Rapid and sparse reconstruction of high-speed steady-state and transient compressible flow fields using physics-informed graph neural networks

Explosion flow fields are characterized by shock waves with varying intensity and position (i.e., explosive loads), which are the primary causes of structural damage. Accurate and rapid prediction of explosive loads is crucial for structural blast-resistant design and daily security management. While existing empirical models and numerical simulation methods can capture the propagation characteristics of explosive shock waves, high-precision simulation requires a massive computational workload, which is insufficient to meet the fast computational demands of various explosive scenarios. To address this contradiction, this study constructed a sparse reconstruction model for two-dimensional explosion fields based on machine learning algorithms. The model utilizes sparse observational data to establish a mapping relationship to the distribution of the entire flow field. The model is built by a physics-informed graph neural network (PIGN). The graph neural network is employed to associate node features, while the physical network is utilized to control model convergence, aiming to enhance model performance. Using the constructed dataset, the PIGN model was tested. Performance and generalization capabilities of the model were assessed by comparing its results with numerical simulation. This evaluation analyzed the relative error distribution and error statistical results of the reconstructed flow field. The results indicate that the PIGN model can effectively reconstruct explosion fields, with an average error in the reconstructed flow field below 4%. Furthermore, when the number of probe points reaches 10, the average error of the flow field reconstructed by the model is close to 6%. This model not only provides a highly reliable distribution of explosion overpressure and pressure-time variations but also, with a well-trained model, accomplishes flow field reconstruction within 1 ms. It offers a novel approach for achieving rapid and reasonable prediction of explosion fields or two-dimensional compressible flow fields.