Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Physics-Informed Diffusion Models for Vehicle Speed Trajectory Generation

Vadim Sokolov, Farnaz Behnia, Dominik Karbowski

TL;DR

This paper introduces physics-informed diffusion models for conditional generation of vehicle speed micro-trips, comparing a 1D U-Net diffusion model and a transformer-based Conditional Score-based Diffusion Imputation (CSDI) approach on 6,367 CMAP micro-trips. The authors show that soft physics constraints embedded in CSDI improve distributional fidelity (e.g., speed and acceleration) and boundary compliance, while delivering strong downstream utility for energy assessment tasks. Compared with Markov baselines and other deep generative methods, CSDI achieves superior Wasserstein distances (e.g., speed ≈ 0.30, acceleration ≈ 0.026) and a discriminative score near 0.49, with efficient generation and clear conditioning control over trip statistics and vehicle dynamics. The work demonstrates that diffusion-based, physics-informed generation can produce realistic, controllable speed profiles for ITS applications, and provides open-source code and data to enable reproducibility and further research.

Abstract

Synthetic vehicle speed trajectory generation is essential for evaluating vehicle control algorithms and connected vehicle technologies. Traditional Markov chain approaches suffer from discretization artifacts and limited expressiveness. This paper proposes a physics-informed diffusion framework for conditional micro-trip synthesis, combining a dual-channel speed-acceleration representation with soft physics constraints that resolve optimization conflicts inherent to hard-constraint formulations. We compare a 1D U-Net architecture against a transformer-based Conditional Score-based Diffusion Imputation (CSDI) model using 6,367 GPS-derived micro-trips. CSDI achieves superior distribution matching (Wasserstein distance 0.30 for speed, 0.026 for acceleration), strong indistinguishability from real data (discriminative score 0.49), and validated utility for downstream energy assessment tasks. The methodology enables scalable generation of realistic driving profiles for intelligent transportation systems (ITS) applications without costly field data collection.

Physics-Informed Diffusion Models for Vehicle Speed Trajectory Generation

TL;DR

This paper introduces physics-informed diffusion models for conditional generation of vehicle speed micro-trips, comparing a 1D U-Net diffusion model and a transformer-based Conditional Score-based Diffusion Imputation (CSDI) approach on 6,367 CMAP micro-trips. The authors show that soft physics constraints embedded in CSDI improve distributional fidelity (e.g., speed and acceleration) and boundary compliance, while delivering strong downstream utility for energy assessment tasks. Compared with Markov baselines and other deep generative methods, CSDI achieves superior Wasserstein distances (e.g., speed ≈ 0.30, acceleration ≈ 0.026) and a discriminative score near 0.49, with efficient generation and clear conditioning control over trip statistics and vehicle dynamics. The work demonstrates that diffusion-based, physics-informed generation can produce realistic, controllable speed profiles for ITS applications, and provides open-source code and data to enable reproducibility and further research.

Abstract

Synthetic vehicle speed trajectory generation is essential for evaluating vehicle control algorithms and connected vehicle technologies. Traditional Markov chain approaches suffer from discretization artifacts and limited expressiveness. This paper proposes a physics-informed diffusion framework for conditional micro-trip synthesis, combining a dual-channel speed-acceleration representation with soft physics constraints that resolve optimization conflicts inherent to hard-constraint formulations. We compare a 1D U-Net architecture against a transformer-based Conditional Score-based Diffusion Imputation (CSDI) model using 6,367 GPS-derived micro-trips. CSDI achieves superior distribution matching (Wasserstein distance 0.30 for speed, 0.026 for acceleration), strong indistinguishability from real data (discriminative score 0.49), and validated utility for downstream energy assessment tasks. The methodology enables scalable generation of realistic driving profiles for intelligent transportation systems (ITS) applications without costly field data collection.
Paper Structure (19 sections, 25 equations, 13 figures, 5 tables)

This paper contains 19 sections, 25 equations, 13 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Data
  4. Exploratory Data Analysis
  5. Methodology
  6. Baseline: Markov Chain Approach
  7. Conditional Diffusion Model with 1D U-Net
  8. Forward Diffusion Process
  9. Training Objective
  10. Reverse Sampling (Generation)
  11. Conditional Score-based Diffusion Imputation (CSDI)
  12. Physics-Informed Training
  13. Optimization of Kinematic Quality
  14. CSDI Sampling and Post-Processing
  15. Alternative Generative Approaches
  16. ...and 4 more sections

Figures (13)

  • Figure 1: Data distributions for trip duration, distance, and average speed. Histograms show the empirical distributions from 6,367 micro-trips with mean (red dashed) and median (orange dashed) markers. The distributions exhibit substantial heterogeneity, reflecting diverse driving contexts from urban congestion to highway cruising.
  • Figure 2: PCA
  • Figure 3: t-SNE
  • Figure 5: Arterial, Cluster 0.
  • Figure 6: Highway, Cluster 1.
  • ...and 8 more figures