Network-wide Freeway Traffic Estimation Using Sparse Sensor Data: A Dirichlet Graph Auto-Encoder Approach

TL;DR

The paper addresses network-wide traffic state estimation from sparse sensors by introducing a directed-graph extension of Dirichlet Energy-based Feature Propagation (DEFP4D) and integrating it into a Graph Auto-Encoder (DGAE). By learning latent space representations with DEFP4D and applying physics-guided, decoupled propagation for congested and free-flow patterns, the approach avoids zero-filling biases and improves inference for unobserved nodes. Empirical results on METR-LA, PEMS-BAY, and PEMSD7(M) show significant accuracy gains (average ~7.25% improvement, up to 10.53%) and strong cross-city generalization, with a lightweight DEFP4D variant performing well under very sparse sensor conditions. The work highlights practical benefits for deployment, including reduced sensor requirements (≈14.5% fewer sensors) and robust transferability, while outlining future directions in uncertainty quantification, infrastructure-aware modeling, and privacy-preserving data fusion.

Abstract

Network-wide Traffic State Estimation (TSE), which aims to infer a complete image of network traffic states with sparsely deployed sensors, plays a vital role in intelligent transportation systems. With the development of data-driven methods, traffic dynamics modeling has advanced significantly. However, TSE poses fundamental challenges for data-driven approaches, since historical patterns cannot be learned locally at sensor-free segments. Although inductive graph learning shows promise in estimating states at locations without sensor, existing methods typically handle unobserved locations by filling them with zeros, introducing bias to the sensitive graph message propagation. The recently proposed Dirichlet Energy-based Feature Propagation (DEFP) method achieves State-Of-The-Art (SOTA) performance in unobserved node classification by eliminating the need for zero-filling. However, applying it to TSE faces three key challenges: inability to handle directed traffic networks, strong assumptions in traffic spatial correlation modeling, and overlooks distinct propagation rules of different patterns (e.g., congestion and free flow). We propose DGAE, a novel inductive graph representation model that addresses these challenges through theoretically derived DEFP for Directed graph (DEFP4D), enhanced spatial representation learning via DEFP4D-guided latent space encoding, and physics-guided propagation mechanisms that separately handles congested and free-flow patterns. Experiments on three traffic datasets demonstrate that DGAE outperforms existing SOTA methods and exhibits strong cross-city transferability. Furthermore, DEFP4D can serve as a standalone lightweight solution, showing superior performance under extremely sparse sensor conditions.

Figures (7)

• Figure 1: Illustration of foundational framework Dirichlet graph auto-encoder.
• Figure 2: Illustration of bidirectional diffusion dynamics of traffic flow: an evidence from U.S. Highway 101.
• Figure 3: Illustration of the refined DGAE architecture. The Graph Encoder structure, identical to the Graph Decoder, is omitted here for brevity. MLP denotes Multi-Layer Perceptron, ReLU denotes the activation function and $\oplus$ represents element-wise addition operation.
• Figure 4: State estimation results for METR-LA: (a) Sensor #1, (b) Sensor #70, (c) Sensor #131.
• Figure 5: Model performance with different sensor deployment density on METR-LA dataset. The first row of x-ticks labels indicates the number of VS, while the second row shows the number of VS.