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

arXiv: https://arxiv.org/abs/2609.06961 · HTML: https://mlsanity.com/paper/2609.06961/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 44 references that are in the map.
- First posted on arXiv 7 Sep 2026.

## Builds on (most cited first, 25 of 25)

- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [AgentFormer: Agent-Aware Transformers for Socio-Temporal Multi-Agent Forecasting](https://mlsanity.com/paper/2103.14023/) (2021)
- [Wayformer: Motion Forecasting via Simple & Efficient Attention Networks](https://mlsanity.com/paper/2207.05844/) (2022)
- [The highD Dataset: A Drone Dataset of Naturalistic Vehicle Trajectories on German Highways for Validation of Highly Automated Driving Systems](https://mlsanity.com/paper/1810.05642/) (2018)
- [MotionDiffuser: Controllable Multi-Agent Motion Prediction using Diffusion](https://mlsanity.com/paper/2306.03083/) (2023)
- [Transformer Networks for Trajectory Forecasting](https://mlsanity.com/paper/2003.08111/) (2020)
- [Scene Transformer: A unified architecture for predicting multiple agent trajectories](https://mlsanity.com/paper/2106.08417/) (2021)
- [MTR++: Multi-Agent Motion Prediction with Symmetric Scene Modeling and Guided Intention Querying](https://mlsanity.com/paper/2306.17770/) (2023)
- [EqMotion: Equivariant Multi-agent Motion Prediction with Invariant Interaction Reasoning](https://mlsanity.com/paper/2303.10876/) (2023)
- [An LSTM Network for Highway Trajectory Prediction](https://mlsanity.com/paper/1801.07962/) (2018)
- [Multi-Modal Trajectory Prediction of Surrounding Vehicles with Maneuver based LSTMs](https://mlsanity.com/paper/1805.05499/) (2018)
- [Dissipation of stop-and-go waves via control of autonomous vehicles: Field experiments](https://mlsanity.com/paper/1705.01693/) (2017)
- [FJMP: Factorized Joint Multi-Agent Motion Prediction over Learned Directed Acyclic Interaction Graphs](https://mlsanity.com/paper/2211.16197/) (2022)
- [Data-driven Traffic Simulation: A Comprehensive Review](https://mlsanity.com/paper/2310.15975/) (2023)
- [FollowNet: A Comprehensive Benchmark for Car-Following Behavior Modeling](https://mlsanity.com/paper/2306.05381/) (2023)
- [UniTraj: Learning a Universal Trajectory Foundation Model from Billion-Scale Worldwide Traces](https://mlsanity.com/paper/2411.03859/) (2024)
- [Unified Uncertainty-Aware Diffusion for Multi-Agent Trajectory Modeling](https://mlsanity.com/paper/2503.18589/) (2025)
- [Are commercially implemented adaptive cruise control systems string stable?](https://mlsanity.com/paper/1905.02108/) (2019)
- [openACC. An open database of car-following experiments to study the properties of commercial ACC systems](https://mlsanity.com/paper/2004.06342/) (2020)
- [A Hybrid Rule-Based and Data-Driven Approach to Driver Modeling through Particle Filtering](https://mlsanity.com/paper/2108.12820/) (2021)
- [CogDrive: Cognition-Driven Multimodal Prediction-Planning Fusion for Safe Autonomy](https://mlsanity.com/paper/2512.02777/) (2025)
- [A knowledge-augmented dataset of high-risk driving scenarios with LLM annotations for autonomous driving](https://mlsanity.com/paper/2607.07103/) (2026)
- [TSGN: Temporal Scene Graph Neural Networks with Projected Vectorized Representation for Multi-Agent Motion Prediction](https://mlsanity.com/paper/2305.08190/) (2023)
- [Unveiling Uniform Shifted Power Law in Stochastic Human and Autonomous Driving Behavior](https://mlsanity.com/paper/2511.00659/) (2025)

## Abstract (arXiv)

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.