Geometric Reconstruction of Enclosed Spaces from Limited Frequency-Domain Acoustic Measurements

Reconstructing the geometry of a closed domain from limited acoustic measurements constitutes a highly ill-posed nonlinear inverse problem. The ill-posedness arises from the non-uniqueness of the mapping from interior acoustic measurements to boundary geometry, as well as the pronounced sen-sitivity to measurement noise. Nevertheless, biological echolocation demonstrates that spatial geom-etry can still be effectively discriminated under severely constrained sensing conditions. In contrast, conventional inversion approaches often suffer from limited accuracy and high computational cost. In this work, we develop a deep learning–based inversion framework capable of reconstructing the geometry of a closed region using frequency-domain acoustic pressure measurements acquired at a small number of spatial locations. In enclosed environments, multiple scattering combined with broadband excitation induces a highly nonlocal acoustic response to boundary geometry, thereby al-lowing global geometric information to be implicitly encoded in sparse measurements. The proposed approach exploits this structure by learning a low-dimensional topological representation of geomet-ric configurations via an autoencoder, and subsequently establishing a mapping from sparse acoustic observations to this representation through an inverse inference network. Numerical simulations and experimental results demonstrate that the proposed method accurately recovers complex closed ge-ometries while maintaining strong robustness to noise. Even with noise levels reaching 30%, the re-constructed geometries achieve a structural similarity index exceeding 0.93. These results indicate that multiple scattering and broadband acoustic excitation in enclosed spaces can partially mitigate the ill-posedness inherent in geometric inversion problems, offering a viable paradigm for wave-based inverse problems under severely limited data and providing quantitative insight into spatial perception mechanisms in echolocation.