Physics-Embedded Gaussian Process for Traffic State Estimation

2025-12-03

AI Summary

Low probe vehicle penetration and sparse observations hinder reliable traffic state estimation (TSE) and well-calibrated uncertainty quantification. To address this, we propose a Physics-Embedded Gaussian Process (PEGP) framework. PEGP explicitly incorporates the LWR and ARZ macroscopic traffic flow models into a multi-output kernel function via linearized partial differential operators, enabling tight coupling of physical priors with data-driven learning—without requiring pseudo-observations. Coupled with variational inference for Gaussian process regression, PEGP ensures physical interpretability, adaptive uncertainty quantification, and strong generalization. Evaluations on HighD and NGSIM datasets show that PEGP-ARZ exhibits superior robustness under sparse observation regimes, whereas PEGP-LWR achieves higher accuracy under dense observations. Residual analysis confirms both physical consistency and proper uncertainty calibration.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification
• Planning, Routing, and Scheduling: Model-Based Reasoning

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Traffic state estimation (TSE) becomes challenging when probe-vehicle penetration is low and observations are spatially sparse. Pure data-driven methods lack physical explanations and have poor generalization when observed data is sparse. In contrast, physical models have difficulty integrating uncertainties and capturing the real complexity of traffic. To bridge this gap, recent studies have explored combining them by embedding physical structure into Gaussian process. These approaches typically introduce the governing equations as soft constraints through pseudo-observations, enabling the integration of model structure within a variational framework. However, these methods rely heavily on penalty tuning and lack principled uncertainty calibration, which makes them sensitive to model mis-specification. In this work, we address these limitations by presenting a novel Physics-Embedded Gaussian Process (PEGP), designed to integrate domain knowledge with data-driven methods in traffic state estimation. Specifically, we design two multi-output kernels informed by classic traffic flow models, constructed via the explicit application of the linearized differential operator. Experiments on HighD, NGSIM show consistent improvements over non-physics baselines. PEGP-ARZ proves more reliable under sparse observation, while PEGP-LWR achieves lower errors with denser observation. Ablation study further reveals that PEGP-ARZ residuals align closely with physics and yield calibrated, interpretable uncertainty, whereas PEGP-LWR residuals are more orthogonal and produce nearly constant variance fields. This PEGP framework combines physical priors, uncertainty quantification, which can provide reliable support for TSE.

Problem

• Estimates traffic states under low probe-vehicle penetration and sparse observations.
• Integrates physical traffic models with data-driven methods to improve generalization.
• Addresses uncertainty calibration and sensitivity to model mis-specification in estimation.

Innovation

• Embedded physics via multi-output kernels in Gaussian process
• Applied linearized differential operator from traffic flow models
• Calibrated uncertainty quantification with interpretable residuals