WindMiL: Equivariant Graph Learning for Building Wind Loads

Wind loading prediction is safety-critical for building design, yet it is largely absent from ML benchmarks because high-fidelity aerodynamic labels are expensive to generate and defined on irregular building surfaces. Current practice relies on wind tunnel testing, design codes, and computational fluid dynamics with large-eddy simulation (LES), where each case requires more than 24 hours, making parametric exploration infeasible. Here we introduce WindMiL, a graph learning framework that advances both ML and wind engineering: it provides a realistic LES-based benchmark for studying physical inductive bias, extrapolation, and symmetry, while enabling LES-based surrogate prediction of pressure loads on buildings. We generate 462 LES simulations of low-rise buildings under realistic atmospheric boundary layer flow, spanning roof shapes and wind directions. The central challenge is not only accuracy, but also respecting the physical constraints: reflecting a building–wind configuration should reflect its predicted pressure field. However, training on reflected examples does not guarantee this consistency. WindMiL encodes this order-2 symmetry directly in the architecture, creating a testbed for equivariance versus data augmentation. We compare it with a pointwise MLP, GraphSAGE, and reflection-augmented GraphSAGE at different data splits. Across random, barycentric extrapolation, and edge-extrapolation splits, WindMiL achieves the highest overall accuracy for surface pressure coefficients while maintaining exact reflection symmetry. In the OOD edge extrapolation, WindMiL reduces mean $C_p$ RMSE by 7.9% relative to reflection-augmented GraphSAGE and improves hitrate relative to non-augmented GraphSAGE, by approximately 5%. These gains also translate to integrated drag and lift coefficients, with best hitrates and exact symmetry. These results show how a task-specific symmetry can improve generalization while enforcing a physical constraint that data augmentation only approximates. This study establishes wind loading prediction as a benchmark for geometric deep learning and ML-based computational wind engineering.