Cross-Resolution Attention Network for High-Resolution PM2.5 Prediction
Authors: Ammar Kheder, Helmi Toropainen, Wenqing Peng, Samuel Antão, Zhi-Song Liu, Michael Boy
Organizations: Department of Computational Engineering, LUT University, Finland · Atmospheric Modelling Centre Lahti (AMC-Lahti), Finland · Institute for Atmospheric and Earth System Research, University of Helsinki, P.O. Box 64, Helsinki 00014, Finland · Advanced Micro Devices (AMD), Munich, Germany
Vision Transformers have achieved remarkable success in spatio-temporal prediction, but their scalability remains limited for ultra-high-resolution, continent-scale domains required in real-world environmental monitoring. A single European air-quality map at 1 km resolution comprises 29 million pixels, far beyond the limits of naive self-attention. We introduce CRAN-PM, a dual-branch Vision Transformer that leverages cross-resolution attention to efficiently fuse global meteorological data (25 km) with local high-resolution PM2.5 at the current time (1 km). Instead of including physically driven factors like temperature and topography as input, we further introduce elevation-aware self-attention and wind-guided cross-attention to force the network to learn physically consistent feature representations for PM2.5 forecasting. CRAN-PM is fully trainable and memory-efficient, generating the complete 29-million-pixel European map in 1.8 seconds on a single GPU. Evaluated on daily PM2.5 forecasting throughout Europe in 2022 (362 days, 2,971 European Environment Agency (EEA) stations), it reduces RMSE by 4.7% at T+1 and 10.7% at T+3 compared to the best single-scale baseline, while reducing bias in complex terrain by 36%.
Figures & tables
Figure 1: CRAN-PM predicts daily PM 2.5 at 1 km resolution across Europe. (a) Full European prediction for January 25, 2022 (T+1 horizon). Red rectangles indicate zoom regions. (b–e) Regional details for Po Valley, Paris, Malmö, and Silesia. Colored circles represent independent EEA ground station measurements. Annual T+1 performance: RMSE = 5.99 µg/m 3 , r = 0.74.
Figure 2: Architecture of CRAN-PM. A global branch (top) encodes coarse meteorological fields with wind-guided token reordering and elevation-aware attention; a local branch (bottom) encodes high-resolution PM 2.5 subimages. Two wind-biased cross-attention layers fuse the branches (fine queries coarse). A PixelShuffle-based Upblock (red inset) reconstructs the residual. The yellow inset details elevation-aware attention.
Figure 3: Europe-wide PM 2.5 evaluation (2022). (a) GT (GHAP, 1 km), Jan. 25, 2022. (b) CRAN-PM T+1; inset: Po Valley. (c,d) RMSE across T+1–T+3 at 1 km and 25 km. CRAN-PM (red stars) consistently outperforms all baselines.
T+1 (24 h)
T+2 (48 h)
T+3 (72 h)
Method
Res.
#Param
RMSE ↓
MAE ↓
SSIM ↑
Δ (%)
RMSE ↓
MAE ↓
SSIM ↑
Δ (%)
RMSE ↓
MAE ↓
SSIM ↑
Δ (%)
Evaluated at 1 km resolution
CAMS † [ 13 ]
1 km
–
12.35
7.34
0.38
–
12.41
7.45
0.36
–
12.45
7.51
0.34
–
ConvLSTM [ 31 ]
25 km
8.2M
7.27
3.24
0.48
–
9.07
4.08
0.45
–
9.66
4.44
0.42
–
SimVP [ 11 ]
25 km
4.9M
7.22
3.27
0.51
–
8.93
4.05
0.48
–
9.51
4.40
0.45
–
Earthformer [ 12 ]
25 km
61M
7.34
3.31
0.49
–
9.24
4.14
0.46
–
9.83
4.50
0.44
–
Table 1: Quantitative comparison on European PM 2.5 prediction. Top : evaluated at 1 km (coarser methods bilinearly interpolated). Bottom : evaluated at 25 km (CRAN-PM spatially averaged). † : zero-shot. Bold : best. Underline : second best.
All Stations ( N = 2971)
Flat ( σz< 50 m, N = 2096)
Complex ( σz≥ 50 m, N = 875)
Method
RMSE ↓
MAE ↓
SSIM ↑
Bias
RMSE ↓
MAE ↓
SSIM ↑
Bias
RMSE ↓
MAE ↓
SSIM ↑
Bias
CAMS †
13.08
6.16
0.52
− 3.48
10.83
6.26
0.58
− 3.81
17.35
5.90
0.45
− 2.69
ConvLSTM [ 31 ]
11.94
4.96
0.68
− 1.14
9.18
4.96
0.72
− 1.04
16.80
4.95
0.58
− 1.39
SimVP [ 11 ]
11.91
4.97
0.70
− 1.14
9.14
4.97
0.73
− 1.05
16.79
4.97
0.60
− 1.37
Earthformer [ 12 ]
11.91
5.02
0.69
− 1.18
9.16
5.03
0.72
− 1.12
16.75
5.00
0.59
− 1.32
ClimaX [ 24 ]
11.97
5.02
0.67
− 1.13
9.22
5.01
0.71
− 1.00
16.79
5.04
0.57
− 1.44
Table 2: Validation against EEA ground monitoring stations (2022, T+1). Stations grouped by terrain complexity ( σz : elevation s.d. within 25 km radius). Bold : best. † : physical model.
Figure 4: Temporal PM 2.5 evolution (2022, T+1). Blue: GHAP; red: CRAN-PM. Six regions. CRAN-PM achieves lowest RMSE in all regions.
Figure 5: Regional PM 2.5 comparison at 1 km (T+1). Rows: Po Valley, Paris, Silesia, Rhine-Ruhr, London. (a) GT, (b) CAMS, (c) ClimaX, (d) CRAN-PM, (e) error (SSIM ≥ 0.63).
Coarse Branch
Cross-Scale Attn
Elev. Bias
Wind Scan/Bias
PixelShuffle Dec.
Delta Prediction
FFL ( λ=0.1 )
Station Loss ( λ=0.1 )
Day − 1 Context
Val RMSE ↓
Δ
(a) Cross-attention fusion design
Q
K/V
all other components fixed
(i)
No cross-attention
–
–
5.102
+ 0.150
(ii)
Feature addition
Sum
5.021
+ 0.069
(iii)
FiLM conditioning
Modul.
5.036
+ 0.084
(iv)
Concat + Self-Attn
Joint
5.040
+ 0.088
Table 3: Ablation study. (a) Cross-attention fusion strategy. (b) Progressive improvements. (c) Removal study. Val RMSE (µg/m 3 ) at T+1, 2022 European test set.
Figure 6: Ablation: progressive improvements at 1 km (T+1). (a) GT, (b) baseline (SSIM ≤ 0.34), (c) +FFL, (d) CRAN-PM full (RMSE = 4.95), (e) error.
Figure S1: CRAN-PM architecture overview. Left : naive 1 km processing is intractable ( ∼ 115 K tokens, ∼ 300 GB VRAM). Centre : dual-branch design with Global Branch (735 tokens, 25 km) and Local Branch (1,024 tokens/tile, 1 km), fused by Cross-Resolution Attention with wind bias. Right : full-domain output from 126 overlapping tiles with cosine blending ( < 2 GB/tile, ∼ 1.8 s).
Figure S2: Zero-shot transfer to USA/Canada (2022-09-18, wildfire episode). RMSE = 0.71 µg/m 3 overall; Oregon Cascades = 1.1, Idaho Rockies = 2.4, N. California = 1.1.
Figure S3: Zero-shot transfer to India (2022-03-17, IGP hotspot day). RMSE = 13.83 µg/m 3 overall; Delhi NCR = 22.4, Bihar/IGP = 24.4. IGP concentrations (up to 80 µg/m 3 ) are 3–5 × the European training range.
Figure S4: Annual mean scatter plots (2022) for both OOD regions. Left (USA/Canada): RMSE = 0.62, Bias = + 0.44, R2 = 0.938 ( n = 21.3M px); slope y=1.02x+0.3 confirms near-unity scaling. Right (India): RMSE = 7.88, Bias = − 3.27, R2 = 0.880 ( n = 5.6M px); systematic underestimation above 40 µg/m 3 .
Department of Earth, Environmental, and Atmospheric Sciences, Western Kentucky University, Bowling Green, KY, USA · NASA Goddard Space Flight Center, Greenbelt, MD, USA · The University of Texas at Austin, Austin, TX, USA +3
Department of Computational Engineering, Lappeenranta–Lahti University of Technology LUT, Finland · Atmospheric Modelling Centre Lahti, Lahti University Campus, Finland · Institute for Atmospheric and Earth System Research, University of Helsinki, P.O. Box 64, Helsinki 00014, Finland +2