An Analytical-Prior Framework for Data-Efficient Prediction of Sound-Reduction Frequencies in Rectangular Side-Branch Helmholtz Resonators

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 dat