SSP-DMGTimeNet: Physics-Constrained Learning for Spatiotemporal Trajectory Prediction of Vehicle Platoons

Yuhang Wang; Kailang Ma; Zirui Li; Mingfeng Fan; Kitae Jang; Changju Lee; Heye Huang

cs.AISep 7, 2026

SSP-DMGTimeNet: Physics-Constrained Learning for Spatiotemporal Trajectory Prediction of Vehicle Platoons

Authors: Yuhang Wang, Kailang Ma, Zirui Li, Mingfeng Fan, Kitae Jang, Changju Lee, Heye Huang

Organizations: Cho Chun Shik Graduate School of Mobility, Korea Advanced Institute of Science & Technology (KAIST), Daejeon 34051, Republic of Korea. · Chinese Academy of Sciences, Beijing 100864, China. · School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore. · Department of Mechanical Engineering, National University of Singapore, Singapore 119077, Singapore.

Abstract

Existing car-following prediction methods mainly optimize trajectory accuracy, while rarely considering whether predicted disturbances propagate realistically along a vehicle platoon. This limitation may lead to accurate but string-unstable predictions. We propose SSP-DMGTimeNet, a physics-constrained learning framework for spatiotemporal trajectory prediction of vehicle platoons. The model combines multi-scale temporal representations with cross-vehicle interaction features to capture complex and time-varying platoon dynamics. A propagation-delay-aware causal attention mechanism explicitly models upstream-to-downstream disturbance propagation by learning response delays between adjacent vehicles and accumulating them along the platoon. In addition, time- and frequency-domain string-stability losses relieve disturbance amplification across both adjacent vehicles and arbitrary sub-platoons during training. Experiments on HighD show that SSP-DMGTimeNet achieves an unstable-window rate of 0.65% for five-vehicle platoons and a maximum head-to-tail amplification of 0.898 on the ground-truth excitation subset, while maintaining competitive trajectory prediction performance. In zero-shot evaluation on NGSIM US-101 and I-80, the model achieves velocity MAEs of 1.316~~m/s and 1.252~~m/s, with unstable-window rates of 3.90% and 4.10%, respectively. These results demonstrate that incorporating platoon-level physical constraints can effectively balance trajectory prediction accuracy and disturbance propagation stability.

Figures & tables

Figure 1: Illustration of disturbance propagation in a vehicle platoon. A small braking disturbance is introduced by the leading vehicle $\mathrm{V}_{1}$ and propagates backward to the following vehicles. In a string-stable platoon, the disturbance-response amplitude attenuates along the vehicle chain; in a string-unstable platoon, it is progressively amplified, potentially resulting in larger speed fluctuations and reduced inter-vehicle gaps.

Figure 2: Overview of SSP-DMGTimeNet. The framework consists of four main components: multi-scale temporal token extraction, Hierarchical Gated Fusion (HGF), Cross-Vehicle Cointegration Feature Extraction (CFE), and Sequence Propagation Delay-Aware Causal Attention (SP-DACA).

Figure 3: Architecture of the proposed SP-DACA, which integrates a learned propagation-delay bias with a joint temporal–vehicle causal mask. The delay-centered Gaussian kernel emphasizes upstream states consistent with the expected disturbance-propagation delay.

Model	$v$ -MAE $\downarrow$	$v$ -RMSE	$s$ -MAE	$s$ -RMSE	$a$ -MAE	$a$ -RMSE	Tail $v$ -MAE	Unstable windows (%) ∗
Int-LSTM	0.102	0.158	0.262	0.374	0.068	0.115	0.114	91.30
Transformer	0.158	0.215	0.399	0.544	0.079	0.128	0.170	85.71
Full-graph Attention	0.164	0.225	0.306	0.447	0.081	0.130	0.169	84.62
LSTM	0.213	0.282	0.511	0.728	0.074	0.118	0.209	95.12
IDM cascade †	0.366	0.543	0.446	0.733	0.315	0.446	0.365	—
CNN-Int-LSTM-IDM	0.564	0.815	0.633	1.030	0.254	0.561	0.543	88.89

Table 1: Trajectory prediction performance on the HighD test set.

Model	Unstable (%) ∗	Max. amp. ∗	Exceedance area ∗	Valid windows ∗	GT unstable (%)	GT max. amp.	GT valid windows	RMS jerk
Int-LSTM	91.30	2.865	12.794	23	88.89	2.865	18	0.125
Transformer	85.71	2.735	20.277	28	83.33	2.735	24	0.107
Full-graph Attention	84.62	3.529	15.752	26	86.36	3.529	22	0.106
LSTM	95.12	3.240	11.625	41	100.00	3.240	11	0.121
IDM cascade †	—	—	—	0	—	—	0	0.572
CNN-Int-LSTM-IDM	88.89	7.253	27.744	18	93.33	7.253	15	2.727

Table 2: Platoon-level stability on the HighD test set under the per-model and GT-excitation criteria.

Model	$v$ -MAE $\downarrow$	Tail $v$ -MAE	Unstable (%) ∗	GT-subset unstable (%)	GT-subset max. amp.	GT-subset valid/3665	RMS jerk
Int-LSTM	3.343	3.252	96.10	96.08	16.581	3396	1.037
Transformer	1.340	1.241	95.61	95.49	9.235	1243	0.505
Full-graph Attention	1.321	1.190	90.69	90.87	10.022	1238	0.479
LSTM	2.333	1.962	88.72	88.55	6.359	3512	0.668
IDM cascade †	0.811	0.798	—	—	—	0	0.118
CNN-Int-LSTM-IDM	1.286	1.183	92.74	92.77	390152.344	1507	1.288

Table 3: Zero-shot evaluation on NGSIM US-101 using models trained on HighD.

Model	$v$ -MAE $\downarrow$	Tail $v$ -MAE	Unstable (%) ∗	GT-subset unstable (%)	GT-subset max. amp.	GT-subset valid/3485	RMS jerk
Int-LSTM	3.721	3.823	96.27	96.21	20.399	3142	1.028
Transformer	1.277	1.247	97.33	97.29	8.499	921	0.504
Full-graph Attention	1.256	1.182	88.71	88.54	9.407	960	0.474
LSTM	2.148	1.735	87.52	86.83	5.004	3310	0.644
IDM cascade †	0.781	0.811	—	—	—	0	0.178
CNN-Int-LSTM-IDM	1.108	1.049	93.95	93.99	262334.781	1298	1.363

Table 4: Zero-shot evaluation on NGSIM I-80 using models trained on HighD.

Figure 4: Performance under different platoon lengths ( $N=3,5,6,7$ ): (a) unstable-window rate, (b) velocity MAE, and (c) maximum amplification on the GT-excitation subset.

Variant	$v$ -MAE	Unstable (%) ∗	Max. amp. ∗	Exceedance area ∗	Max. freq. gain	GT unstable (%)	GT max. amp.
SSP (full)	0.347	0.65	1.457	1.237	2.165	0.00	0.898
Full graph	0.372	0.49	1.256	0.705	2.593	0.00	0.926
Fixed $\tau$	0.375	0.97	1.244	1.375	2.037	1.61	1.101
No delay bias	0.382	0.38	1.328	0.680	2.111	0.00	0.896
No CFE	0.385	0.22	1.184	0.270	1.832	0.00	0.936
No HGF	0.371	0.60	1.306	1.170	3.746	1.61	1.036

Table 5: Ablation results on HighD with stability evaluated on 62 GT-excitation windows.

Figure 5: Learned propagation delays in SP-DACA. The red dashed line indicates the initialization midpoint of 1.40 s, and the shaded region denotes the physically plausible range of 0.8–1.2 s.

Figure 6: Consistency between ground-truth and predicted propagation delays. The dashed line $y=x$ indicates ideal recovery.

Figure 7: Velocity-disturbance heatmaps of the ground truth and each model. The diagonal pattern reflects disturbance propagation from the leader ( $i=0$ ) to the tail vehicle ( $i=4$ ).

Figure 8: Distributions of adjacent-vehicle amplification factors $A_{i}$ . Values below one (dashed line) indicate string-stable attenuation.

Figure 9: Frequency-domain transfer gains $G(f)$ over 0.05–0.5 Hz. Gains above one indicate frequency-selective disturbance amplification.

Vehicle Trajectory Prediction

Vehicle trajectory prediction forecasts how vehicles will move from their histories, road maps, traffic interactions, and driving intentions.

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Oct 8, 2026J/K move · Enter open · S save

Uncertainty-Aware Optimization for Physics-Aware Highway Trajectory Prediction

Aanchal Rajesh Chugh, Sebastian Dorn

Technische Hochschule Augsburg TTZ Landsberg am Lech

Probabilistic Trajectory Prediction Trajectory Prediction Vehicle Trajectory Prediction

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Accurate trajectory forecasting and well-defined predictive uncertainty are crucial for reliable, safety-critical applications such as autonomous driving. Most trajectory prediction approaches provide point estimates only, while uncertainty-aware approaches typically quantify uncertainty only in the trajectory space. In physics-aware approaches, uncertainty in the predicted motion variables should be explicitly modeled and propagated through the vehicle dynamics. Otherwise, the resulting trajectory-space uncertainty may not fully reflect the variability introduced by the underlying motion prediction. Therefore, in this work, uncertainty-aware extensions of X-TRACK (X-TRACK-DE and X-TRACK-MCD), a physics-aware trajectory prediction framework, are proposed. The proposed framework predicts future vehicle motion variables and models both aleatoric and epistemic uncertainties by propagating motion space uncertainty to trajectory space. Additionally, conformal prediction is applied to the trajectory space predictive covariance to construct uncertainty regions targeting a desired marginal coverage level. Evaluation on the highD dataset shows that X-TRACK-DE improves trajectory prediction accuracy over the deterministic baseline, while both uncertainty-aware variants provide predictive uncertainty that can be conformally calibrated to the desired marginal coverage level.

Abstract

Vehicle Trajectory Prediction

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