Data-driven reconstruction of 3D particle distributions in composite materials using wave measurements and deep learning

Abstract

Accurate reconstruction of particle distributions in three-dimensional particle-reinforced materials is essential for understanding their mechanical behavior and performance. However, recovering internal particle configurations from boundary-measured wave signals remains a challenging inverse problem due to complex wave interactions, multiple scattering, and high-dimensional uncertainty. In this study, a data-driven framework is proposed to reconstruct particle distributions directly from wave measurements. A large synthetic dataset is generated using numerical simulations of wave propagation in cubic domains containing randomly distributed spherical particles under geometric constraints. A temporal convolutional neural network is trained to learn the nonlinear mapping between multi-sensor wave responses and particle locations. The reconstruction task is formulated as a point-set prediction problem, where a permutation-invariant Chamfer distance is employed to account for the unordered nature of particle distributions, and a repulsion regularization term is introduced to enforce spatial separation and physical plausibility. Beyond baseline reconstruction accuracy, the influences of dataset size, particle diameter, particle number, and sensor configurations are systematically investigated, including reduced sensing scenarios with measurements from a single boundary. In addition, coordinate-wise prediction is examined using independent models for each spatial direction. The results demonstrate that the proposed framework achieves accurate, stable, and generalizable reconstruction across diverse conditions. This study provides insights into the interplay between physical parameters and sensing strategies and offers an efficient data-driven approach for wave-based characterization of complex three-dimensional microstructures.