# WindMiL: Equivariant Graph Learning for Wind Loading Prediction

arXiv: https://arxiv.org/abs/2511.01226 · HTML: https://mlsanity.com/paper/2511.01226/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 28 references that are in the map.
- First posted on arXiv 3 Nov 2025.

## Builds on (most cited first, 10 of 10)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [PolyGNN: Polyhedron-based Graph Neural Network for 3D Building Reconstruction from Point Clouds](https://mlsanity.com/paper/2307.08636/) (2023)
- [A systematic dataset generation technique applied to data-driven automotive aerodynamics](https://mlsanity.com/paper/2408.07318/) (2024)
- [From large-eddy simulations to deep learning: A U-net model for fast urban canopy flow predictions](https://mlsanity.com/paper/2507.06533/) (2025)

## Abstract (arXiv)

Accurate prediction of wind loading on buildings is crucial for structural safety and sustainable design, yet conventional approaches such as wind tunnel testing and large-eddy simulation (LES) are prohibitively expensive for large-scale exploration. Each LES case typically requires at least 24 hours of computation, making comprehensive parametric studies infeasible. We introduce WindMiL, a new machine learning framework that combines systematic dataset generation with symmetry-aware graph neural networks (GNNs). First, we introduce a large-scale dataset of wind loads on low-rise buildings by applying signed distance function interpolation to roof geometries and simulating 462 cases with LES across varying shapes and wind directions. Second, we develop a reflection-equivariant GNN that guarantees physically consistent predictions under mirrored geometries. Across interpolation and extrapolation evaluations, WindMiL achieves high accuracy for both the mean and the standard deviation of surface pressure coefficients (e.g., RMSE ≤ 0.02 for mean Cp) and remains accurate under reflected-test evaluation, maintaining hit rates above 96% where the non-equivariant baseline model drops by more than 10%. By pairing a systematic dataset with an equivariant surrogate, WindMiL enables efficient, scalable, and accurate predictions of wind loads on buildings.