Transformer-based Neural Operators for 3D Wind Field Prediction over Complex Mountainous Terrain

Accurate prediction of three-dimensional (3D) wind fields over complex mountainous terrain is essential for renewable energy deployment and regional weather modeling. Traditional computational fluid dynamics (CFD) simulations face two fundamental bottlenecks: expert-intensive mesh generation around irregular topography, and iterative solvers that require hours to days even on high-performance clusters. Recent neural operator approaches accelerate inference, but typically fail to resolve the sharp, localized velocity gradients induced by complex terrain features. Here, we present a transformer-based dual-attention neural-operator framework for 3D wind field prediction over complex mountainous terrain, and validate its effectiveness through two instantiations on representative point-based (mesh-free) and graph-based neural-operator architectures, namely Patch-solver and Patch-GTO. Trained on a large CFD-generated dataset spanning diverse terrain geometries and inflow conditions, the framework enables rapid prediction of steady-state wind field while maintaining competitive accuracy. It also demonstrates robust zero-shot transfer to real-world mountainous sites across several diverse locations, outperforming existing neural operator baselines by 10% in relative error. We further verify that incorporating sparse observational data (1% spatial coverage) reduces prediction error by 16.89% relative to the corresponding model without sparse data input and by 32.75% relative to advanced neural operator baselines on unseen terrains. This framework establishes a generalizable computational paradigm across domains, promising to be a real-time tool for wind resource assessment over complex mountainous terrain and related atmosphere-surface interaction studies.