Knowledge-data fusion dominated vehicle platoon dynamics modeling and analysis: A physics-encoded deep learning approach (PeMTFLN)

This repository contains the official PyTorch implementation for the paper: "Knowledge-data fusion dominated vehicle platoon dynamics modeling and analysis: A physics-encoded deep learning approach", accepted by the journal Information Fusion.

[Paper Link]

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Abstract

Nonlinear platoon dynamics modeling is essential for predicting and optimizing vehicle interactions. However, existing approaches often struggle to capture platoon-scale interaction features while maintaining both high accuracy and physical analyzability. To address these challenges, this paper introduces a novel Physics-encoded Deep Learning Network (PeMTFLN) for modeling nonlinear vehicle platoon dynamics. The framework features an Analyzable Parameters Encoded Computational Graph (APeCG) to ensure physically consistent and stable platoon responses, and a Multi-scale Trajectory Feature Learning Network (MTFLN) to learn driving patterns from trajectory data. Trained on the HIGHSIM dataset, PeMTFLN outperforms baseline models in prediction accuracy and successfully replicates real-world platoon stability and safety characteristics, demonstrating a superior balance of predictive accuracy and physical interpretability.

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Framework

The overall architecture of our proposed Parameters Encoder Multi-scale Trajectory Feature Learning Network (PeMTFLN) integrates a multi-scale feature learning network (MTFLN) to learn driving patterns from data and an analyzable parameters encoded computational graph (APeCG) to ensure physical consistency and stability.

Figure: The architecture of PeMTFLN under the PeDL Framework, consisting of (a) Vehicle-level Feature Learning, (b) Platoon-level Feature Learning, (c) Non-Autoregressive Parameters Decoder, and (d) Analyzable Parameters Encoded Computational Graph.

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Main Contributions

• A novel vehicle platoon dynamics modeling framework (PeDL) with both interpretability and high accuracy is proposed. It focuses on directly learning and encoding the physical parameters of a generalized platoon model and can be scaled to model platoons with varying numbers of vehicles.
• A multi-scale trajectory feature learning network (MTFLN) is designed to facilitate the end-to-end learning of the parameters required by PeDL, capturing features at both vehicle and platoon levels.
• The model's effectiveness is validated on the real-world HIGH-SIM dataset. PeMTFLN accurately reproduces platoon following behavior, including stability and safety evolution, and shows robust generalization on the NGSIM dataset.

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Environment Setup

1. Clone the repository:

git clone [https://github.com/HaoLyu666/PeMTFLN.git](https://github.com/HaoLyu666/PeMTFLN.git)
cd PeMTFLN

2. Create a Conda Environment (Recommended):

conda create -n pemtfln python=3.8
conda activate pemtfln

3. Install Dependencies: This project relies on several Python libraries. You can install them via pip.

pip install torch numpy tqdm pandas matplotlib
# Install PyTorch according to your CUDA version
# e.g., for CUDA 11.3:
# pip install torch==1.12.1+cu113 torchvision==0.13.1+cu113 -f [https://download.pytorch.org/whl/torch_stable.html](https://download.pytorch.org/whl/torch_stable.html)

• OS: Ubuntu 20.04
• CUDA Version: 11.4
• PyTorch Version: 1.12.1+

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Data Preparation

• Dataset: The primary dataset is extracted from HIGH-SIM, containing platoon trajectories of seven vehicles. Generalization experiments are conducted on the NGSIM dataset.
• Data Format: The preprocessed data is stored in a .npz file (platoons_data_split.npz), which contains training, validation, and test sets. The data loading logic can be found in loader2.py.
• Data Structure: Each data sample consists of hist (historical trajectory features like gap, speed, etc.), fut (future ground truth gap and speed), and nextv (the lead vehicle's future velocity). This structure is defined in loader2.py.

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Usage

Configuration

All hyperparameters for the model and training process are defined in config.py. You can modify this file to adjust settings like batch_size, learning_rate, in_length, out_length, etc.

Model Training

Run the following script to start training the model. Model checkpoints will be saved in the checkponint/ directory, and results will be logged in the result/ directory. The training process is detailed in train_highsim.py.

python train_highsim.py

Model Evaluation

After training, use the evaluate_highsim.py script to evaluate the model's performance on the test set. You need to specify the model epoch to load by modifying the names variable within the script.

# In evaluate_highsim.py, modify the 'names' variable
# names = '20' # Loads the model from the 20th epoch

python evaluate_highsim.py

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Results

Quantitative Results

PeMTFLN was compared with several baseline models on the HIGH-SIM dataset. As shown in the table below, our model achieves state-of-the-art performance in both velocity and gap prediction across various metrics.

Model	Velocity RMSE (m/s) Avg	Gap RMSE (m) Avg	Velocity MAPE (%) Avg	Gap MAPE (%) Avg
PerIDM	1.705	2.034	9.95	8.61
PerACC	1.561	1.398	10.63	5.24
KoopmanNet	0.684	0.983	4.91	3.36
Seq2Seq	0.472	0.922	3.42	3.21
Transformer	0.476	0.797	3.26	2.81
PeLSTM	0.492	0.689	3.48	2.12
PeTransformer	0.479	0.666	3.25	1.99
PeMTFLN (Ours)	0.469	0.643	3.09	1.91

Qualitative Results

Trajectory Reproduction: PeMTFLN accurately reproduces platoon trajectories under various driving scenarios, including continuous acceleration, oscillation, and deceleration.

Stability Analysis: The model successfully replicates the stability evolution of real-world platoons, which validates its capability for physical analysis.

Safety Analysis: The model's predictions align closely with ground-truth data in terms of surrogate safety measure distributions, such as Post-Encroachment Time (PET) and Safe Stopping Distance Difference (SSDD).

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Citation

If you use this work in your research, please cite our paper:

@article{lyu2025knowledge,
title = {Knowledge-data fusion dominated vehicle platoon dynamics modeling and analysis: A physics-encoded deep learning approach},
journal = {Information Fusion},
pages = {103622},
year = {2025},
issn = {1566-2535},
doi = {https://doi.org/10.1016/j.inffus.2025.103622},
}

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Contact

If you have any questions, please feel free to email the authors:

• Hao Lyu: lyu_hao@seu.edu.cn
• Yanyong Guo (Corresponding Author): guoyanyong@seu.edu.cn

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License

This project is released under the MIT License.