Spatiotemporal reconstruction of unsteady bridge flow field via hierarchical graph neural networks with causal attention

When calculating the transient flow around a bridge structure, traditional computational fluid dynamics methods are extremely time-consuming, especially for multiparameter optimization analyses. Inspired by the development of deep graph neural networks with a mesh structure, this paper describes a spatiotemporal prediction framework for the rapid reconstruction and prediction of transient flows on large-scale unstructured grids. To ensure stability and reliability during self-supervised training, a causal self-attention mechanism is employed in the temporal model. The framework is trained and tested on a dataset containing 40 000 snapshots of bridge flow fields with Reynolds numbers ranging from $104$ to $105$⁠. The relative mean square error of the model in predicting the velocity and pressure fields is found to be in the order of $10−3$ and the relative error does not exceed $10%$⁠. This demonstrates that the model is capable of reconstructing high-dimensional flow field information from low-dimensional data. Furthermore, the proposed model achieves a computational speedup by two orders of magnitude compared with traditional computational fluid dynamics methods with respect to the temporal inference. To validate its ability to infer bridge aerodynamic characteristics, the model is used to predict the bridge surface pressure, aerodynamic coefficients, streamlines, and vorticity. The results demonstrate that the proposed model has reliable accuracy, representation, and stability in predicting bridge flow fields and identifying multiscale characteristics.