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Description
The accurate prediction of low-frequency room acoustics relies on modal frequencies, traditionally computed using expensive numerical methods such as the Finite Element Method (FEM). This paper presents HERMES (Hierarchical Estimator for Room Modal Eigenvalue Synthesis), a physics-informed hierarchical mesh transformer that predicts the first 200 modal frequencies directly from 3D surface meshes of rooms with diverse geometries. The architecture employs a two-phase transformer backbone that leverages object-level structure for efficient processing of complex meshes, combined with an LSTM-based prediction head grounded in Weyl's law to incorporate physical priors. Trained and evaluated on a synthetic dataset of 7,500 rooms with various shapes and sizes, HERMES achieves a mean absolute error of 0.59 Hz across all room types, consistently outperforming an analytical scaled box baseline, while reducing computational cost by approximately three orders of magnitude compared to conventional eigenvalue solvers. Additionally, we present a sensitivity analysis which quantifies how modal frequency prediction uncertainties propagate into derived acoustic pressure fields. By demonstrating that deviations remain within a stable, linear regime for the error range achieved by HERMES, we confirm our neural approach provides both the efficiency and precision required for reliable acoustic engineering.