End-to-end data-driven prediction of urban airflow and pollutant dispersion

Nishant Kumar; Franck Kerhervé; Lionel Agostini; Laurent Cordier

cs.LGMar 18, 2026

End-to-end data-driven prediction of urban airflow and pollutant dispersion

Authors: Nishant Kumar, Franck Kerhervé, Lionel Agostini, Laurent Cordier

Organizations: Institut Pprime, CNRS, Université de Poitiers, ISAE-ENSMA, Curiosity Team, Bât. H2 - Bd. Marie & Pierre Curie TSA 51124, 86073 Poitiers Cedex 9, France

Abstract

Climate change and the rapid growth of urban populations are intensifying environmental stresses within cities, making the behavior of urban atmospheric flows a critical factor in public health, energy use, and overall livability. This study targets to develop fast and accurate models of urban pollutant dispersion to support decision-makers, enabling them to implement mitigation measures in a timely and cost-effective manner. To reach this goal, an end-to-end data-driven approach is proposed to model and predict the airflow and pollutant dispersion in a street canyon in skimming flow regime. A series of time-resolved snapshots obtained from large eddy simulation (LES) serves as the database. The proposed framework is based on four fundamental steps. Firstly, a reduced basis is obtained by spectral proper orthogonal decomposition (SPOD) of the database. The projection of the time series snapshot data onto the SPOD modes (time-domain approach) provides the temporal coefficients of the dynamics. Secondly, a nonlinear compression of the temporal coefficients is performed by autoencoder to reduce further the dimensionality of the problem. Thirdly, a reduced-order model (ROM) is learned in the latent space using Long Short-Term Memory (LSTM) netowrks. Finally, the pollutant dispersion is estimated from the predicted velocity field through convolutional neural network that maps both fields. The results demonstrate the efficacy of the model in predicting the instantaneous as well as statistically stationary fields over long time horizon.

Figures & tables

Panel of Figure 1 — Figure 1: (a) Overview of the simulated street canyon geometry (not to scale). The bounds of the computational domain is indicated by dashed line along with the boundary conditions. The pollutant source is indicated by the red line which spans the center of the canyon base. The vertical sampling plane located mid-span of the canyon is indicated in green. (b) Mean velocity magnitude with streamlines on the $x$ - $z$ plane. (c) Mean concentration of the pollutant emitted from source.

Panel of Figure 2 — Figure 2: Schematic of the neural network architectures used in the ROM framework: (a) Autoencoder, (b) Long Short-Term Memory (LSTM) cell, and (c) Convolutional Neural Network (CNN).

Figure 3: Schematic of the data-driven ROM framework. The offline stage involves training the three independent neural network architectures – AE, LSTM and CNN. The online stage utilizes the trained models to forecast the velocity and concentration fields from an initial condition.

Panel of Figure 4 — Figure 4: (a) Spectrum of the two leading SPOD eigenvalues ( $\lambda_{f_{k}}^{(1)}$ – solid, and $\lambda_{f_{k}}^{(2)}$ – dashed) for five values of the block size $N_{\mathrm{fft}}$ . The numbers at the end of the colored arrows indicate the resulting number of blocks $N_{\mathrm{blk}}$ . (b) Eigenvalue spectrum showing the $95\%$ confidence intervals (shaded area) for three values of $N_{\mathrm{fft}}$ .

Panel of Figure 5 — Figure 5: (a) Eigenvalue spectrum of SPOD modes for $N_{\mathrm{fft}}=4096$ and $N_{\mathrm{blk}}=34$ . (b) Contour of nondimensional eigenvalues with respect to both the frequency and the spatial mode number. The summed eigenvalues along the frequency and the spatial mode number are also plotted in the top and right insets respectively. Here $\sum_{k}$ and $\sum_{n}$ denote summation of the eigenvalues over all the discrete frequencies and modes.

Panel of Figure 6 — Figure 6: Real component of the SPOD modes at reduced frequencies (a,b) $f^{\ast}=0.5$ and (c,d) $f^{\ast}=1.0$ . The leading optimal modes $\boldsymbol{\phi}_{f_{k}}^{(1)}$ are shown in (a,c), while the suboptimal modes $\boldsymbol{\phi}_{f_{k}}^{(2)}$ are shown in (b,d).

Panel of Figure 7 — Figure 7: (a) Relative information content (RIC) as a function of the number of retained leading frequencies. (b) Eigenvalue separation $\Delta\lambda_{f_{k}}$ spectrum. The green and red vertical lines indicate the preserved and discarded frequencies respectively.

Panel of Figure 8 — Figure 8: (a) Spatial similarity coefficient $\gamma$ computed with respect to the target mode $\boldsymbol{\phi}_{f_{31}}^{(1)}$ (indicated by the blue square). (b) Real part of the target mode. (c) Real part of the most similar neighboring mode ( $\boldsymbol{\phi}_{f_{32}}^{(1)}$ ), illustrating the redundancy in spatial structures across frequencies.

Panel of Figure 9 — Figure 9: Sensitivity analysis for the similarity threshold $\varepsilon_{\gamma}$ : (a) Number of preserved modes; (b) Fraction of preserved TKE relative to the full basis; (c) Normalized mean-squared error (NMSE) of the reconstruction.

Figure 10: Instantaneous velocity fluctuation fields at

tU_{\mathrm{ref}}/H=540

. (a) Reference field. (b-d) Reconstructions using bases pruned with

\varepsilon_{\gamma}=1.0,0.2,0.1

. The right column in each panel displays the local

L_{1}

-error.

Figure 11: Comparison of the SPOD eigenvalue spectra for different levels of reconstruction of velocity fields (

\varepsilon_{\gamma}=1.0,0.2,0.1

) to reference data (LES). The solid lines correspond to the first mode and the dashed lines to the second mode.

Encoder layers	Decoder layers	Activation	Batch size	Learning rate	Epochs
[1024, 512, 256, 128, 64, 32]	[32, 64, 128, 256, 512, 1024]	$\tanh$	2048	0.001	5000

Table 1: Hyperparameters for the autoencoder (AE) training.

Panel of Figure 12 — Figure 12: Comparison of the reconstructed time trajectory for the real component of the dominant SPOD coefficient $a_{31}^{(1)}(t)$ (corresponding to the target mode in Fig. 8(a) ). The reference SPOD trajectory is compared with AE reconstructions using latent dimensions of (a) $N_{z}=5$ and (b) $N_{z}=30$ .

Panel of Figure 13 — Figure 13: (a) Evolution of training (solid) and validation (dashed) losses for AEs with latent sizes $N_{z}=5,15,30$ (first 1000 epochs shown). (b) Time evolution of the normalized mean-squared error (NMSE) for the velocity magnitude field. The AE reconstruction errors are compared against the baseline SPOD projection error (blue line). The horizontal lines indicate the time-averaged error.

Figure 14: Instantaneous velocity magnitude field reconstructed using the AE with latent dimension $N_{z}=30$ .

$N_{h}$	Batch size	Learning rate	Epochs	Trials
[50, 200]	[500, 1000]	[0.0005, 0.0010]	100	20

Table 2: Search space for LSTM hyperparameter optimization.

Panel of Figure 15 — Figure 15: Contours of the objective value (validation error) as a function of hidden size ( $N_{h}$ ) and batch size for the LSTM training on the (a) real and (b) imaginary components of the latent vector. The points represent completed optimization trials.

Component	$N_{t,\text{in}}$	$N_{t,\text{out}}$	$N_{h}$	Batch size	Learning rate	Epochs
$\mathrm{Re}(\mathbf{z})$	10	1	134	855	0.00084	10000
$\mathrm{Im}(\mathbf{z})$	10	1	131	805	0.00057	10000

Table 3: Optimized LSTM hyperparameters for the real and imaginary components.

Panel of Figure 16 — Figure 16: Comparison of the temporal evolution of the (a) real and (b) imaginary components of the first latent variable $z_{1}(t)$ . The LSTM forecast (red) is compared against the reference trajectory from the AE (grey). The vertical dashed line marks the end of the input sequence ( $N_{t,in}$ ) and the start of the autonomous prediction.

Panel of Figure 17 — Figure 17: Poincaré sections defined by the hyperplane $z_{1}(t)=0$ with $\mbox{\,d}z_{1}(t)/\mbox{\,d}t>0$ . The contours represent the joint Probability Density Function (PDF) of the intersection points in the $z_{2}$ - $z_{3}$ phase plane. (a) Training set, and (b) Validation set. Gray contours: Reference; Red contours: LSTM prediction.

Panel of Figure 18 — Figure 18: (a, b) Temporal evolution of the predicted (red) and reference (grey) real component of the SPOD coefficient $a_{31}^{(1)}(t)$ in the (a) training and (b) testing windows. (c) Probability density functions (PDFs) of the predicted coefficients for selected dominant modes in the test window.

Panel of Figure 19 — Figure 19: Time evolution of the normalized mean-squared error (NMSE) of the velocity magnitude field. The error is computed between the LSTM-ROM reconstruction and the reduced SPOD reference. Dashed lines indicate the time-averaged error.

Channels	Filter size	Kernel size	Padding	Batch size	Learning rate	Epochs
[2, 32, 64, 128, 64, 32, 1]	$96\times 96$	5	2	16	0.001	1000

Table 4: CNN hyperparameters for the velocity-to-concentration mapping.

Figure 20: Instantaneous reconstructed concentration field obtained from the CNN in the validation window.

Figure 21: Contours of the mean concentration field computed over the test window.

Panel of Figure 22 — Figure 22: (a) Comparison of the mean total vertical mass flux of the pollutant across the canopy interface ( $z/H=1$ ). (b) Time evolution of pollutant concentration at two probe locations: Outside the canyon ( $x=0.60H,z=1.01H$ ) and inside the canyon on the leeward face ( $x=-0.49H,z=0.50H$ ).

Air Quality Prediction

Air quality prediction estimates future pollutant levels and maps local exposure to support health warnings, planning, and pollution control.

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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.

Abstract

Air Quality Prediction

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