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Rooftop Wind Field Reconstruction Using Sparse Sensors: From Deterministic to Generative Learning Methods

Conference: CVPR 2026 arXiv: 2603.13077 Code: github.com/Yng314/windreconstruction Area: Other / Fluid Reconstruction Keywords: wind field reconstruction, sparse sensors, UNet, ViTAE, CWGAN, PIV experimental data, sensor optimization

TL;DR

This work establishes a learning-observation framework based on PIV wind tunnel experimental data, systematically comparing Kriging interpolation with three deep learning models (UNet/ViTAE/CWGAN) for rooftop wind field reconstruction under 5–30 sparse sensors. It demonstrates that under multi-direction training (MDT), deep learning consistently outperforms Kriging (SSIM improvement of 18–34%), and sensor placement robustness is enhanced by up to 27.8% via QR decomposition-based sensor layout optimization.

Background & Motivation

Background: Rooftop spaces increasingly host UAV/UAM landing pads, solar panels, HVAC systems, and other functions, making real-time full-field wind information critical for safe operation. Rooftop flow fields are highly complex—dominated by building geometry effects, they exhibit flow separation, conical vortices, and cross-directional variability. Traditional CFD is computationally expensive and lacks real-time capability, while practical sensor deployments remain extremely sparse.

Limitations of Prior Work: - Existing studies predominantly rely on CFD simulation data for training, failing to capture real measurement noise and turbulence characteristics → models may fail in real-world deployment - Most studies evaluate only a single network architecture, lacking systematic comparison across different DL methods - Direction-specific training (training and testing on a single wind direction) limits cross-directional generalization - Sensor layouts typically follow uniform grids, lacking data-driven optimization

Key Insight: This paper is the first to use real PIV wind tunnel experimental data for a comprehensive benchmark, systematically comparing traditional Kriging with three representative DL architectures (deterministic UNet, hybrid ViTAE, generative CWGAN) across two training strategies (single-direction SDT / multi-direction MDT), six sensor densities (5–30), sensor position perturbations, and QR-optimized layouts.

Method

Overall Architecture

PIV wind tunnel experimental data (15×15 grid, u/v velocity components) → sparse sensor sampling (Voronoi uniform layout or QR-optimized layout) → four reconstruction methods → evaluation via four metrics: SSIM/NMSE/FAC2/MG. Input dimensions are 15×15×3 (u velocity, v velocity, sensor mask); output is 15×15×2 (reconstructed u/v velocity fields).

Experimental data were acquired in the boundary layer wind tunnel at the Institute of Industrial Science, University of Tokyo. The test object is a 1:200 scale rectangular building model (height:width:length = 1:1:2). Instantaneous velocity fields on the rooftop plane (z/H = 1.05) were measured via PIV under three inflow wind directions (0°, 22.5°, 45°), with a temporal resolution of 0.001 s and spatial resolution of 0.035H. Each 8-second acquisition produced 7,999 temporal snapshots.

Key Designs

  1. Complementary Design of Four Comparison Methods:
  2. Kriging interpolation: traditional geostatistical method with Gaussian variogram (correlation length 0.5–10.0 grid units), zero nugget effect enforcing exact interpolation, reliant on spatial stationarity assumptions; serves as baseline
  3. UNet (472K parameters / 0.03 GFLOPs): encoder-decoder with skip connections, deterministic mapping, 3-layer downsampling (16→8→4→2), filters scaling from 32 to 128 channels, 1×1 convolution output
  4. ViTAE (467K parameters / 0.02 GFLOPs): Transformer–CNN hybrid architecture, 3×3 patch partitioning producing 25 patches, linearly projected to 64 dimensions, 8-layer Transformer encoder (8-head attention), CNN decoder restoring spatial resolution
  5. CWGAN (8.77M parameters / 1.3 GFLOPs): conditional Wasserstein GAN; generator follows UNet architecture (64→128→256 channels); discriminator uses strided convolutions + LeakyReLU, with sigmoid removed to accommodate the Wasserstein distance

  6. Design Motivation: the three DL architectures represent three distinct modeling philosophies—deterministic mapping, hybrid attention, and generative adversarial modeling

  7. SDT vs. MDT Training Strategies:

  8. SDT (single-direction training): trained exclusively on three experimental runs at 0°, tested on 22.5° and 45° for cross-directional generalization
  9. MDT (multi-direction training): one experimental run per wind direction (\(\mathcal{D}_{0°}^{(1)}, \mathcal{D}_{22.5°}^{(1)}, \mathcal{D}_{45°}^{(1)}\)) used for training; remaining independent runs used for testing
  10. Data splits are performed by independent experimental runs rather than random snapshot sampling; no temporal continuity exists across runs → prevents temporal leakage

  11. Design Motivation: wind direction varies in real-world deployment; MDT evaluates model generalization under realistic conditions

  12. QR Decomposition-Based Sensor Placement Optimization:

  13. A wind field data matrix \(\mathbf{Y} \in \mathbb{R}^{N \times 450}\) is constructed from training data; after centering, SVD extracts POD modes, retaining the top \(r=40\) modes (covering 84.6% of total energy) to form the reduced basis matrix \(\boldsymbol{\Psi}_r \in \mathbb{R}^{450 \times r}\)
  14. Column-pivoted QR decomposition is applied to \(\boldsymbol{\Psi}_r^T\): \(\boldsymbol{\Psi}_r^T \mathbf{P} = \mathbf{Q}\mathbf{R}\); the column ordering of the permutation matrix \(\mathbf{P}\) yields the sensor importance ranking
  15. Design Motivation: maximizes the linear independence of the measurement matrix \(\mathbf{H}\boldsymbol{\Psi}_r\), ensuring selected sensors provide maximum information about dominant flow structures

Loss & Training

  • UNet/ViTAE: MSE loss, Adam optimizer, adaptive learning rate decay + early stopping (patience = 20), 80-20 train/validation split
  • CWGAN: Wasserstein distance + L1 reconstruction loss (weight ratio 1:100), 5 discriminator updates per generator update, Adam optimizer (lr = 0.0001) + early stopping

Key Experimental Results

Main Results: Performance of Each Method Under MDT at Varying Sensor Densities

# Sensors Method SSIM↑ FAC2↑ Inference Time (ms)
5 Kriging 0.415 — ~1.493
5 UNet 0.531 — ~0.109
5 CWGAN 0.550 — ~0.164
20 UNet ~0.78 >0.80 ~0.109
20 CWGAN ~0.80 >0.80 ~0.164
30 Kriging ~0.78 ~0.778 ~1.493
30 UNet ~0.82 ~0.808 ~0.109
30 CWGAN ~0.85 ~0.811 ~0.164

Under MDT, DL vs. Kriging: SSIM +18.2–33.5%, FAC2 +3.5–24.2%, NMSE −10.2–27.8%.

Computational Efficiency and Robustness Comparison

Model Parameters GFLOPs Size (MB) SSIM Drop (Perturbation) QR Optimization Gain
UNet 471,586 0.0285 1.80 6.5–14.8% −0.7% (SDT) / +0.4% (MDT)
ViTAE 467,491 0.0210 1.78 6.7–16.8% +2.6% / +4.8%
CWGAN 8,770,000 1.301 33.46 3.3–8.2% +6.5% / +1.8%
Kriging — — — 5.4–13.9% +4.1% / +7.9%

Key Findings

  • Kriging outperforms DL under SDT: with only 5 sensors and single-direction training, Kriging achieves SSIM = 0.502, far exceeding DL's 0.194–0.237 (a 52–61% gap) → under extreme sparsity and low training diversity, spatial correlation assumptions prove more effective
  • MDT is the critical turning point for DL: switching to MDT yields 131–146% SSIM improvement for DL at 5 sensors, while Kriging degrades as its spatial stationarity assumption is violated by multi-directional flow fields
  • 20 sensors marks the performance crossover: under SDT, DL begins to comprehensively surpass Kriging on NMSE at this density
  • CWGAN's "deterministic" behavior: the 100:1 L1 weighting causes CWGAN to behave effectively as a deterministic mapping, with virtually no variation across multiple samples
  • 0° wind direction is the most difficult to reconstruct: the largest boundary-center discrepancy and velocity class imbalance make it the primary cause of Kriging degradation under MDT
  • QR optimization is more effective under MDT: 90% of cases show positive improvement vs. 60% under SDT

Highlights & Insights

  • First systematic DL wind field reconstruction benchmark using real PIV data—eliminating CFD simulation bias and directly targeting real deployment conditions
  • The SDT vs. MDT comparison clearly reveals the decisive influence of training data diversity on DL methods—a conclusion that generalizes to other flow field reconstruction tasks
  • QR sensor optimization combines POD dimensionality reduction with information-theoretic principles, providing a theoretically grounded approach to data-driven sensor placement
  • The practical guidance on method selection by scenario is valuable: single-direction, few sensors → Kriging; multi-direction, more sensors → UNet (balanced and stable); highest accuracy required → CWGAN (high computational cost); resource-constrained → ViTAE

Limitations & Future Work

  • Only 2D planar wind fields (15×15 grid), limited to a single height z/H = 1.05, with 3D structure absent
  • Only three wind direction angles (0°/22.5°/45°); generalization beyond this range requires additional experimental data or transfer learning
  • CWGAN has 18.6× more parameters than UNet (8.77M vs. 471K) but achieves only 5–9% SSIM improvement, indicating a poor efficiency ratio
  • Evaluated on a single isolated rectangular building; applicability to complex multi-building configurations is unverified
  • Each snapshot is reconstructed independently, without exploiting temporal dynamics for multi-step prediction
  • vs. traditional POD-LSE methods: linear dimensionality reduction methods underperform in the presence of nonlinear turbulent features → DL shows clear advantages at medium-to-high sensor densities
  • vs. CFD-trained studies: systematic biases in CFD (turbulence closure models, discretization errors) may introduce training-deployment domain gaps; PIV experimental data directly eliminates this issue
  • Insights: the sparse-to-dense reconstruction framework is transferable to flow field monitoring in meteorology, oceanography, and indoor environments; QR sensor optimization is conceptually linked to compressed sensing theory

Rating

⭐⭐⭐⭐ (4/5)

Overall assessment: no novel architectural contributions at the methodological level, but the experimental design is exceptionally comprehensive (4 methods × 2 strategies × 6 sensor configurations × perturbation analysis × QR optimization × temporal averaging strategies). The systematic benchmark on real PIV data offers high practical value for the built environment engineering community. Code is open-sourced with good reproducibility.