Organizations: Peter L. Reichertz Institute for Medical Informatics, Hannover Medical School, Hannover, Germany · Lower Saxony Center for Artificial Intelligence and Causal Methods in Medicine (CAIMed), Hannover, Germany
Spatio-temporal processes often exhibit highly heterogeneous and non-intuitive responses to localized disruptions, limiting the effectiveness of conventional message passing approaches in modeling local heterogeneity. We reformulate spatio-temporal forecasting as the problem of learning information flow over locally structured spaces, rather than propagating globally aligned node representations. To this end, we introduce a spatio-temporal sheaf diffusion graph neural network (ST-Sheaf GNN) that embeds graph topology into sheaf-based vector spaces connected by learned linear restriction maps. Unlike prior approaches relying on static or globally shared transformations, our model learns dynamic restriction maps that evolve over time and adapt to local spatio-temporal patterns, enabling more expressive interactions. The proposed framework both theoretically guarantees and empirically demonstrates evidence that the proposed diffusion mechanism mitigates oversmoothing, preserving discriminative node representations even with increasing diffusion layer depth. Experiments on diverse real-world spatio-temporal forecasting benchmarks across multiple domains demonstrate state-of-the-art performance, highlighting the effectiveness of sheaf topological representations as a principled foundation for spatio-temporal graph learning. The code is available at: https://anonymous.4open.science/r/ST-SheafGNN-6523/.
Figures & tables
Figure 1.1 : Spatio-temporal traffic dynamics across three sensor nodes in PEMS dataset [ 20 ] . Node 2 exhibits a strong temporal correlation with the significant speed drop at Node 1, whereas Node 3, despite similar spatial proximity, remains unaffected.
Figure 3.1 : Overview of the proposed ST-Sheaf GNN. Multivariate time-series signals on a graph are first encoded with multi-head attention to capture temporal dependencies. The resulting representations are then projected into a sheaf space, where dynamic restriction maps are computed. Sheaf diffusion layers propagate information by preserving local distinct node representation. The diffused features are finally decoded by an MLP to produce node-level forecasts.
Figure 3.2 : Sheaf graph representation with learned dynamic restriction maps. Each node is associated with a vertex stalk, and each edge is associated with an edge stalk. Restriction maps define the relation between vertex stalks and edge stalks.
Data
Model
15min / horizon 3
30min / horizon 6
60min / horizon 12
MAE
RMSE
MAPE
MAE
RMSE
MAPE
MAE
RMSE
MAPE
NAVER-Seoul
ARIMA [ 20 ]
5.51
8.15
15.33
6.11
9.22
18.45
7.85
12.23
22.16
STGCN [ 29 ]
4.63
6.92
14.49
5.50
8.83
17.37
6.77
10.89
20.42
DCRNN [ 20 ]
4.86
7.12
15.35
5.67
8.80
18.38
6.40
10.06
21.09
GW-Net [ 27 ]
4.91
7.24
14.86
5.26
8.13
16.16
5.55
8.77
16.97
GMAN [ 30 ]
5.20
8.32
16.98
5.35
8.67
17.47
5.48
8.94
17.89
Table 5.1: Performance on NAVER-Seoul Dataset and METR-LA dataset.
Model
Molene (weather)
Air Quality (PM2.5)
PEMS04
PEMS08
step-1
step-2
step-3
step-4
step-5
1-12 h
13-24 hr
25-48 hr
MAE
RMSE
MAPE
MAE
RMSE
MAPE
ARIMA [ 20 ]
0.445
0.750
1.041
1.327
1.592
30.14
38.98
44.10
33.73
48.80
24.18
31.09
44.32
22.73
STGCN [ 29 ]
1.066
1.552
1.933
2.225
2.698
22.77
31.59
35.59
22.70
35.55
14.59
18.02
27.83
11.40
DCRNN [ 20 ]
0.396
0.635
0.907
1.164
1.419
24.28
32.95
36.11
24.70
38.12
17.12
17.86
27.83
11.45
GW-Net [ 27 ]
0.855
1.124
1.455
1.865
2.104
22.42
30.29
34.73
25.45
39.70
17.29
19.13
31.05
12.68
GMAN [ 30 ]
0.962
1.424
1.882
2.022
2.417
24.11
32.80
36.25
20.23
32.17
17.06
16.47
25.72
10.48
Table 5.2: Performance on Molene weather, Air Quality in MAE and PEMS04, PEMS08 traffic datasets.
Figure 5.1 : Case study of spatiotemporal dependency modeling on METR-LA test set: A congestion event originating at sensor 36 propagates to affect sensor 62 afterwards. The ST - Sheaf model captures this cascade effect in the prediction, while baseline methods fail to predict the induced slowdown.
Figure 5.2 : Oversmoothing Analysis: ST-Sheaf GNN diffusion vs. traditional GCN diffusion. The y-axis is the average Euclidean Distance of hidden representation between Connected nodes at each layer.
Dataset (Graph Size)
CITRUS
STDN
ST-Sheaf
Time (s)
#Parameters
Time (s)
#Parameters
Time (s)
#Parameters
PEMS08 (N=170)
114.0
85,951
240.1
5,876,387
28.5 ↓
39,554 ↓
METR-LA (N=207)
114.1
86,743
419.6
5,971,107
40.9 ↓
40,738 ↓
PEMS04 (N=307)
116.2
90,335
649.3
6,227,107
53.2 ↓
43,938 ↓
NAVER-Seoul (N=774)
231.7
105,279
833.1
7,422,627
149.2 ↓
58,882 ↓
Table 5.3: Number of model parameters, model scalability with respect to graph size N , and training time per epoch for different datasets compared to the most state-of-the-art methods: CITRUS (NeurIPS 2024), STDN (AAAI 2025).
Stalk Dim
Epoch Time (s)
#Parameters
MAE
d=1
0.358
15490
1.533
d=4
0.369
17002
1.418
d=8
0.392
19410
1.378
d=16
0.453
25570
1.370
d=32
0.608
43266
1.362
d=64
0.864
100162
1.361
Table 5.4 : Effect of stalk dimension (d) on performance and efficiency on Molene dataset, horizon 5, temporal heads=4, sheaf layers=2.
Dataset
Component
H1
H2
H3
METR-LA
Static restriction Maps
2.75
3.04
3.38
W/o Sheaf Diffusion
3.05
3.57
4.44
W/o Temporal Encoding
2.61
2.98
3.30
ST-Sheaf (Full Model)
2.56
2.96
3.25
Molene
Static restriction Maps
0.44
0.92
1.46
W/o Sheaf Diffusion
0.56
1.13
1.62
Table 5.5 : Ablation Studies on the effect of each of the model components on different datasets in MAE. For Molene, we select (step-1, 3, 5 as H1, H2, H3).
METR-LA
NAVER-Seoul
PEMS04
PEMS08
Molene
AirQuality
Spatial Units
207
774
307
170
32
437
Timesteps
34,272
26,208
16992
17856
744
8760
Sampling Time
5 minutes
5 minutes
5 minutes
5 minutes
1 hour
1 hour
Start Time
03.2012
09.2020
01.2018
07.2016
01.2014
05.2014
End Time
06.2012
12.2020
02.2018
08.2016
01.2014
04.2015
Region
Los Angeles
Seoul
Bay Area
San Bernardino
Brest (France)
43 Chinese cities
Table C.1 : Summary of datasets characteristics.
Figure D.1 : Forecasting error (MAE) across increasing prediction horizons on METR-LA, NAVER-Seoul, and Air Quality datasets. ST-Sheaf exhibits slower error accumulation over longer horizons compared to strong baselines.