A hierarchical machine learning framework for real-time reconstruction of urban wind fields from sparse sensor networks

Real-time urban wind-field awareness is increasingly needed for structural health monitoring and digital-twin applications, yet high-fidelity CFD/LES and wind-tunnel testing remain too computationally intensive or scenario-specific for operational use, while field measurements provide only sparse information. This paper presents a sensor-driven hierarchical reconstruction framework for estimating time-resolved, high-resolution wind fields from constrained sensor networks. Unlike conventional single-stage approaches, which become ineffective when the resolution gap between sparse measurements and the target flow field is large, the proposed hierarchical formulation addresses the ill-conditioned nature of sparse-to-full-field reconstruction by replacing a single difficult inversion with successive coarse-to-fine mappings. This strategy promotes stable learning of multi-scale urban flow structures, improves reconstruction fidelity, and enables accurate real-time wind-field reconstruction under practical sensor constraints. The approach combines (i) progressive coarse-to-fine enrichment through intermediate resolution levels to avoid a single ill-conditioned sparse-to-high-resolution mapping, (ii) reduced-order learning in a Proper Orthogonal Decomposition (POD) coefficient space at each hierarchical level, thereby reducing dimensionality and improving learning tractability, (iii) LSTM-based temporal modeling to capture unsteady dynamics, and (iv) a constraint-aware sensor-placement strategy that integrates practical deployment considerations with QR pivoting on retained POD modes. The framework is evaluated on a three-dimensional half-cylinder benchmark spanning multiple Reynolds numbers and vertical planes, and on a large-eddy-simulation dataset of a real urban district (Niigata, Japan) under multiple heights and inflow wind directions. The results demonstrate accurate recovery of dominant spatial structures and temporal dynamics, with robust generalization to unseen conditions including an unseen Reynolds number, held-out height levels, and unseen temporal segments under different inflow directions. The framework consistently achieves high reconstruction accuracy across all evaluated protocols, supporting near-real-time operations under practical sensor constraints.