AdaST: Adaptive Coupling for Spatial-Temporal Forecasting

Zhenyu Lei; Chenghao Liu; Yushun Dong; Qi R. Wang; Jundong Li

cs.AISep 28, 2026

AdaST: Adaptive Coupling for Spatial-Temporal Forecasting

Authors: Zhenyu Lei, Chenghao Liu, Yushun Dong, Qi R. Wang, Jundong Li

Organizations: University of Virginia Charlottesville, VA, USA · Datadog Paris, France · Florida State University Tallahassee, FL, USA · Northeastern University Boston, MA, USA

Abstract

Spatial-temporal (ST) forecasting underpins many real-world systems such as traffic, climate, and energy networks. While existing methods implicitly assume strong spatiotemporal coupling, we observe that real-world ST data exhibits distinct coupling regimes, ranging from temporal-dominated and spatial-dominated to strongly coupled patterns. This mismatch causes current models to suffer from spurious dependencies and degraded performance when one correlation dominates. To overcome this limitation, we aim to dynamically modulate spatial and temporal modeling based on the data's inherent coupling structure. However, three key challenges exist: unknown coupling structure, heterogeneous coupling dynamics, and suboptimal spatial modeling. We propose AdaST, an adaptive ST forecasting framework that tackles these challenges through a decompose-recompose paradigm. AdaST factorizes inputs into components capturing different coupling patterns using heterogeneity-aware experts. Each component is processed by role-aligned modules, and a correlation-informed adaptive recomposer integrates them for final prediction. Extensive experiments confirm that AdaST significantly outperforms state-of-the-art baselines, validating the necessity of an adaptive approach.

Figures & tables

Correlation	TD	SD	SC
Temporal	$\textbf{0.63}\pm 0.07$	$0.25\pm 0.01$	$0.54\pm 0.05$
Spatial	$-0.05\pm 0.06$	$\textbf{0.33}\pm 0.12$	$0.21\pm 0.02$

Table 1: Average temporal and spatial correlation coefficient in three synthetic datasets. Bold values indicate dominant correlations matching the intended coupling regime.

Figure 1 : Performance of different architectures on synthetic datasets with known coupling structures. Darker colors indicate lower normalized MAE.

Figure 2 : The overall framework of AdaST. Different colors denote different components.

Dataset	PurpleAir			PEMS04			PEMS07			PEMS08
Dataset	MAE	RMSE	MAPE	MAE	RMSE	MAPE	MAE	RMSE	MAPE	MAE	RMSE	MAPE
HI	$3.430$	$5.983$	$72.52\%$	$42.35$	$61.66$	$29.92\%$	$49.03$	$71.18$	$22.75\%$	$36.66$	$50.45$	$21.63\%$
DeepAR	$0.994$	$1.817$	$32.48\%$	$20.64$	$32.35$	$14.28\%$	$22.00$	$35.44$	$9.31\%$	$16.80$	$26.38$	$10.66\%$
NBeats	$\underline{0.511}$	$1.100$	$23.30\%$	$25.30$	$39.65$	$17.66\%$	$26.14$	$42.72$	$11.37\%$	$18.90$	$31.39$	$12.11\%$
GWNet	$0.514$	$\underline{1.012}$	$23.51\%$	$18.80$	$30.14$	$13.19\%$	$20.47$	$33.47$	$8.61\%$	$14.67$	$23.55$	$9.46\%$
DCRNN	$0.656$	$1.268$	$26.99\%$	$19.63$	$31.26$	$13.59\%$	$21.16$	$34.14$	$9.02\%$	$15.22$	$24.17$	$10.21\%$

Table 2 : Main results on PurpleAir and PEMS benchmarks. The best and second-best scores are highlighted in bold and underlined . AdaST achieves the best performance across all datasets.

Dataset	PurpleAir			PEMS07
Dataset	MAE	RMSE	MAPE	MAE	RMSE	MAPE
w/o $\mathbf{E_{n}}$	$0.519$	$1.072$	$23.79\%$	$19.44$	$32.84$	$8.49\%$
w/o $\mathbf{E_{h}}$	$\underline{0.495}$	$\underline{0.999}$	$\underline{22.50\%}$	$20.39$	$34.14$	$8.68\%$
w/o $\mathbf{E_{w}}$	$0.498$	$1.023$	$22.85\%$	$\underline{19.21}$	$\underline{32.63}$	$\underline{8.07\%}$
w/o $\mathbf{E_{a}}$	$0.516$	$1.075$	$23.47\%$	$20.16$	$33.23$	$11.26\%$
SpaAtt	$0.518$	$1.072$	$23.42\%$	$19.35$	$32.93$	$8.11\%$

Table 3: Ablation study on PurpleAir and PEMS07. Removing each component results in performance drop.

Figure 3 : Average gate scores of different datasets, revealing data-specific coupling structures.

Figure 4 : Gate scores across different time periods and locations, illustrating dynamic coupling.

Figure 5 : T-SNE visualization of learned representations for temporal (T), spatial (S), and spatial-temporal-coupling (ST) components, demonstrating clear separation and effective disentanglement.

Appendix figures & tables10 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 6 : Visualization of three synthetic datasets with distinct coupling structures: (a) Temporal-Dominated (TD), (b) Spatial-Dominated (SD), and (c) Strongly-Coupled (SC).

Figure 7 : Temporal correlation (ACF) analysis: TD data exhibits strong autocorrelation while SD data shows weak temporal dependencies.

Figure 8 : Spatial correlation (Pearson) analysis: SD data exhibits the strongest spatial dependencies while TD data shows negligible spatial correlation.

Model	PEMS04	PEMS07	PEMS08	PurpleAir
SpaMixer	$233$ s	$1154$ s	$141$ s	$66$ s
SpaAtt	$341$ s	$2160$ s	$220$ s	$134$ s
Speedup	$1.5\times$	$1.9\times$	$1.6\times$	$2.0\times$

Appendix

Table 4 : Average training time per epoch (seconds) comparing spatial mixer and spatial attention.

Method	ExchangeRate	ETTh1	METR-LA	PurpleAir	PEMS08	Avg. Rank
Method	MAE / Rank	MAE / Rank	MAE / Rank	MAE / Rank	MAE / Rank	Avg. Rank
PatchTST	0.073 / 1	$0.461$ / 4	$4.762$ / 5	$\underline{0.505}$ / 2	$22.07$ / 5	3.4
DLinear	$0.077$ / 3	$\underline{0.444}$ / 2	$4.820$ / 6	$0.525$ / 3	$22.51$ / 6	4.0
STID	$\underline{0.075}$ / 2	$0.466$ / 5	$3.146$ / 3	$0.563$ / 4	$14.21$ / 4	3.6
STNorm	$0.108$ / 5	$0.492$ / 6	$3.153$ / 4	$0.574$ / 5	$15.41$ / 3	4.6
HimNet	$0.124$ / 6	$0.458$ / 3	$\underline{3.131}$ / 2	$0.574$ / 5	$\underline{13.52}$ / 2	3.6

Appendix

Table 5 : Results on additional benchmarks. Best and second-best scores are in bold and underlined .

Variant	PEMS04			PEMS08
Variant	MAE	RMSE	MAPE	MAE	RMSE	MAPE
w/o $\mathbf{E_{n}}$	${18.45}$	${29.93}$	${12.76\%}$	${13.68}$	${23.37}$	${9.64\%}$
w/o $\mathbf{E_{h}}$	$18.58$	$30.15$	${12.42\%}$	${14.65}$	${23.94}$	${9.51\%}$
w/o $\mathbf{E_{w}}$	$\underline{18.35}$	$\underline{29.88}$	${12.68\%}$	${13.60}$	${23.36}$	${9.25\%}$
w/o $\mathbf{E_{a}}$	$18.36$	$29.96$	$\underline{12.23\%}$	${13.70}$	${23.70}$	${9.03\%}$
SpaAtt	18.28	$30.15$	${12.28\%}$	$\underline{13.51}$	$\underline{23.26}$	${9.03\%}$

Appendix

Table 6 : Ablation study on PEMS04 and PEMS08.

Figure 9 : Normalized correlation measures across datasets, further validating the adaptive recomposition mechanism. Strong correspondence with gate scores in Figure 3 confirms that correlation measures reliably reflect each component’s information content.

Figure 10 : Fine-grained temporal visualization (1-day span) of predictions and gate scores for 2 locations in PEMS07. More accurate predictions correspond to more dynamic gate score trajectories.

Figure 11 : Fine-grained temporal visualization (10-hour span) of predictions and gate scores for 2 locations in PEMS07. Location 0 achieves better accuracy alongside more adaptive gate score dynamics than location 1.

Figure 12 : Heatmap of gate scores across 160 spatial locations, showing a globally stable coupling structure with local variations that motivate the use of spatial heterogeneity experts.

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Spatio-Temporal Forecasting Kolmogorov-Arnold Networks Temporal Attention

Open paper AskPDF arXiv

Real-world traffic data exhibit heterogeneous spatial correlations and nonlinear temporal dynamics, posing substantial challenges for accurate spatio-temporal forecasting. Existing approaches have developed increasingly sophisticated graph, attention, and decomposition architectures, while the influence of the underlying nonlinear function approximator has received comparatively less attention. In this work, we propose STKAN, a spatio-temporal forecasting architecture that introduces Taylor-polynomial Kolmogorov--Arnold Network modules into spatial and temporal token mixing. STKAN first constructs high-level spatial representations through a learnable soft node-group assignment mechanism, applies group-wise spatial mixing, and subsequently models temporal dependencies over the compressed sequence. Spatial and temporal self-attention layers are further employed to capture long-range interactions. Experiments on five traffic forecasting benchmarks show that STKAN achieves competitive performance and performs better than the evaluated MLP-based variant in the tested settings. These results suggest that the design of nonlinear function approximators can serve as a useful complement to architectural design in spatio-temporal forecasting.

Abstract

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