AI 中文总结
本研究提出分析先验学习框架，复用低成本分析模型提升有限高保真模拟数据下的预测效率，在矩形侧支亥姆霍兹消声器降噪频率预测中，其性能优于直接学习方法，可满足不同部署需求。
AI 中文摘要
高保真有限元模拟可为侧支消声器提供准确的数值预测，但生成大规模模拟数据集成本高昂，且在模拟标注数据稀缺时，纯数据驱动的代理模型可能变得不可靠。本研究开发了一种分析先验学习框架，该框架复用低成本分析模型，以在有限的高保真模拟预算下提高数据效率。该框架考虑了两种互补路径：当分析模型在推理阶段仍可用时，将其保留为显式基线，仅利用模拟数据学习分析模型与模拟结果之间的差异；当需要自包含预测器时，先从大量低成本评估中提取分析映射关系作为学习到的先验，再用有限的模拟数据对其进行校准。该框架在矩形侧支亥姆霍兹消声器上进行评估，使用了86个模拟标注几何结构和8998个不重叠的仅分析几何结构。分析模型的平均绝对误差（MAE）为1.333 Hz；直接支持向量回归（SVR）的MAE为3.375 Hz，而残差SVR将MAE降至0.426 Hz；直接多层感知器（MLP）的MAE为1.109 Hz，而分析先验预训练在冻结先验残差适配下将误差降至0.556 Hz，在全模型微调下降至0.371 Hz。在20至70个模拟标注样本的训练预算范围内，分析校正和分析先验预训练均比直接学习持续提高了数据效率。这些结果表明，当模拟数据稀缺时，分析先验信息可显著提高高保真预测性能，显式校正和先验提取可满足互补的部署需求。
英文摘要
High-fidelity finite-element simulations can provide accurate numerical predictions for side-branch resonators, but large simulation datasets are expensive to generate and purely data-driven surrogates may become unreliable when simulation-labelled data are scarce. This study develops an analytical-prior learning framework that reuses a low-cost analytical model to improve data efficiency under limited high-fidelity simulation budgets. Two complementary routes are considered. When the analytical model remains available at inference, it is retained as an explicit baseline and the simulation data are used to learn only the analytical-to-simulation discrepancy. When a self-contained predictor is required, the analytical mapping is first distilled from abundant low-cost evaluations into a learned prior and then calibrated with the limited simulation data. The framework is evaluated on rectangular side-branch Helmholtz resonators using 86 simulation-labelled geometries and 8,998 non-overlapping analytical-only geometries. The analytical model achieved a mean absolute error (MAE) of 1.333 Hz. Direct support vector regression (SVR) achieved 3.375 Hz, while residual SVR reduced the MAE to 0.426 Hz. A direct multilayer perceptron (MLP) achieved 1.109 Hz, whereas analytical-prior pretraining reduced the error to 0.556 Hz with frozen-prior residual adaptation and 0.371 Hz with full-model fine-tuning. Across training budgets of 20 to 70 simulation-labelled cases, both analytical correction and analytical-prior pretraining consistently improved data efficiency relative to direct learning. These results show that analytical prior information can substantially improve high-fidelity prediction when simulation data are scarce, with explicit correction and prior distillation serving complementary deployment needs.
Comments13 pages, 5 figures, 1 table
