Physics- and position-aware GNNs for explosion-induced strain field reconstruction

In summary, the main contributions of this work are as follows: • To address the common neglect of spatial dependencies in existing strain field reconstruction methods, the study proposes a Position- and Physics-aware Graph Neural Network (PPA-GNN) method to solve the problem of neglection of spatial dependencies in existing strain field reconstruction methods. By incorporating both the spatial positions and topological relationships among observation points, the model explicitly captures spatial correlations, leading to enhanced reconstruction accuracy. • To mitigate overfitting caused by limited training data, the study introduces a staged training strategy based on curriculum learning. This approach first guides the model to learn fundamental deformation patterns from densely observed scenarios, and then progressively adapt to sparse observation conditions, ultimately enabling accurate strain prediction using only a few measurement points. • Experiments demonstrate that the method proposed in the study significantly outperforms d backpropagation (BP) neural network in strain field reconstruction tasks. Notably, under extremely sparse conditions with only eight observation points, PPA-GNN achieves an R² value of 0.9030, maintaining high reconstruction accuracy and stability, and highlighting its robustness and strong generalization capability. High-fidelity strain measurements of plate and shell structures are crucial for elucidating failure mechanisms and deformation evolution. These data provide the basis for quantitative damage detection, design optimization, and structural health monitoring. However, laboratory constraints often preclude the acquisition of high-resolution full-field strains, limiting observations to a sparse set of discrete points. Reconstructing complete strain fields from these sparse measurements has therefore become a pressing challenge, for which few effective solutions exist. Motivated by the spatial correlations exhibited under blast loading, we develop a position- and physics-aware graph neural network (PPA-GNN) to recover transient strain fields in plate structures subjected to explosive impacts. The model employs graph-based message passing to encode both spatial topology and governing physical constraints among sensor nodes, markedly improving reconstruction fidelity. To cope with severe data sparsity in practice, we further devise a curriculum-learning schedule that gradually transitions training from dense to extremely sparse sampling, thereby enhancing robustness. The experimental results indicate that the PPA-GNN achieves an R 2 value of 0.903 when only eight observation points are used, thereby demonstrating its capability for reliable full-field reconstruction under minimal sensing conditions.