EigenRR: Learning Tetrahedral Search Subspaces for Impact Sound Synthesis

Synthesizing a realistic sound for a struck object first requires computing how that object vibrates. Physically, the object is meshed into many small tetrahedra (a finite-element discretization), and a very large eigenvalue problem is then solved. Classical solvers such as ARPACK and LOBPCG are accurate but too slow. Learning-based approaches either regress modal quantities directly or learn a search subspace on a voxelized mesh that requires interpolation to tetrahedral FEM meshes, risking transfer error. EigenRR learns an overcomplete search subspace on the tetrahedral FEM mesh, and Rayleigh–Ritz extracts approximate eigenpairs using that mesh's assembled stiffness and mass matrices. The resulting modes are consistent with the physical operator, so they also warm-start an iterative solver. Twenty LOBPCG steps from this prediction reach a mel-frequency error of $2.4\times 10^{-4}$, $1.55\times$ and $63\times$ more accurate than NeuralSound and random initializations under the same budget. One forward pass already beats 20 iterations from a random start. We build VibraVerse++, a geometry–acoustics dataset of tetrahedral meshes. We train and evaluate on it, and release the meshes together with the assembled FEM matrices and reference eigenspectra. The method returns accurate frequencies and mode shapes at interactive speed.