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

Yihang Zhou; Chao Lin; Hideki Kikumoto; Ryozo Ooka; Sibo Cheng

cs.CVMar 13, 2026

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

Authors: Yihang Zhou, Chao Lin, Hideki Kikumoto, Ryozo Ooka, Sibo Cheng

Organizations: Department of Computing, Imperial College London, London, UK · Institute of Industrial Science, The University of Tokyo, Tokyo, Japan · CEREA, ENPC, EDF R&D, Institut Polytechnique de Paris, Île-de-France, France

Abstract

Real-time rooftop wind-speed distribution is important for the safe operation of drones and urban air mobility systems, wind control systems, and rooftop utilization. However, rooftop flows show strong nonlinearity, separation, and cross-direction variability, which make flow field reconstruction from sparse sensors difficult. This study develops a learning-from-observation framework using wind-tunnel experimental data obtained by Particle Image Velocimetry (PIV) and compares Kriging interpolation with three deep learning models: UNet, Vision Transformer Autoencoder (ViTAE), and Conditional Wasserstein GAN (CWGAN). We evaluate two training strategies, single wind-direction training (SDT) and mixed wind-direction training (MDT), across sensor densities from 5 to 30, test robustness under sensor position perturbations of plus or minus 1 grid, and optimize sensor placement via Proper Orthogonal Decomposition with QR decomposition. Results show that deep learning methods can reconstruct rooftop wind fields from sparse sensor data effectively. Compared with Kriging interpolation, the deep learning models improved SSIM by up to 32.7%, FAC2 by 24.2%, and NMSE by 27.8%. Mixed wind-direction training further improved performance, with gains of up to 173.7% in SSIM, 16.7% in FAC2, and 98.3% in MG compared with single-direction training. The results also show that sensor configuration, optimization, and training strategy should be considered jointly for reliable deployment. QR-based optimization improved robustness by up to 27.8% under sensor perturbations, although with metric-dependent trade-offs. Training on experimental rather than simulated data also provides practical guidance for method selection and sensor placement in different scenarios.

Figures & tables

Main Notations
$u$ , $v$	Velocity components in $x$ , $y$ directions
$w_{s}$	Normalized horizontal wind speed
$U_{H}$	Reference velocity at model height $H$
$WS$ , $ws_{SD}$	Time-averaged wind speed and its standard deviation
$(x,y,z)$	Spatial coordinates
$H$	Model height

Table 1

Figure 1: End-to-end workflow of real-time rooftop wind field reconstruction from PIV observations using sparse sensors, model comparison, and QR-based sensor optimization. For each wind direction

\theta\in\{0^{\circ},\,22.5^{\circ},\,45^{\circ}\}

, we collected

n_{\theta}

realizations (

n_{0^{\circ}}=3

n_{22.5^{\circ}}=2

n_{45^{\circ}}=3

). Let

\mathcal{D}_{\theta}^{(k)}

denote the

k

-th realization for direction

\theta

Figure 2: UNet architecture.

Figure 3: CWGAN architecture.

Figure 4: ViTAE architecture.

Figure 5: Wind tunnel experiment layout.

Figure 6: Distributions of time-averaged value and standard deviation of horizontal wind velocity in $z$ / $H$ = 1.05 under different wind directions.

Figure 7: Ground truth, uniform sensor placement and perturbed sensor placement examples for different sensor quantities, white dots represent the sensor positions. Polygonal boundaries show Voronoi cells, each cell contains all points closest to that cell’s sensor (white dot), ensuring uniform spatial coverage.

Panel of Figure 8 — Figure 8: Comparison of metrics across models with standard sensor placement under different training strategies.

Figure 9: Visualization of predictions from 5 sensors under SDT (samples 805 and 6001 correspond to the 22.5° direction, whereas samples 33367 and 34140 correspond to 45° direction). Kriging outperforms deep learning methods at 5 sensors under SDT.

Figure 10: Prediction visualization across sensor counts under SDT (sample 34140 from 45° direction). As the sensor number increases, deep learning methods gradually close the gap in performance with Kriging.

Figure 11: Sample 36386, 38206, and 29561 correspond to the 45° direction, whereas sample 2552 corresponds to the 0° direction. As described in Section 4.1, under MDT, deep learning methods generally outperform Kriging, particularly at 5 sensors. The figure shows predictions from 5 sensors under different wind directions training, demonstrating that deep learning methods provide more accurate predictions compared to Kriging. The predictions from Kriging deviate significantly from the ground truth, while the predictions from deep learning methods are closer to the ground truth.

Figure 12: Prediction visualization across sensor counts under MDT (sample 29561 from 45° direction). For complex rooftop flow features (e.g., the top-left low-speed region), Kriging interpolation shows large deviations from the ground truth and fails to recover fine-scale structures, whereas deep learning methods better preserve local details. As the number of sensors increases, deep learning reconstructions converge toward the ground truth, consistent with the trends in Fig. 8(b) (deep learning method performs better especially at sparse sensor configurations).

Model	Parameters	GFLOPs	Model Size (MB)	Inference Time (per snapshot)
UNet	471,586	0.0285	1.80	1 $\times$ ( $\sim$ 0.109 ms)
ViTAE	467,491	0.0210	1.78	2.1 $\times$ ( $\sim$ 0.229 ms)
CWGAN	8,770,000	1.301	33.46	1.5 $\times$ ( $\sim$ 0.164 ms)
Kriging	-	-	-	13.7 $\times$ ( $\sim$ 1.493 ms)

Table 1: Computational complexity and model characteristics of deep learning architectures. The inference time is normalized by the UNet baseline (approx. 0.109 ms per snapshot on an NVIDIA GeForce RTX 3080 Ti), and the deep learning methods show a significant advantage over Kriging.

Panel of Figure 13 — Figure 13: Temporal averaging strategies for data-limited scenarios.

Panel of Figure 14 — Figure 14: Sensor importance ranking results from QR analysis for (left) SDT and (right) MDT. Each panel shows the spatial distribution of the top 30 most important sensor positions, with ranking order indicated by numbers.

Strategy	SDT					MDT
Strategy	SSIM	NMSE	MG	FAC2	Overall	SSIM	NMSE	MG	FAC2	Overall
Kriging	-0.0	+18.1	-2.2	+0.8	+4.1	+12.5	+9.9	+5.6	+3.7	+7.9
UNet	+14.2	-11.6	-6.9	+1.4	-0.7	+5.1	-1.7	-4.7	+3.1	+0.4
ViTAE	-2.7	+12.2	-0.1	+1.1	+2.6	+1.1	+9.9	+7.7	+0.4	+4.8
CWGAN	+0.2	+27.8	-2.1	+0.4	+6.5	+1.3	+3.2	+1.1	+1.5	+1.8

Table 2: Average QR robustness improvements (%) for both methods. QR improvement represents the difference in robustness (percentage performance retention under sensor perturbations) between optimized and standard placements, averaged across sensor counts (5–30).

Panel of Figure 15 — Figure 15: Comparison of Metrics Across Models with QR-based Sensor Placement under different training strategies.

Appendix figures & tables11 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 1: Figure A1: Spatial NMSE distribution of 0° wind direction for SDT with 5 sensors helps visualize which part of the wind field is difficult to predict. With low sensor density, Kriging exhibits better performance compared to deep learning methods, which corresponds to Fig. 8(a) .

Figure 2: Spatial NMSE distribution of 0° wind direction for MDT with 5 sensors. Even with low sensor density, deep learning methods still show potential advantage over Kriging, especially for 0° wind direction, which corresponds to Fig. 8(b) .

Feature	0°	22.5°	45°
Boundary–center difference	0.772	0.210	0.372
Coefficient of variation (CV)	0.507	0.566	0.229
Spatial gradient	0.143	0.127	0.096

Appendix

Table 1: Spatial features of 0°, 22.5° and 45° wind directions. Boundary–center difference measures spatial non-stationarity; high values challenge Kriging’s stationarity assumption. Coefficient of variation quantifies velocity heterogeneity; high CV indicates coexisting high and low speed regions that complicate reconstruction. Spatial gradient measures the rate of velocity change; high gradients create sharp transitions difficult to capture from sparse sensors.

Figure 3: High-speed and low-speed sample counts in the training and testing datasets using a threshold of 0.6 m/s. All spatial points in each wind field snapshot are counted, with velocities greater than or equal to 0.6 m/s classified as high-speed and velocities below 0.6 m/s classified as low-speed.

Panel of Figure 1 — Figure 1: Analysis of asymmetric sensor placement: (a) Top 10 sensor placement in the SDT after QR-based optimization. (b) Variance of the 0° wind direction dataset, green crosses indicate the top 5 sensors. There is a clear pattern that the top 5 sensors are concentrated in the bottom of the field, where the variance is highest.

Sensor Counts	Metrics	Original (Single Run)		30_avg (Ensemble)
		Low L1	High L1 (Proposed)	Low L1	High L1 (Proposed)
5	MG	1.4357	1.0423	1.4420	1.0421
	NMSE	2.9615	1.1196	3.0701	1.1553
	FAC2	0.6704	0.7568	0.6706	0.7568
	SSIM	0.1406	0.1487	0.1413	0.1487
25	MG	0.9914	1.0333	0.9924	1.0333

Appendix

Table 1: Performance comparison of CWGAN with reduced L1 weight (Low L1) versus the proposed configuration (High L1). The results show that relaxing the L1 constraint leads to performance degradation.

Sensor Counts	Metrics	Original	5_avg	10_avg	30_avg
5	MG	1.0423	1.0427	1.0422	1.0421
	NMSE	1.1196	1.1427	1.1466	1.1553
	FAC2	0.7568	0.7568	0.7568	0.7568
	SSIM	0.1487	0.1487	0.1487	0.1487
10	MG	1.2406	1.2349	1.2399	1.2446
	NMSE	1.2898	1.2482	1.2481	1.245

Appendix

Table 2: Comparison of CWGAN performance averaged over different prediction samples. Bold values indicate the best performance, though the differences between them are minimal.

Figure 1: Comparison of CWGAN performance averaged over different prediction samples. The differences are visually negligible.

Panel of Table 1 — Table 1: Structural similarity (SSIM) between different realizations ( $\mathcal{D}_{\theta}^{(1)},\mathcal{D}_{\theta}^{(2)},\mathcal{D}_{\theta}^{(3)}$ ) within the same wind direction ( $\theta$ ). Values close to 1.0 indicate high similarity, while values below 1.0 (with 3-4% structural differences) confirm independence between realizations.

Sensor	Model	SSIM Diff%	FAC2 Diff%	NMSE Diff%	MG Diff%
5	UNet	$-4.24$ %	$-1.01$ %	$7.46$ %	$-2.48$ %
	CWGAN	$6.25$ %	$1.89$ %	$-6.46$ %	$-5.90$ %
	ViTAE	$-1.36$ %	$0.12$ %	$13.49$ %	$-9.72$ %
	Kriging	$-5.36$ %	$-0.30$ %	$11.69$ %	$-2.06$ %
10	UNet	$-2.39$ %	$-0.51$ %	$15.61$ %	$-1.26$ %
	CWGAN	$-1.28$ %	$0.60$ %	$14.38$ %	$-0.09$ %

Appendix

Table 2: Sensitivity analysis of MDT split by changing training realization selection. Values represent percentage differences between the alternative split (Realization 2 for training) and the original split (Realization 1 for training). SSIM and FAC2 show minimal variation (mostly within

\pm

2%), while NMSE variations include a theoretical baseline offset of approximately 9.21% due to test set composition changes.

Sensor	Model	SSIM Diff%	FAC2 Diff%	NMSE Diff%	MG Diff%
5	UNet	$-9.34$ %	$-2.92$ %	$3.43$ %	$4.06$ %
	CWGAN	$-10.40$ %	$-3.18$ %	$0.83$ %	$-6.26$ %
	ViTAE	$-5.66$ %	$-2.58$ %	$1.60$ %	$-0.19$ %
	Kriging	$0.00$ %	$0.00$ %	$0.00$ %	$0.00$ %
10	UNet	$-7.23$ %	$-2.14$ %	$5.93$ %	$0.16$ %
	CWGAN	$-7.05$ %	$-1.44$ %	$5.45$ %	$-2.23$ %

Appendix

Table 3: Performance comparison between excluding 22.5° from training (0° + 45° only) versus the original MDT (0° + 22.5° + 45°). Values represent percentage differences. Kriging shows 0% difference as it does not rely on training data. Deep learning methods show modest degradation, confirming the value of multi-direction training.

Jul 28, 2026

Zhinv: Real-time hub-height wind field reconstruction using only local sparse observations

The high proportion of wind power connected to the grid places higher demands on fine-grained knowledge of regional wind fields. Since the wind information directly obtainable in actual operations is mostly sparse, discrete, and irregularly distributed local observations, it is difficult to directly meet the needs of tasks such as wind power regulation, wind resource assessment, and low-altitude environmental perception of continuous regional wind fields. Therefore, we propose Zhinv, an end-to-end reconstruction framework that directly weaves sparse and irregular observations into a fine-grid wind field at hub-height. Experiments in Northeast China, Europe, and Southeast Asia demonstrate that Zhinv can accurately, robustly, and efficiently reconstruct fine-grid wind fields from sparse observations, reducing the error by about 66% compared with Kriging. With local wind-power observations as input, Zhinv enables wind power centers to bypass NWP and complex assimilation processes, supporting direct and real-time wind resource assessment from locally available data.

Zongwei Zhang, Chin Chun Ooi, Lianlei Lin +8

School of Electronic and Information Engineering, Harbin Institute of Technology, Harbin, 150001, Heilongjiang, China · Centre for Frontier AI Research, Agency for Science, Technology and Research (A*STAR), Singapore 138632, Singapore · Technological Innovation Center of Littoral Test, China +2

Sparse Recovery

Ask PDF

Jan 16, 2026

GenDA: Generative Data Assimilation on Complex Urban Areas via Classifier-Free Diffusion Guidance

Urban wind flow reconstruction is essential for assessing air quality, heat dispersion, and pedestrian comfort, yet remains challenging when only sparse sensor data are available. We propose GenDA, a generative data assimilation framework that reconstructs high-resolution wind fields on unstructured meshes from limited observations. The model employs a multiscale graph-based diffusion architecture trained on computational fluid dynamics (CFD) simulations and interprets classifier-free guidance as a learned posterior reconstruction mechanism: the unconditional branch learns a geometry-aware flow prior, while the sensor-conditioned branch injects observational constraints during sampling. This formulation enables obstacle-aware reconstruction and generalization to held-out mesh geometries, wind directions, and sensor configurations within the studied urban-flow setting, without retraining. We consider both sparse fixed sensors and trajectory-based observations using the same reconstruction procedure. When evaluated against supervised graph neural network (GNN) baselines and classical reduced-order data assimilation methods, GenDA reduces the relative root-mean-square error (RRMSE) by 25-57% and increases the structural similarity index (SSIM) by 23-33% across the tested meshes. Experiments are conducted on Reynolds-averaged Navier-Stokes (RANS) simulations of a real urban neighborhood in Bristol, United Kingdom, at a characteristic Reynolds number of

\mathrm{Re}\approx2\times10^{7}

, featuring complex building geometry and irregular terrain. The proposed framework provides a scalable path toward generative, geometry-aware data assimilation for environmental monitoring in complex domains.

Francisco Giral, Álvaro Manzano, Ignacio Gómez +2

Applied Mathematics Department, ETSIAE-School of Aeronautics, Universidad Politécnica de Madrid, Spain · Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109, USA.

Diffusion Model Guidance Data Assimilation Diffusion Models Computational Fluid Dynamics

Ask PDF

Jul 1, 2026

Wind-Aware Reinforcement Learning Control of a Small Quadrotor Using Learned Onboard Wind Estimation in Simulated Atmospheric Turbulence

Small multirotor aircraft are increasingly tasked with operations in the atmospheric boundary layer, where turbulent winds comparable to the vehicle's airspeed degrade trajectory tracking and can defeat conventional feedback control. This work illustrates a two-stage learning pipeline that first estimates the local wind from onboard kinematics and dynamics and then exploits that estimate inside a reinforcement learning (RL) flight controller. The wind estimator, an attention-augmented gated recurrent network trained on thousands of simulated flights through von Karman turbulence with power-law shear and veer, recovers the horizontal wind vector with a per-flight root-mean-square error of 0.40 m/s and a direction error of 3.2 degrees on unseen wind regimes, an accuracy near the floor imposed by unresolved turbulence, and generalizes to vertical ascent profiles with a skill score of 0.861 over a constant-wind reference. A proximal policy optimization controller receiving the frozen estimator's output reduces horizontal trajectory tracking error by 48% relative to a wind-blind proportional-derivative baseline across mean winds of 4 m/s to 12 m/s, winning on 100% of evaluation episodes. A three-way ablation decomposes this improvement into a kinematic component, available without wind information, and a wind-perception component; the perception share rises with wind speed, from small in light winds toward roughly half the total benefit in strong winds, consistent with the quadratic scaling of aerodynamic drag. The controller degrades gracefully on out-of-distribution winds of 13 m/s to 15 m/s, where the baseline fails catastrophically.

Abdullah Al Tasim, Wei Sun

University of Oklahoma, Norman, Oklahoma, 73019

RL Control Aerial Robotics Quadrotor Control Atmospheric Turbulence Mitigation

Ask PDF

Abstract

Explore similar work

Zhinv: Real-time hub-height wind field reconstruction using only local sparse observations

GenDA: Generative Data Assimilation on Complex Urban Areas via Classifier-Free Diffusion Guidance

Wind-Aware Reinforcement Learning Control of a Small Quadrotor Using Learned Onboard Wind Estimation in Simulated Atmospheric Turbulence