Anchored-Branched Steady-state WInd Flow Transformer (AB-SWIFT): a metamodel for 3D atmospheric flow in urban environments

Armand de Villeroché; Rem-Sophia Mouradi; Vincent Le Guen; Sibo Cheng; Marc Bocquet; Alban Farchi; Patrick Armand; Patrick Massin

cs.LGMar 26, 2026

Anchored-Branched Steady-state WInd Flow Transformer (AB-SWIFT): a metamodel for 3D atmospheric flow in urban environments

Authors: Armand de Villeroché, Rem-Sophia Mouradi, Vincent Le Guen, Sibo Cheng, Marc Bocquet, Alban Farchi, Patrick Armand, Patrick Massin

Organizations: CEREA, ENPC, EDF R&D, Institut Polytechnique de Paris, Île-de-France, France · EDF R&D, Île-de-France, France · SINCLAIR AI Laboratory, Saclay, Île-de-France, France · CEA, DAM, DIF, F-91297 Arpajon, France

Abstract

Air flow modeling at a local scale is essential for applications such as pollutant dispersion modeling or wind farm modeling. To circumvent costly Computational Fluid Dynamics (CFD) computations, deep learning surrogate models have recently emerged as promising alternatives. However, in the context of urban air flow, deep learning models struggle to adapt to the high variations of the urban geometry and to large mesh sizes. To tackle these challenges, we introduce Anchored Branched Steady-state WInd Flow Transformer (AB-SWIFT), a transformer-based model with an internal branched structure uniquely designed for atmospheric flow modeling. We train our model on a specially designed database of atmospheric simulations around randomised urban geometries and with a mixture of unstable, neutral, and stable atmospheric stratifications. Our model reaches the best accuracy on all predicted fields compared to state-of-the-art transformers and graph-based models. Our code and data is available at https://github.com/cerea-daml/abswift.

Figures & tables

Figure 1: Our proposed model architecture. AB-SWIFT separately encodes the terrain and obstacles to yield one embedded geometry sequence, and encodes the physical context and the volume prediction points. The geometry and encoded prediction points are then processed together. Finally the decoder predicts physical fields from processed latent states of volume points.

Name	Description	Value
AB-SWIFT specific parameters
$d$	Hidden dimension of the latent states	192
$n_{\mathrm{obs}}$	Number of points describing obstacles	4096
$n_{\mathrm{gnd}}$	Number of points describing the terrain	4096
$n_{\mathrm{obs\text{-}sn}}$	Number of obstacles supernodes	1024
$r_{\mathrm{obs}}$	Radius for obstacles’ supernodes pooling	1

Table 1: AB-SWIFT hyperparameters and used values.

Figure 2: Left: $4$ building configuration, taken from the $210$ different configurations present in our dataset. Right: used values of $1/L_{\mathrm{mo}}$ and $z0$ . Purple points represent the training split, blue the validation split, and yellow the test split.

	unstable	neutral	stable	total
training	53	15	70	138
validation	6	1	3	10
test	35	11	34	80

Table 2: Dataset split between training, validation and test samples with stability repartition for each split.

	Input format	Input features
AB-SWIFT	Terrain, obstacles and volume point clouds	Atmospheric profiles $1/L_{\mathrm{mo}}$ and $z_{0}$ in the terrain point cloud
AB-UPT	Geometry and volume point clouds	$1/L_{\mathrm{mo}}$ and $z_{0}$ in the geometry point cloud
GAOT	Volume point cloud	$1/L_{\mathrm{mo}},z_{0}$ , one-hot encoded point type
Transolver	Volume point cloud	$1/L_{\mathrm{mo}},z_{0}$ , one-hot encoded point type
BSMGN	Graph from volume mesh connectivity	$1/L_{\mathrm{mo}},z_{0}$ , one-hot encoded node type

Table 3: Inputs format and used features of our different tested models. For all models outputs are

\textbf{v},\theta,p,\log k,\text{and}\log\epsilon

model (# of trainable parameters)	training time (one epoch)	training VRAM requirement	inference time (one sample)
AB-SWIFT (6.5M)	$8\text{\,}\mathrm{s}$	$1.21\text{\,}\mathrm{G}\mathrm{b}$	$0.39\text{\,}\mathrm{s}$
AB-UPT (6.5M)	$7.5\text{\,}\mathrm{s}$	$1.20\text{\,}\mathrm{G}\mathrm{b}$	$0.43\text{\,}\mathrm{s}$
GAOT (6.6M)	$17\text{\,}\mathrm{s}$	$10\text{\,}\mathrm{G}\mathrm{b}$	$0.23\text{\,}\mathrm{s}$
Transolver (6.0M)	$27\text{\,}\mathrm{s}$	$23\text{\,}\mathrm{G}\mathrm{b}$	$0.31\text{\,}\mathrm{s}$
BSMGN (0.4M)	$90\text{\,}\mathrm{s}$	$36\text{\,}\mathrm{G}\mathrm{b}$	$0.60\text{\,}\mathrm{s}$

Table 4: Resource requirements of all models for training and inference. Training and inference speeds are measured on a A100 GPU with 40Gb of VRAM. Memory cost is shown for a batch size of

1

		AB-SWIFT (ours)	AB-UPT	GAOT	Transolver	BSMGN
v	NMSE	$\textbf{0.3}\pm\textbf{0.4}$	$0.8\pm 1.3$	$13.1\pm 7.4$	$2.1\pm 1.5$	$\textit{0.8}\pm\textit{1.0}$
	L1 err	$\textbf{2.2}\pm\textbf{1.3}$	$5.3\pm 3.9$	$20.4\pm 8.0$	$5.6\pm 2.4$	$\textit{4.6}\pm\textit{2.7}$
	L2 err	$\textbf{3.7}\pm\textbf{1.8}$	$\textit{6.2}\pm\textit{3.8}$	$29.3\pm 9.1$	$9.8\pm 3.7$	$6.3\pm 3.2$
$p$	NMSE	$\textbf{2.0}\pm\textbf{3.5}$	$\textit{5.7}\pm\textit{6.7}$	$96.8\pm 412.3$	$14.5\pm 25.3$	$6.4\pm 9.4$
	L1 err	$\textbf{9.3}\pm\textbf{7.8}$	$22.1\pm 14.2$	$62.3\pm 76.5$	$23.9\pm 18.6$	$\textit{20.2}\pm\textit{13.7}$
	L2 err	$\textbf{9.8}\pm\textbf{9.2}$	$\textit{18.5}\pm\textit{12.5}$	$64.2\pm 68.4$	$26.4\pm 24.1$	$18.6\pm 14.6$

Table 5: Benchmark results of AB-SWIFT and literature baselines. NMSE is in percent of the variance over a given simulation, and L1 and L2 errors are in percent of the ground truth value. We report mean and standard deviation of metrics computed on the test split of the dataset for all trained models. For all metrics, the best model is shown in bold, and the second best in italic. *NMSE for

\theta

is computed on stable and unstable cases only.

Figure 3: Norm of the velocity field predicted by all models, $2\text{\,}\mathrm{m}$ above ground, for an unstable stratification (Left), a neutral stratification (Middle left), and two stable stratifications (Middle right and Right). All shown geometries and stability parameters are from the test split of the dataset.

Figure 4: Horizontal slice at height $h=$2\text{\,}\mathrm{m}$$ of the fields predicted by AB-SWIFT for a stable stratification ( $1/L_{\mathrm{mo}}=$0.15\text{\,}{\mathrm{m}}^{-1}$,z_{0}=$0.06\text{\,}\mathrm{m}$)$ . Buildings are shown in teal color. — Figure 4: Horizontal slice at height $h=$ 2\text{,}\mathrm{m}$$ of the fields predicted by AB-SWIFT for a stable stratification ( $1/L_{\mathrm{mo}}=$ 0.15\text{,}{\mathrm{m}}^{-1} $,z_{0}=$ 0.06\text{,}\mathrm{m} $)$ . Buildings are shown in teal color.

		Step 0	Step 1	Step 2	Step 3	Step 4
		AB-UPT				AB-SWIFT
v	NMSE	$1.5\pm 1.5$	$0.6\pm 0.6$	$0.6\pm 1.4$	$0.4\pm 0.5$	$0.3\pm 0.4$
	L1 error	$8.5\pm 5.3$	$3.7\pm 2.5$	$3.5\pm 3.5$	$2.5\pm 1.6$	$2.2\pm 1.3$
	L2 error	$8.9\pm 4.7$	$5.1\pm 2.6$	$4.8\pm 3.4$	$4.3\pm 2.2$	$3.7\pm 1.8$
$p$	NMSE	$8.5\pm 12.6$	$4.8\pm 7.3$	$3.8\pm 6.9$	$2.7\pm 4.5$	$2.0\pm 3.5$
	L1 error	$26.6\pm 19.9$	$16.2\pm 13.0$	$14.1\pm 10.7$	$10.9\pm 8.9$	$9.3\pm 7.7$

Table 6: Ablation study results. Starting from AB-UPT, we build AB-SWIFT step by step. Step 1: we merge the geometry and surface branches. Step 2: we encode separately obstacles and terrain. Step 3: we encode profiles directly. Step 4: we split the final decoder layer per predicted fields, resulting in the final AB-SWIFT proposed model. Reported metrics are the mean and standard deviation for each trained intermediate model over the test split of the dataset. NMSE is in percent of the variance over a given simulation, and L1 and L2 errors are in percent of the ground truth value.

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 5: Mesh arrangements used to generate database samples. Buildings are clustered in the black area. For machine learning, only the dark blue zone of interest with an horizontal refinement up to $5\text{\,}\mathrm{m}$ is kept and up to a height of $50\text{\,}\mathrm{m}$ to reduce the mesh size.

Description	Value
Number of input points for the geometry, randomly subsampled from mesh points adjacent to the ground and buildings	$8192$
Number of supernodes for the geometry	$2048$
Number of anchor points in the surface point cloud, randomly subsampled from mesh points adjacent to the ground and buildings	$2048$
Hidden dimension	$192$
Number of anchor points in the volume point cloud, randomly subsampled from mesh cell centers	$8192$
Number of attention heads	$3$

Appendix

Table 7: AB-UPT’s chosen hyperparameters values

Description	Value
Number of latent tokens in $x$ , $y$ , and $z$ dimensions	$32,32,8$
Multiscale radii in the MAGNO encoder and decoder	$1,5,10,20,50$
Learnable scale weights in the MAGNO encoder and decoder	True
Number of MLP layers at the end of the MAGNO encoder	$3$
Hidden size of the MAGNO encoder and decoder	$64$
Hidden size of MAGNO’s output	$128$

Appendix

Table 8: GAOT’s chosen hyperparameters values.

Description	Value
Number of physics attention layers	$8$
Number of physics attention slices	$64$
Hidden size	$256$
Number of attention heads	$8$
Activation function	GeLU

Appendix

Table 9: Transolver’s chosen hyperparameters values.

Description	Value
single-scale MGN processor size	$0$ (i.e. not used)
Number of u-net like mesh levels	$5$
Hidden size	$64$
Number of hidden layers per message passing	2
Number of calls to the bistride processor	1

Appendix

Table 10: BSMGN’s chosen hyperparameters values.

Neural Surrogate Modeling

Neural surrogate modeling uses learned models to approximate costly simulations, enabling faster prediction, design, control, and inference.

See all 410 papers

Fast localized urban microclimate emulator: wind and temperatures in unseen urban morphologies
Mar 25, 2025Shaoxiang Qin, Theodore Potsis, Dongxue Zhan +3PDE Surrogate Modeling Computational Fluid Dynamics
Department of Building, Civil and Environmental Engineering, Cetner Zero Energy Building Studies, Concordia University, Montreal, Canada · School of Computer Science, McGill University, Montreal, Canada · Mohamed bin Zayed University of Artificial Intelligence, Abu Dhabi, United Arab Emirates
FluidFlow: a flow-matching generative model for fluid dynamics surrogates on unstructured meshes
Mar 30, 2026David Ramos, Lucas Lacasa, Fermín Gutiérrez +2PDE Surrogate Modeling Computational Fluid Dynamics
ETSIAE-UPM-School of Aeronautics, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros 3, E-28040 Madrid, Spain · Institute for Cross-Disciplinary Physics and Complex Systems (IFISC, CSIC-UIB), 07122 Palma de Mallorca (Spain) · Center for Computational Simulation, Universidad Politécnica de Madrid, Campus de Montegancedo, Boadilla del Monte, 28660 Madrid, Spain
Pretrained Video Models as Differentiable Physics Simulators for Urban Wind Flows
Mar 22, 2026Janne Perini, Rafael Bischof, Moab Arar +4Video Diffusion Models PDE Surrogate Modeling
1Computational Design Lab, ETH Zurich, Switzerland · 2Tel Aviv University, Israel · 3Architecture and Building Systems, ETH Zurich, Switzerland +2

Mar 25, 2025J/K move · Enter open · S save

Fast localized urban microclimate emulator: wind and temperatures in unseen urban morphologies

Shaoxiang Qin, Theodore Potsis, Dongxue Zhan, Xue Liu+2

Department of Building, Civil and Environmental Engineering, Cetner Zero Energy Building Studies, Concordia University, Montreal, Canada · School of Computer Science, McGill University, Montreal, Canada · Mohamed bin Zayed University of Artificial Intelligence, Abu Dhabi, United Arab Emirates

PDE Surrogate Modeling Computational Fluid Dynamics

Open paper AskPDF arXiv

Urban microclimate, encompassing wind and temperature fields shaped by building geometry, strongly affects building energy use, pedestrian wind comfort, pollutant dispersion, the urban heat island, and public health. Conventional Computational Fluid Dynamics (CFD) is computationally prohibitive for rapid assessments, while many deep learning approaches require extensive training data and struggle with generalization to unseen configurations. In this work, we present the Fast Localized Urban Microclimate Emulator (FLUME), a rapid, data-efficient, and geometry-aware framework based on a Fourier neural operator for predicting three-dimensional wind and temperature fields. FLUME assumes that, under prescribed inflow and thermal forcing, much of the spatial variation of these mean fields is controlled by surrounding building geometry. The framework introduces a Multi-Directional Distance Feature (MDDF), which captures geometry over adaptive, visibility-defined spatial scales. By decomposing simulations of only 23 urban blocks into smaller 3D patches enriched with precomputed MDDF information, FLUME enables learning from limited CFD data. The model achieves mean absolute errors of 0.2 m/s for streamwise velocity and 0.19

^{\circ}

C for temperature on unseen urban configurations. A deep ensemble provides a practical proxy for epistemic uncertainty, and conformal prediction transforms these estimates into calibrated prediction intervals. Ensemble spread is positively related to local prediction error, with greater uncertainty in roof-level shear layers, building wakes, and vertical velocity near the ground. These results indicate FLUME's potential for rapid scenario assessment in urban design and urban climate studies.

Abstract

Neural Surrogate Modeling

Explore similar work

Fast localized urban microclimate emulator: wind and temperatures in unseen urban morphologies

FluidFlow: a flow-matching generative model for fluid dynamics surrogates on unstructured meshes

Pretrained Video Models as Differentiable Physics Simulators for Urban Wind Flows