Deep learning based reconstruction of particle reinforced materials from wave measurements

Accurate characterization of particle distributions in particle-reinforced materials is important for understanding their mechanical performance. However, estimating internal particle configurations from boundary wave measurements remains a challenging inverse problem due to complex wave–particle interactions, multiple scattering effects, and the high dimensionality of the unknown microstructure. In this study, a data-driven framework is proposed to investigate the feasibility of estimating particle distributions from boundary-measured wave signals. A synthetic dataset is generated using numerical simulations of wave propagation in two-dimensional heterogeneous plates containing randomly distributed particles under controlled geometric constraints. A temporal convolutional neural network is developed to learn the nonlinear relationship between multi-sensor wave responses and particle center coordinates. The reconstruction problem is formulated as a point-set prediction task, and a permutation-invariant Chamfer distance is employed to account for the unordered nature of particle distributions. The results demonstrate that the proposed framework is capable of recovering the major spatial characteristics of particle distributions across a wide range of configurations. Systematic parametric studies further reveal that reconstruction performance is influenced by particle size, particle number, inter-particle spacing, excitation frequency, and sensor configuration. In addition, the results provide insights into how wave–particle interactions affect the identifiability and learnability of the inverse problem. Overall, this study demonstrates the feasibility of combining wave-based measurements with deep learning for particle-distribution estimation and provides a foundation for future research toward data-driven material characterization and nondestructive evaluation.