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

2026-10-04

AI Summary

This study addresses the difficulty of enforcing local mass conservation and wall impermeability when neural agents predict urban wind fields. To this end, we propose Sculpt, a nested potential framework that directly embeds geometric constraints into the parameterization space. By generating divergence-free velocity updates via discrete curl operations, the method simultaneously satisfies physical constraints without requiring stepwise pressure projection. Furthermore, a multi-resolution potential parameterization is introduced to capture large-scale flow structures. Validation on three-dimensional staggered grids using large-eddy simulation (LES) datasets demonstrates that the proposed framework strictly enforces kinematic admissibility while maintaining high predictive accuracy. Consequently, Sculpt significantly enhances the physical consistency of urban microclimate simulations.

Abstract

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.

Problem

• urban wind prediction
• kinematic admissibility
• mass conservation
• wall impermeability
• neural surrogate

Innovation

• Nested Potentials
• Kinematic Admissibility
• Divergence-free Velocity
• Neural Surrogate
• Urban Wind Prediction