Shaping the Wind: Nested Potentials for Kinematically Admissible Urban Wind Prediction

Predicting transient urban winds is fundamental to understanding urban microclimates and designing climate-resilient cities. Building-resolving large-eddy simulation produces detailed incompressible urban wind fields at substantial computational cost for each layout. Neural surrogates offer a faster alternative by learning to predict the evolution of velocity fields. However, minimizing velocity prediction error does not guarantee local mass conservation and wall impermeability, which together define kinematic admissibility. This limitation stems from an unconstrained output representation: geometry conditioning guides predictions but does not restrict them to admissible velocity fields. Correcting boundary violations in these outputs changes the flux balance in adjacent fluid cells and may consequently compromise local mass conservation. To address the challenge, we propose Sculpt, a nested potential framework that builds the coupled, geometry-dependent constraints directly into its parameterization. This nested parameterization generates divergence-free velocity updates through the discrete curl of a volume vector potential on the native three-dimensional staggered grid. A shared scalar potential constrains the vector potential's boundary values so that the same operator also enforces impermeability, without a per-step pressure projection. Because backpropagation through this curl attenuates large-scale gradient signals, we parameterize the volume potential at multiple resolutions to better capture large-scale flow structures. We introduce UrbanWindFlow, an LES dataset spanning urban morphologies and inflow conditions, to evaluate accuracy and kinematic admissibility together. Across all three evaluation settings, Sculpt consistently outperforms both the reduced-order and the neural baselines, reducing mean squared error by $11.7$–$39.3\%$ while maintaining constraint residuals near numerical precision.