Hierarchical physics-guided neural network for sparse-data heterogeneous material identification

Physics-informed neural networks (PINNs) have garnered increasing attention in computational solid mechanics for their potential in inverse problem solving. However, conventional PINNs often suffer from slow convergence and suboptimal accuracy when identifying heterogeneous material properties, especially under sparse data labels. To overcome these limitations, this paper proposes a novel hierarchical physics-guided neural network (HPGNN) framework for efficient and accurate inverse identification of heterogeneous material properties using only sparse observational data. In HPGNN, all unknown domain-wise parameters are embedded as trainable variables within the neural network, enabling a seamless integration of finite element method (FEM)-based domain discretization with neural network–driven inverse parameter identification. The hierarchical strategy progressively reconstructs the heterogeneous material field from coarse to fine scales, ensuring both global consistency and local accuracy under sparse supervision. To improve practical convergence robustness, an LBFGS restart mechanism is incorporated to overcome optimization stagnation, markedly accelerating convergence compared with traditional training schemes. A series of validation experiments are conducted and demonstrate that HPGNN achieves high computational efficiency and low error level cross multiple random field realizations. Additional investigations considering random-input perturbations, extreme initial guesses, variations in mesh resolution, and label noise further confirm the robustness of the proposed framework. A direct comparison with an operator-learning baseline (DeepONet) highlights the advantage of HPGNN inversion under sparse data condition, achieving lower reconstruction error. This study highlights the potential of HPGNN for further development and practical applications in the heterogeneous materials inverse analysis.