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

TL;DR

GenDA addresses the challenge of reconstructing high-resolution urban wind fields from sparse observations by marrying geometry-aware diffusion with classifier-free guidance on unstructured meshes. It introduces a multiscale graph diffusion model that learns a geometry-conditioned prior and uses a sensor-conditioned branch to inject observations, effectively sampling from a tempered posterior $p_\gamma(u|y,G) ∝ p(u|G) p(y|u)^{\gamma}$ with a controllable guidance weight $\gamma$. The architecture couples a fine and a reduced graph via o2o, o2r, r2r, and r2o connections, enabling efficient propagation of information across scales while preserving obstacle boundaries. Empirical results on RANS data from a real Bristol urban neighborhood show GenDA achieving lower RRMSE and higher SSIM/MAC than supervised GNNs and reduced-order baselines, particularly at low observation densities, and demonstrate robustness to different sensor layouts. The work offers a scalable, uncertainty-aware path toward real-time environmental monitoring in complex cities and can be extended to volumetric 3D domains and dynamic sensing scenarios.

Abstract

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 across unseen geometries, wind directions, and mesh resolutions 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 neighbourhood 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.

Figures (11)

• Figure 1: Sparse sensor measurements provide partial information on the flow, and the generative model $D_\theta$ reconstructs a physically plausible velocity field consistent with the observations and the urban geometry.
• Figure 2: (a) 3D geometry of the modeled Bristol's neighbourhood, including buildings and underlying terrain. (b) Example of a horizontal slice normal to the vertical ($z$) axis, resulting in a 2D unstructured mesh used for graph-based diffusion. More information can be found at modelair.eu.
• Figure 3: Multiscale mesh hierarchy used in the proposed framework. The original node-dense mesh (left) provides the high-resolution representation where sensor observations and predictions are defined. The reduced mesh (center) is obtained through optimal decimation and supports efficient long-range message passing.
• Figure 4: Generative data assimilation with classifier-free guidance. At each diffusion step, an unconditional denoiser estimates the geometry-conditioned prior, while a sensor-conditioned denoiser incorporates measurement information. Their difference provides an observation-driven correction, and the guidance weight $\gamma$ controls the strength of this correction.
• Figure 5: Reconstruction of velocity magnitude $|\mathbf{u}|$ for multiple wind directions (angles and sensor layouts selected as representative examples from the test set; observation counts are shown above each column). Top row: ground truth $|\mathbf{u}|$. Second row: sensor locations. Rows 3--6: reconstructions from MeshGraphNet (single-scale), multiscale MeshGraphNet, Low-Cost SVD (LCSVD, non-learned), and GenDA. For each wind direction, the left panel shows the reconstructed $|\mathbf{u}|$ field and the right panel shows the corresponding pointwise relative error, highlighting spatial regions where each method deviates from the ground truth.