Organizations: Department of Computer & Information Science & Engineering, University of Florida · Department of Computer Science, University of Kentucky
Traffic forecasting uses recent measurements by sensors installed at chosen locations to forecast the future road traffic. Existing work either assumes all locations are equipped with sensors or focuses on short-term forecast. This paper studies partial sensing forecast of long-term traffic, assuming sensors are available only at some locations. The problem is challenging due to the unknown data distribution at unsensed locations, the intricate spatio-temporal correlation in long-term forecasting, as well as noise to traffic patterns. We propose a Spatio-temporal Long-term Partial sensing Forecast model (SLPF) for traffic prediction, with several novel contributions, including a rank-based embedding technique to reduce the impact of noise in data, a spatial transfer matrix to overcome the spatial distribution shift from sensed locations to unsensed locations, and a multi-step training process that utilizes all available data to successively refine the model parameters for better accuracy. Extensive experiments on several real-world traffic datasets demonstrate its superior performance. Our source code is at https://github.com/zbliu98/SLPF
Figures & tables
Figure 1: Flow rates of three locations for two days
Figure 2: Noise has the greatest impact on GinAR for long-term partial sensing than for long-term full sensing, which is in turn more sensitive to noise than traditional short-term full sensing.
Figure 3: The model training phase consists of three steps above. After the model is trained and deployed, only XM,T is collected for input, and XM′,T′ is output.
Dataset
PEMS03
PEMS04
PEMS08
PEMS-BAY
METR-LA
Area
in CA, USA
Time Span
9/1/2018 -
1/1/2018 -
7/1/2016 -
1/1/2017 -
3/1/2012 -
11/30/2018
2/28/2018
8/31/2016
5/31/2017
6/30/2012
Time Interval
5 min
Number of Locations, n
358
307
170
325
207
Number of Time Intervals
26,208
16,992
17,856
52,116
34,272
Table 1: Basic statistics of the datasets used in our experiments.
Models
PEMS03
PEMS04
PEMS08
PEMSBAY
METRLA
m′=250,m′/n=69%
m′=250,m′/n=81%
m′=150,m′/n=88.2%
m′=250,m′/n=76.9%
m′=150,m′/n=72.4%
MAE
RMSE
MAPE
MAE
RMSE
MAPE
MAE
RMSE
MAPE
MAE
RMSE
MAPE
MAE
RMSE
MAPE
Matrix Factorization ( Lee and Seung, 2000 )
69.01
110.17
135.41
91.38
150.09
129.65
76.01
132.64
85.13
6.25
15.63
20.21
16.72
34.21
49.83
PatchTST* ( Nie et al., 2022 )
57.71
86.33
103.23
58.28
86.15
54.99
43.90
64.68
28.59
4.58
8.66
12.50
11.67
21.81
26.86
iTransformer* ( Liu et al., 2023b )
67.31
103.07
127.88
87.44
125.04
99.1
69.81
91.03
61.24
5.13
9.60
15.62
13.65
22.58
27.51
D2STGNN* ( Shao et al., 2022c )
37.31
61.1
45.69
47.29
75.41
48.98
47.37
67.4
35.2
6.62
10.94
15.52
14.93
27.25
42.33
Table 2: Performance comparison over five datasets, where n is the total number of locations and m′ is the number of unsensed locations. A baseline model with suffix * is the model adapted for the partial sensing task. Our models are in bold at the bottom.
Method
MAE
RMSE
MAPE
SLPF
16.58
29.22
17.85
LPF (1 step, see Fig. 3 , from XM,T to XM′,T′ )
18.47
32.08
18.83
2 Step (from XM,T to XM′,T , then from XM,T , XM′,T to XM′,T′ )
17.24
30.18
18.06
Plain Spatial Transfer Matrix
17.80
32.35
17.87
No Spatial Transfer Matrix
17.76
32.35
17.85
No Rank-based Node Embedding
17.39
31.95
17.89
Table 3: Different ablation methods under weighted selection and m′=50 condition on PEMS08 dataset over the average horizon.
Figure 4: Visualization on different locations when our model with or without ranking embedding.
Figure 5: Performance comparison with varying γ under Gaussian noise on PEMS08 dataset.
Figure 6: Performance comparison with varying γ under Uniform noise on PEMS08 dataset.
Figure 7: Performance comparison with varying γ under Laplace noise on PEMS08 dataset.
Figure 8: Comparing our model SLPF with the baselines in training efficient, in the context of accuracy-efficiency tradeoff, on dataset PEMS08, with weighted selection and m′=50 .
Figure 9: Improvement of SLPF over its variant without rank in bins of 5% forecasts with descending MAE, on dataset PEMS08 dataset with weighted selection and m′=50 .
Figure 10: Accuracy comparison in terms of RMSE with respect to the number of unsensed locations under different selection methods on PEMS08 dataset.
Models
PEMS08
MAE
RMSE
MAPE
STID ( Shao et al., 2022a )
19.59
32.20
13.05
PDFormer ( Jiang et al., 2023a )
18.58
31.86
12.64
STAEFormer ( Liu et al., 2023a )
18.77
32.73
12.10
TESTAM ( Lee and Ko, 2024 )
18.90
32.81
12.45
MegaCRN ( Jiang et al., 2023b )
19.99
33.67
13.09
Table 4: Performance comparison on PEMS08 dataset among the full-sensing baselines with the hypothetical assumption that they have the knowledge of the unsensed locations. The best results are in bold.
Figure 11: Accuracy comparison in terms of RMSE with respect to different forecasting lengths on PEMS08 dataset with the random selection method and the number of unsensed location being m′=50 .
Figure 12: Impact of number of unsensed locations on forecast accuracy (RMSE) of SLPF when it is with or without rank-based node embedding, on PEMS08 dataset with weighted selection.
Figure 13: Parameter sensitivity of the proposed SLPF on the average horizon of PEMS08 with weighted selection and m′=150 .
Spatio-temporal traffic forecasting is a core component of intelligent transportation systems, supporting various downstream tasks such as signal control and network-level traffic management. In real-world deployments, forecasting models must operate under structural and observational uncertainties, conditions that are rarely considered in model design. Recent approaches achieve strong short-term predictive performance by tightly coupling spatial and temporal modeling, often at the cost of increased complexity and limited modularity. In contrast, efficient time-series models capture long-range temporal dependencies without relying on explicit network structure. We propose UniST-Pred, a unified spatio-temporal forecasting framework that first decouples temporal modeling from spatial representation learning, then integrates both through adaptive representation-level fusion. To assess robustness of the proposed approach, we construct a dataset based on an agent-based, microscopic traffic simulator (MATSim) and evaluate UniST-Pred under severe network disconnection scenarios. Additionally, we benchmark UniST-Pred on standard traffic prediction datasets, demonstrating its competitive performance against existing well-established models despite a lightweight design. The results illustrate that UniST-Pred maintains strong predictive performance across both real-world and simulated datasets, while also yielding interpretable spatio-temporal representations under infrastructure disruptions. The source code and the generated dataset are available at https://anonymous.4open.science/r/UniST-Pred-EF27
Traffic prediction is difficult due to the complex interplay of temporal evolution, spatial interactions, and delayed spatio-temporal propagation over road networks. Existing methods either model spatial and temporal dependencies separately or employ unified spatio-temporal structures, but they often insufficiently characterize how neighboring sensors at historical timestamps influence a target node, while complex joint models may incur high computation. This paper proposes STEI-PCN, an efficient pure convolutional network based on spatio-temporal encoding and relation inference. It first builds a local causal joint spatio-temporal graph to restrict candidate interactions, then uses absolute position and relative distance encodings to infer dynamic edge weights. A single-layer graph convolution with a position-aware gated activation unit captures local joint dependencies, and temporal dilated causal convolutions complement long-range temporal patterns. A multi-view prediction module fuses raw, local propagation, and long-range temporal representations for direct multi-step forecasting. Experiments on PeMS03, PeMS04, PeMS07, PeMS08, and PeMS-Bay under multiple horizons show that STEI-PCN achieves competitive accuracy with moderate parameters and low training and inference costs. Ablation and fluctuation analyses further verify the contributions of the main components and empirically analyze the effects of the training-stage constraints under sharp speed changes. Our code is available at a GitHub link https://github.com/Jessez2/STEI-PCN.
Zhifeng Hao, Kai Hu, Juncai Zhang +2
School of Cyberspace Security, Hainan University, Haikou, China
Traffic forecasting is a fundamental component of intelligent transportation systems, yet remains challenging in real-world settings due to irregular sensor distributions and the high computational cost of modeling large-scale spatiotemporal dependencies. In practical traffic networks, sensors are unevenly distributed across regions, leading to non-uniform spatial structures that limit the effectiveness and scalability of existing graph-based and attention-based models. To address these challenges, we propose PatchSTG, a patch-based spatiotemporal graph Transformer designed for efficient forecasting on irregular sensor networks. The key idea is to introduce a hierarchical spatial representation that partitions sensors into balanced, locality-preserving patches based on geographic information. On top of this structure, a dual attention encoder alternates between intra-patch attention for capturing local interactions and inter-patch attention for modeling global dependencies, reducing computational complexity from quadratic to near-linear scaling. We evaluate PatchSTG on real-world traffic data from Rhode Island and additional large-scale datasets. Experimental results demonstrate that the proposed model achieves stable and competitive forecasting performance across multiple horizons, while significantly improving computational efficiency. Ablation studies further validate the effectiveness of spatial partitioning and dual attention in capturing both local and long-range traffic dynamics. These results suggest that patch-based spatiotemporal modeling provides a scalable and effective framework for traffic forecasting under irregular spatial settings.
Jichao Li, Xuanming Shi
Portsmouth Abbey School · CodingFuture (Shanghai) Education Technology Co., Ltd.