed for the first-stage expansion of small-sample data, while the BNN performs the second-stage expansion and quantifies prediction uncertainty, enabling large-scale Monte Carlo simulations with substantially reduced computational cost. Compared with conventional numerical methods, the proposed method achieves efficient large-scale uncertainty analysis while maintaining high computational accuracy. The effectiveness of the approach is validated through stochastic analyses of spherical, sound barrier, and washing machine models. The results demonstrate that the SVD–RBF–BNN framework can significantly enhance the computational efficiency of uncertainty quantification.</p>