High-fidelity flow-field reconstruction from sparse sensors using a hybrid graph neural network-transformer architecture

Reconstructing flow fields from sparse observations constitutes a fundamental challenge in aerodynamic analysis, since existing methods often fail to reconcile accuracy with computational efficiency under severe data constraints. We introduce a Graph Transformer Reconstruction Network (GTREN), a novel model designed to infer latent data patterns from extremely sparse measurements and to reconstruct high-fidelity, full-field flow solutions. The approach represents discrete grid points as nodes within a graph data structure, enabling a principled encoding of spatial relationships. We integrate a Transformer-style attention mechanism into the graph network's message-passing operations, allowing the model to selectively emphasize salient neighbor interactions while attenuating irrelevant signals; this facilitates efficient and stable information propagation. After training, GTREN uncovers implicit correlations among sparse sensor measurements and successfully generalizes these relationships to reconstruct the entire flow field. Results indicate that, with only ten measurement points, the model accurately reconstructs both pressure and velocity distributions across the field. When compared to Computational Fluid Dynamics simulations, the mean squared error (MSE) of the reconstruction is as low as 0.05%. By contrast, a conventional graph neural network yields an MSE of 18.31%. We also provide a systematic analysis of how both the number and spatial arrangement of measurement points affect reconstruction accuracy. Our analysis reveals that, rather than merely increasing sensor count, strategically locating sensors within the core vortex-shedding region of the wake substantially improves reconstruction accuracy—offering practical guidance for flexible sensor deployment. Overall, GTREN achieves high-precision full-field reconstruction with very few pressure sensors, enabling real-time sparse-sensing flow-field monitoring.