VaryST: Generalizable Spatio-Temporal Forecasting Beyond the Closed-World Setting

Shengnan Guo; Jinjun Cheng; Xiaowei Mao; Jianhao Zhang; Haochen Lv; Yang Jiang; YiHeng Huang; Yan Lin

cs.LGOct 14, 2026

VaryST: Generalizable Spatio-Temporal Forecasting Beyond the Closed-World Setting

Authors: Shengnan Guo, Jinjun Cheng, Xiaowei Mao, Jianhao Zhang, Haochen Lv, Yang Jiang, YiHeng Huang, Yan Lin,

Organizations: School of Computer Science and Technology, Beijing Jiaotong University, Beijing, China · Key Laboratory of Big Data & Artificial Intelligence in Transportation, Ministry of Education, Beijing, China · Department of Computer Science, Aalborg University, Aalborg, Denmark · Beijing Key Laboratory of Traffic Data Mining and Embodied Intelligence, Beijing, China

Abstract

Spatio-temporal forecasting is fundamental to many real-world systems, yet deployment environments are inherently varying: temporal distributions may evolve, spatial domains may change, and observation availability may shift from training conditions. Existing models are often tightly coupled to their training environments through node-specific representations, predefined spatial support sets, and reliance on consistently available observations, limiting generalization to changing environments. To this end, we propose VaryST, a compact spatio-temporal forecasting model trained from scratch that achieves strong generalization by dynamically constructing predictive context from available long-term observations. To accommodate temporal changes, VaryST derives node representations from long-term histories, capturing current behavior in the context of longer-term patterns. To adapt to spatial changes, it dynamically selects functionally relevant support nodes beyond predefined neighborhoods and integrates their information with recent and long-term target states and global context. To handle varying observation availability, VaryST selectively masks historical patches on which the model relies most during training, encouraging it to exploit alternative temporal and spatial dependencies for accurate forecasting when key observations become unavailable. Extensive experiments on six real-world datasets against seventeen baselines show that VaryST achieves strong in-domain forecasting accuracy, substantially improves zero- and few-shot generalization under spatial and temporal changes, and remains robust to varying observation availability.

Figures & tables

Figure 1: ST models in varying deployment environments

Figure 2: The architecture of VaryST. It contains Long-term Observation-derived Representations, Dynamic Functional Support Node Retrieval, and Target-centric Hierarchical Contextual Decoding.

Dataset	Nodes	Time Span	Interval	Usage
PEMS03	358	09/01/2018 – 11/30/2018	5 min	RQ1/3/5/6
PEMS04	307	01/01/2018 – 02/28/2018	5 min	RQ1/3/4
PEMS07	883	05/01/2017 – 08/31/2017	5 min	RQ1/3/7
PEMS08	170	07/01/2016 – 08/31/2016	5 min	RQ1/3/4/5/6
PM2.5	12	03/01/2013 – 02/28/2017	60 min	RQ1
PEMSD3-Stream	655	2011 – 2017	5 min	RQ2

Table 1: Dataset statistics.

Models with Short-term History (Input Horizon = 12)
Model	PEMS03			PEMS04			PEMS07			PEMS08
Model	MAE	RMSE	MAPE	MAE	RMSE	MAPE	MAE	RMSE	MAPE	MAE	RMSE	MAPE
ASTGCN	17.85	29.88	17.65%	22.42	34.75	15.87%	25.98	39.65	11.84%	18.86	28.55	12.50%
AGCRN	15.98	28.25	15.23%	19.83	32.26	12.97%	22.37	36.55	9.12%	15.95	25.22	10.09%
SSTBAN	15.90	26.11	17.27%	18.88	31.10	12.56%	20.17	33.45	8.93%	14.39	24.19	10.06%
PDFormer	14.74	25.59	15.35%	18.31	29.97	12.10%	19.83	32.87	8.53%	13.58	23.51	9.05%

Table 2: Overall prediction performance comparison on four PEMS datasets. Models are categorized into short-term, LLM based and long-term groups. Bold : best, underline : second best.

Model	MAE	RMSE	MAPE
ASTGCN	27.42	48.70	52.4%
AGCRN	28.20	49.57	50.1%
SSTBAN	30.22	53.13	53.1%
PDFormer	26.65	47.08	51.5%
iTransformer	29.56	51.80	55.9%
STD-PLM	27.55	48.88	53.3%

Table 3: Performance comparison on PM2.5.

Panel of Figure 3 — Figure 3: Distribution-shift robustness of VaryST.

Panel of Figure 4 — Figure 4: Ablation, hyperparameter and efficiency studies.

Appendix figures & tables11 assets

Supplementary material from the paper’s appendix.

Appendix

Year	Nodes	Time Span	Interval
2011	655	07/10/2011 – 08/31/2011	5 min
2012	715	07/10/2012 – 08/31/2012	5 min
2013	786	07/10/2013 – 08/31/2013	5 min
2014	822	07/10/2014 – 08/31/2014	5 min
2015	834	07/10/2015 – 08/31/2015	5 min
2016	850	07/10/2016 – 08/31/2016	5 min

Appendix

Table 4: Per-year statistics of PEMSD3-Stream.

Hyperparameter	Description	Value or Choices
sample_len	Input history length $T$	2016 (168 on PM2.5)
output_len	Prediction horizon $Q$	12
unit_len	Patch length $L_{p}$	36 (12 on PM2.5)
train_ratio / val_ratio	Chronological train/validation split	0.6 / 0.2
token_dim	Temporal Patch Token dimension $d$	96
emb_dim	backbone dim $D$	96

Appendix

Table 5: Default hyperparameters for the VaryST framework.

Model	MAE	RMSE	MAPE
STOP	13.01	22.44	16.91%
STD-PLM	14.40	25.06	18.55%
VaryST	10.49	18.22	14.05%

Appendix

Table 6: Average Zero-shot performance on PEMSD3-Stream.

Year	VaryST			STOP			STD-PLM
Year	MAE	RMSE	MAPE	MAE	RMSE	MAPE	MAE	RMSE	MAPE
2011	10.64	16.47	13.84	12.34	18.96	16.12	11.96	18.28	16.21
2012	9.97	16.00	13.65	11.86	18.87	16.16	13.54	22.57	17.77
2013	10.01	16.68	13.60	12.27	20.05	16.26	14.24	24.16	18.23
2014	10.61	17.39	14.80	13.24	22.07	17.96	14.62	24.73	19.78
2015	10.55	17.80	14.53	12.99	22.40	17.22	14.32	24.97	18.87

Appendix

Table 7: Year-by-year performance on PEMSD3-Stream. 2011: In-Domain Reference

Model	Source	Target
Model	Source	PEMS03	PEMS04	PEMS07	PEMS08
VaryST	PEMS03	13.95 / 22.73 / 13.59	18.51 / 30.40 / 12.84	20.02 / 32.72 / 8.88	13.81 / 22.70 / 9.31
	PEMS04	14.03 / 22.77 / 13.44	17.56 / 29.35 / 11.81	19.91 / 32.64 / 8.48	13.97 / 22.92 / 9.07
	PEMS07	13.78 / 22.32 / 13.24	18.15 / 29.98 / 12.54	18.21 / 31.05 / 7.64	13.46 / 22.44 / 8.86
	PEMS08	14.88 / 24.45 / 14.61	18.80 / 30.90 / 13.19	19.53 / 32.65 / 8.54	12.89 / 21.99 / 8.50
STD-PLM	PEMS03	14.52 / 24.69 / 14.87	30.90 / 49.01 / 20.88	34.79 / 52.85 / 20.27	25.83 / 39.86 / 25.03

Appendix

Table 8: Zero-shot cross-dataset transfer (12-step prediction). Rows: source dataset used for full training; columns: target dataset evaluated on. Diagonal cells are the in-domain (IID) baselines. Each cell: MAE / RMSE / MAPE (%).

Source: PEMS03
Model	Target	1%			5%			10%
Model	Target	MAE	RMSE	MAPE (%)	MAE	RMSE	MAPE (%)	MAE	RMSE	MAPE (%)
VaryST	PEMS04	18.39	30.39	12.60	18.04	29.93	12.33	17.91	29.78	12.19
	PEMS07	19.16	32.03	8.16	18.60	31.48	7.85	18.63	31.50	7.85
	PEMS08	13.50	22.54	8.91	13.26	22.31	8.75	13.17	22.21	8.69
STD-PLM	PEMS04	46.75	74.69	22.00	24.45	38.70	16.19	23.38	37.08	15.54

Appendix

Table 9: Few-shot cross-dataset transfer (12-step prediction) with 1%, 5% and 10% of the target training data. Each cell: MAE / RMSE / MAPE (%).

Model	10%			30%			50%			70%
Model	MAE	RMSE	MAPE (%)	MAE	RMSE	MAPE (%)	MAE	RMSE	MAPE (%)	MAE	RMSE	MAPE (%)
PEMS04 Point Missing (RM)
FaST †	18.67	30.29	12.89	18.74	30.37	13.01	18.87	30.50	13.05	19.17	30.78	13.14
STID †	18.34	29.92	13.09	18.38	29.98	12.84	18.53	30.20	12.99	18.75	30.40	13.41
BiST †	18.47	29.94	12.88	18.53	29.94	13.25	18.53	30.10	13.22	19.00	30.42	13.69
VaryST	17.60	29.34	11.90	17.40	29.20	11.74	17.47	29.28	11.80	17.70	29.39	11.93

Appendix

Table 10: Overall prediction performance with missing observations on PEMS04 and PEMS08 under missing rates from 10% to 70%. The best and second-best results are in bold and underline , respectively.

Model	10%			30%			50%			70%
Model	MAE	RMSE	MAPE (%)	MAE	RMSE	MAPE (%)	MAE	RMSE	MAPE (%)	MAE	RMSE	MAPE (%)
PEMS04 Point Missing (RM), source = 30%
FaST †	18.69	30.31	12.97	18.74	30.37	13.01	18.88	30.59	13.09	19.22	30.97	13.39
STID †	18.32	29.91	12.80	18.38	29.98	12.84	18.53	30.19	12.91	18.91	30.62	13.19
BiST †	18.49	29.90	13.22	18.53	29.94	13.25	18.66	30.12	13.32	18.98	30.12	13.57
VaryST	17.60	29.35	12.07	17.40	29.20	11.74	17.55	29.38	11.73	18.28	30.12	12.34

Appendix

Table 11: Generalization to unseen missing rates on PEMS04 and PEMS08. Models are trained at a 30% missing rate.

Model	PEMS04						PEMS08
Model	RM $\rightarrow$ CM			CM $\rightarrow$ RM			RM $\rightarrow$ CM			CM $\rightarrow$ RM
	MAE	RMSE	MAPE (%)	MAE	RMSE	MAPE (%)	MAE	RMSE	MAPE (%)	MAE	RMSE	MAPE (%)
FaST †	20.32	32.40	15.19	19.89	32.16	13.62	16.00	26.00	11.87	14.71	24.13	10.46
STID †	19.96	32.14	14.71	19.06	31.41	13.13	15.33	24.85	11.28	14.02	22.95	9.80
BiST †	20.02	31.87	15.06	18.98	30.86	13.38	15.63	25.06	12.33	14.42	23.37	10.31
VaryST	19.51	31.94	13.96	18.40	30.23	12.75	15.00	24.93	10.43	14.14	23.15	9.36

Appendix

Table 12: Cross-pattern generalization at 30% missing rate on PEMS04 and PEMS08.

Variant	PEMS03				PEMS08
Variant	MAE	RMSE	MAPE	MAPE 10	MAE	RMSE	MAPE	MAPE 10
VaryST (full)	13.95	22.73	13.59	11.00	12.89	21.99	8.50	7.29
w/o Laplacian PE	14.13	23.02	13.47	11.04	12.91	22.00	8.57	7.31
w/o Hop-RoPE	14.42	23.75	13.93	11.40	12.93	22.07	8.56	7.32
w/o structural encoding	14.10	23.05	13.55	11.11	12.92	22.06	8.54	7.30
w/o recent-12 token	14.10	23.00	13.35	10.99	12.86	21.97	8.47	7.29

Appendix

Table 13: Ablation study of each component on PEMS03 and PEMS08 (12-step prediction).

Input context length
Setting	PEMS03			PEMS08
Setting	MAE	RMSE	MAPE	MAE	RMSE	MAPE
36	15.30	24.37	14.88	14.78	24.91	9.67
288	14.26	23.08	13.87	13.60	22.79	9.02
864	14.31	23.37	13.65	13.40	22.53	8.90
2016 (default)	13.95	22.73	13.59	12.89	21.99	8.50

Appendix

Table 14: Hyperparameter study on PEMS03 and PEMS08. The best and second-best results are in bold and underline , respectively.

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