💻 computer science

Inpainting U-Net for seamless pedestrian-level wind prediction across urban morphologies

This study proposes a two-stage U-Net framework that combines a baseline patch-based predictor with an iterative inpainting refinement model to efficiently generate seamless, high-resolution pedestrian-level wind speed predictions across diverse urban morphologies, effectively mitigating boundary discontinuities while maintaining computational efficiency.

Original authors: Jingzi Huang, Claire E. Heaney, Tao Li, Xinzhe Li, Graham O. Hughes, Maarten van Reeuwijk

Published 2026-07-07

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CC BY 4.0

Original authors: Jingzi Huang, Claire E. Heaney, Tao Li, Xinzhe Li, Graham O. Hughes, Maarten van Reeuwijk

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to paint a massive, detailed mural of a city's wind patterns. You want to know exactly how the wind feels at street level for pedestrians, but calculating this with traditional physics methods is like trying to paint the whole mural by hand, pixel by pixel—it takes forever and costs a fortune.

This paper introduces a clever, two-step "AI artist" that can paint this wind map in seconds, even for cities of any size, without leaving ugly seams between the brushstrokes.

Here is how it works, using simple analogies:

The Problem: The "Puzzle Piece" Dilemma

To make the AI fast, the researchers broke the city down into small, manageable square tiles (like puzzle pieces). They trained a first AI model (let's call it Model M1) to predict the wind for just one tile at a time.

How M1 works: It looks at the buildings in a specific square and guesses the wind speed there.
The Flaw: Because M1 paints each tile independently, it doesn't know what its neighbors are doing. When you put all the tiles back together, you get a jigsaw puzzle where the edges don't match. One tile might say the wind is calm, while the tile right next to it says it's a gale. These "seams" create unrealistic jumps in the wind data.

The Solution: The "Inpainting" Refiner

To fix these messy seams, the researchers added a second AI model (let's call it Model M2). Think of M2 as a restoration expert or a blending artist.

The Magic Trick (Inpainting): In art, "inpainting" is when you take a damaged photo and ask an AI to fill in the missing parts by looking at the surrounding pixels to guess what should be there.
How M2 works: Instead of looking at just one small tile, M2 looks at a larger window that includes the tile M1 just painted plus the surrounding neighborhood. It sees the "context." If M1 painted a sudden, jarring wind jump at the edge of a tile, M2 looks at the flow from the neighboring tiles and smooths it out, making the transition seamless.

The Process: A Team Effort

The system works like a relay race with a twist:

The Rough Draft (M1): The first model quickly sketches the wind map for the whole city, tile by tile. It gets the big picture right (where the wind is generally fast or slow) but leaves rough, jagged edges between the tiles.
The Polish (M2): The second model goes over the map. It uses a special technique called a Gauss-Seidel scheme. Imagine a group of painters working in a line. As soon as one painter fixes a seam, the next painter immediately sees that fix and uses it to smooth their own section. They keep going back and forth, refining the edges, until the whole map looks like one continuous, smooth painting with no visible cracks.

What Did They Find?

The researchers tested this on real city data (from London, Sydney, Vancouver, etc.) and compared it to high-end physics simulations (which are the "gold standard" but very slow).

The Good News: The two-stage AI is incredibly fast and produces a seamless map. It captures the general flow of the wind very well. It knows where the wind is calm (like in a quiet alley) and where it's breezy (like in an open square).
The Limitations:
- The "Peak" Problem: While the AI is great at predicting average winds, it sometimes misses the very strongest gusts. It tends to be a bit too conservative, underestimating the highest wind speeds near sharp building corners.
- The "Empty Space" Problem: If a tile has almost no buildings (just a huge open park), the AI gets a bit confused because it relies on building shapes to guess the wind. It works best in dense city areas.

The Bottom Line

This paper presents a new tool that acts like a smart, fast, and seamless wind mapper. It solves the problem of "patchy" AI predictions by using a second model to blend the edges, much like a photo editor smoothing out a collage. While it isn't perfect at predicting extreme wind gusts, it offers a highly efficient way to visualize pedestrian wind comfort across entire cities, which is a huge step forward for urban planning.

Technical Summary: Inpainting U-Net for Seamless Pedestrian-Level Wind Prediction

Problem Statement
Pedestrian-level wind prediction is critical for urban design, safety, and wind-comfort assessment. While high-fidelity Computational Fluid Dynamics (CFD), such as Large Eddy Simulation (LES), provides accurate results, it remains computationally expensive, hindering rapid evaluation across diverse urban morphologies. Data-driven surrogate models, particularly Convolutional Neural Networks (CNNs) like U-Net, offer a faster alternative. However, a significant limitation in applying U-Net to large urban domains is the "patch-wise" inference strategy. To manage memory and resolution, the input domain is typically divided into fixed-size tiles processed independently. This approach often results in discontinuities and inconsistencies at patch boundaries when the tiles are assembled into a global solution. Existing post-processing methods (e.g., overlapping-window averaging) smooth these discontinuities statistically but lack an explicit physical basis or the ability to incorporate surrounding flow context effectively.

Methodology
The study proposes a two-stage U-Net framework designed to generate seamless, high-resolution predictions of time-averaged pedestrian-level wind speed over realistic urban morphologies. The framework utilizes the UrbanTALES dataset, a large-scale LES database containing 288 realistic urban configurations with varying densities, layouts, and wind directions.

Data Preprocessing:
- Normalization: Building heights, fetch distances, and wind speeds are normalized to the unit interval using percentile-based scaling (e.g., 95th percentile for height, 99th for speed).
- Rotation and Expansion: To handle arbitrary wind directions without explicit directional inputs, the entire domain is rotated so the approaching wind aligns with the positive x-axis. The domain is expanded into a $3 \times 3$ tiled field under periodic boundary conditions to ensure context availability for edge patches.
- Patch Extraction: Training data is extracted as fixed-size patches.
Stage 1: Baseline Model (M1):
- Architecture: A standard U-Net with four resolution levels, encoder-decoder structure, and skip connections.
- Input: Normalized topography (building mask with height) and normalized fetch (distance to upwind building) for a $128 \times 128$ pixel patch ( $128 \text{m} \times 128 \text{m}$ at $1\text{m}$ resolution).
- Output: Predicted normalized wind speed for the same $128 \times 128$ patch.
- Function: M1 learns the primary mapping from local morphology to wind speed, capturing the general spatial distribution.
Stage 2: Refinement Model (M2) - Inpainting Strategy:
- Architecture: Identical U-Net architecture to M1 but with a larger input/output size ( $192 \times 192$ pixels).
- Input: A composite field consisting of the central $128 \times 128$ region (predicted by M1) surrounded by a margin of ground-truth flow data (during training) or M1 predictions (during inference), along with the corresponding $192 \times 192$ topography.
- Function: M2 acts as an inpainting model. It uses the surrounding flow context to correct boundary discontinuities and refine local details in the M1 prediction.
- Inference Scheme: During full-field inference, M2 is applied iteratively using a Gauss-Seidel scheme. Patches are processed sequentially, and the updated central region is immediately used as context for subsequent patches. An under-relaxation factor ( $\alpha = 0.2$ ) is applied to ensure stability. Iteration continues until the mean absolute difference between consecutive iterations converges.

Key Contributions

Two-Stage Framework: The introduction of a specific two-stage pipeline where a baseline patch-wise model is followed by an inpainting-based refinement model to address boundary artifacts.
Inpainting for Flow Continuity: Unlike traditional smoothing techniques, M2 explicitly learns to reconstruct missing or inconsistent regions using neighboring flow information, effectively treating boundary discontinuities as "missing data" to be filled based on physical context.
Arbitrary Domain Scalability: The framework maintains the flexibility of patch-based inference (allowing prediction over domains of arbitrary size) while achieving seamless full-field outputs through the iterative refinement process.
Rotation-Invariant Training: By rotating inputs to align with the x-axis, the models learn direction-agnostic features, eliminating the need for wind direction as an explicit input channel.

Results

Patch-Level Performance (M1): M1 accurately captures low- and moderate-velocity regions and the general spatial distribution of wind speed. However, it tends to underestimate high-velocity peaks (e.g., near building corners) and performs less effectively on low-density patches with limited morphological information.
Refinement Performance (M2): M2 significantly reduces patch-boundary artifacts and improves spatial coherence. It effectively smooths discontinuities while preserving the overall flow structure. In some cases, M2 improves high-velocity predictions by leveraging boundary information, though it cannot fully correct large-scale structural errors made by M1.
Full-Field Performance: On 18 unseen urban cases, the framework reproduces the mean wind speed and spatial variability (standard deviation) reasonably well compared to LES ground truth. The mean velocity and standard deviation show strong agreement with ground truth. However, maximum velocities remain underestimated, indicating the model struggles with extreme local wind events. The framework shows no significant systematic bias related to wind direction after rotation.

Significance and Claims
The paper claims that the proposed framework provides an efficient and flexible surrogate model for high-resolution pedestrian-level wind prediction across realistic urban morphologies. Its primary significance lies in solving the "patch-boundary" problem inherent in deep learning-based spatial prediction without resorting to ad-hoc post-processing. By integrating an inpainting-based refinement step, the method produces seamless full-field predictions that are physically more consistent than standard patch-wise approaches. The authors note that while the model is effective for general wind comfort assessment, it currently underestimates extreme wind speeds, suggesting that future work should focus on improving the prediction of high-velocity events through reweighted loss functions or targeted sampling.