# Towards better traffic volume estimation: Jointly addressing the underdetermination and nonequilibrium problems with correlation-adaptive GNNs

arXiv: https://arxiv.org/abs/2303.05660 · HTML: https://mlsanity.com/paper/2303.05660/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 79 references that are in the map.
- First posted on arXiv 10 Mar 2023.

## Builds on (most cited first, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Language Modeling with Gated Convolutional Networks](https://mlsanity.com/paper/1612.08083/) (2016)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [GMAN: A Graph Multi-Attention Network for Traffic Prediction](https://mlsanity.com/paper/1911.08415/) (2019)
- [Revisiting Spatial-Temporal Similarity: A Deep Learning Framework for Traffic Prediction](https://mlsanity.com/paper/1803.01254/) (2018)
- [Inductive Graph Neural Networks for Spatiotemporal Kriging](https://mlsanity.com/paper/2006.07527/) (2020)
- [Spatial Aggregation and Temporal Convolution Networks for Real-time Kriging](https://mlsanity.com/paper/2109.12144/) (2021)
- [Missing Slice Recovery for Tensors Using a Low-rank Model in Embedded Space](https://mlsanity.com/paper/1804.01736/) (2018)
- [Correlating sparse sensing for large-scale traffic speed estimation: A Laplacian-enhanced low-rank tensor kriging approach](https://mlsanity.com/paper/2210.11780/) (2022)
- [3D Graph Convolutional Networks with Temporal Graphs: A Spatial Information Free Framework For Traffic Forecasting](https://mlsanity.com/paper/1903.00919/) (2019)
- [Truncated tensor Schatten p-norm based approach for spatiotemporal traffic data imputation with complicated missing patterns](https://mlsanity.com/paper/2205.09390/) (2022)
- [Dynamic Spatiotemporal Graph Convolutional Neural Networks for Traffic Data Imputation with Complex Missing Patterns](https://mlsanity.com/paper/2109.08357/) (2021)
- [Temporal Convolutional Attention-based Network For Sequence Modeling](https://mlsanity.com/paper/2002.12530/) (2020)
- [Joint Modeling of Dense and Incomplete Trajectories for Citywide Traffic Volume Inference](https://mlsanity.com/paper/1902.09255/) (2019)
- [Forecast Network-Wide Traffic States for Multiple Steps Ahead: A Deep Learning Approach Considering Dynamic Non-Local Spatial Correlation and Non-Stationary Temporal Dependency](https://mlsanity.com/paper/2004.02391/) (2020)

## Built on by (most cited first, 9 of 9)

- [ImputeFormer: Low Rankness-Induced Transformers for Generalizable Spatiotemporal Imputation](https://mlsanity.com/paper/2312.01728/) (2023)
- [Spatiotemporal Implicit Neural Representation as a Generalized Traffic Data Learner](https://mlsanity.com/paper/2405.03185/) (2024)
- [Joint Estimation and Prediction of City-wide Delivery Demand: A Large Language Model Empowered Graph-based Learning Approach](https://mlsanity.com/paper/2408.17258/) (2024)
- [Network-wide Freeway Traffic Estimation Using Sparse Sensor Data: A Dirichlet Graph Auto-Encoder Approach](https://mlsanity.com/paper/2503.15845/) (2025)
- [Contextualizing MLP-Mixers Spatiotemporally for Urban Data Forecast at Scale](https://mlsanity.com/paper/2307.01482/) (2023)
- [MoGERNN: An Inductive Traffic Predictor for Unobserved Locations](https://mlsanity.com/paper/2501.12281/) (2025)
- [Calibration of Vehicular Traffic Simulation Models by Local Optimization](https://mlsanity.com/paper/2502.11585/) (2025)
- [Network-Wide Traffic Volume Estimation from Speed Profiles using a Spatio-Temporal Graph Neural Network with Directed Spatial Attention](https://mlsanity.com/paper/2512.13758/) (2025)
- [Metropolis-Scale Resilient and Trustworthy Traffic Flow Inference Using Multi-Source Data](https://mlsanity.com/paper/2605.25004/) (2026)

## Abstract (arXiv)

Traffic volume is an indispensable ingredient to provide fine-grained information for traffic management and control. However, due to limited deployment of traffic sensors, obtaining full-scale volume information is far from easy. Existing works on this topic primarily focus on improving the overall estimation accuracy of a particular method and ignore the underlying challenges of volume estimation, thereby having inferior performances on some critical tasks. This paper studies two key problems with regard to traffic volume estimation: (1) underdetermined traffic flows caused by undetected movements, and (2) non-equilibrium traffic flows arise from congestion propagation. Here we demonstrate a graph-based deep learning method that can offer a data-driven, model-free and correlation adaptive approach to tackle the above issues and perform accurate network-wide traffic volume estimation. Particularly, in order to quantify the dynamic and nonlinear relationships between traffic speed and volume for the estimation of underdetermined flows, a speed patternadaptive adjacent matrix based on graph attention is developed and integrated into the graph convolution process, to capture non-local correlations between sensors. To measure the impacts of non-equilibrium flows, a temporal masked and clipped attention combined with a gated temporal convolution layer is customized to capture time-asynchronous correlations between upstream and downstream sensors. We then evaluate our model on a real-world highway traffic volume dataset and compare it with several benchmark models. It is demonstrated that the proposed model achieves high estimation accuracy even under 20% sensor coverage rate and outperforms other baselines significantly, especially on underdetermined and non-equilibrium flow locations. Furthermore, comprehensive quantitative model analysis are also carried out to justify the model designs.