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 sensitivity to measurement noise. Nevertheless, biological echolocation demonstrates that spatial geometry 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 non-local acoustic response to boundary geometry, thereby allowing global geometric information to be implicitly encoded in sparse measurements. The proposed approach exploits this structure by learning a low-dimensional topological representation of geometric 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 geometries while maintaining strong robustness to noise. Even with noise levels reaching 30%, the reconstructed 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.