Accurate simulation of acoustic wave propagation in complex structures is of great importance in engineering design, noise control, and related research areas. Although traditional numerical simulation methods can provide precise results, they often face high computational costs when applied to complex models or problems involving parameter uncertainties, particularly in the presence of multiple coupled parameters or intricate geometries. To address these challenges, this study proposes an efficient algorithm for simulating the acoustic field of structures with adhered sound-absorbing materials while accounting for ground reflection effects. The proposed method integrates Catmull-Clark subdivision surfaces with the boundary element method (BEM). Subdivision surfaces generate smooth, high-quality meshes that accurately represent complex geometries, thereby enhancing the accuracy of acoustic analysis while avoiding excessive mesh refinement. To further reduce the computational burden associated with generating high-quality meshes and performing uncertainty quantification, a deep neural network (DNN) surrogate model is developed to accelerate calculations. Trained on BEM simulation data, the DNN can rapidly predict sound pressure responses under varying input parameters, significantly speeding up the overall simulation process and reducing computation time. Numerical examples demonstrate that the DNN surrogate model achieves high predictive accuracy while enabling fast and precise analysis of uncertainties in acoustic problems. These results indicate that the proposed approach provides a practical and efficient tool for engineering applications, facilitating rapid evaluations and design optimization in complex acoustic environments.

This study introduces a hybrid Cuckoo Search-Deep Neural Network (CS-DNN) model for uncertainty quantification and composition optimization of Na_1/2Bi_1/2TiO₃ (NBT)-based dielectric energy storage ceramics. Addressing the limitations of traditional ferroelectric materials—such as hysteresis loss and low breakdown strength under high electric fields—we fabricate (1 − x)NBBT8-xBMT solid solutions via chemical modification and systematically investigate their temperature stability and composition-dependent energy storage performance through XRD, SEM, and electrical characterization. The key innovation lies in integrating the CS metaheuristic algorithm with a DNN, overcoming local minima in training and establishing a robust composition-property prediction framework. Our model accurately predicts room-temperature dielectric constant (ε_r), maximum dielectric constant (ε_max), dielectric loss (tan δ), discharge energy density (W_rec), and charge-discharge efficiency (η) from compositional inputs. A Monte Carlo-based uncertainty quantification framework, combined with the 3σ statistical criterion, demonstrates that CS-DNN outperforms conventional DNN models in three critical aspects: Higher prediction accuracy (R² = 0.9717 vs. 0.9382 for ε_max); Tighter error distribution, satisfying the 99.7% confidence interval under the 3σ principle; Enhanced robustness, maintaining stable predictions across a 25% composition span in generalization tests. While the model’s generalization is constrained by both the limited experimental dataset (n = 45) and the underlying assumptions of MC-based data augmentation, the CS-DNN framework establishes a machine learning-guided paradigm for accelerated discovery of high-temperature dielectric capacitors through its unique capability in quantifying composition-level energy storage uncertainties.