mlsanityData to 7 Oct 2026

Macroscopic Traffic Flow Modeling with Physics Regularized Gaussian Process: A New Insight into Machine Learning Applications

arXiv 2002.02374 ↗First posted 6 Feb 2020stat.ML cs.LGcited by 25

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Abstract (arXiv)

Despite the wide implementation of machine learning (ML) techniques in traffic flow modeling recently, those data-driven approaches often fall short of accuracy in the cases with a small or noisy dataset. To address this issue, this study presents a new modeling framework, named physics regularized machine learning (PRML), to encode classical traffic flow models (referred as physical models) into the ML architecture and to regularize the ML training process. More specifically, a stochastic physics regularized Gaussian process (PRGP) model is developed and a Bayesian inference algorithm is used to estimate the mean and kernel of the PRGP. A physical regularizer based on macroscopic traffic flow models is also developed to augment the estimation via a shadow GP and an enhanced latent force model is used to encode physical knowledge into stochastic processes. Based on the posterior regularization inference framework, an efficient stochastic optimization algorithm is also developed to maximize the evidence lowerbound of the system likelihood. To prove the effectiveness of the proposed model, this paper conducts empirical studies on a real-world dataset which is collected from a stretch of I-15 freeway, Utah. Results show the new PRGP model can outperform the previous compatible methods, such as calibrated pure physical models and pure machine learning methods, in estimation precision and input robustness.

Key facts. Cited by 25 papers in the map (data through 7 Oct 2026). First posted on arXiv 6 Feb 2020.

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Citing papers per year: 2021: 6; 2022: 5; 2023: 5; 2024: 1; 2025: 8.

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  1. 2021A Physics-Informed Deep Learning Paradigm for Traffic State and Fundamental Diagram Estimationcited by 37
  2. 2021Low-Rank Hankel Tensor Completion for Traffic Speed Estimationcited by 22
  3. 2021Incorporating Kinematic Wave Theory into a Deep Learning Method for High-Resolution Traffic Speed Estimationcited by 12
  4. 2023Fourier neural operator for learning solutions to macroscopic traffic flow models: Application to the forward and inverse problemscited by 12
  5. 2022Quantifying Uncertainty In Traffic State Estimation Using Generative Adversarial Networkscited by 7
  6. 2021Short-term traffic prediction using physics-aware neural networkscited by 6
  7. 2023Traffic State Estimation from Vehicle Trajectories with Anisotropic Gaussian Processescited by 6
  8. 2025Network-wide Freeway Traffic Estimation Using Sparse Sensor Data: A Dirichlet Graph Auto-Encoder Approachcited by 4
  9. 2022PAGP: A physics-assisted Gaussian process framework with active learning for forward and inverse problems of partial differential equationscited by 3
  10. 2022IDM-Follower: A Model-Informed Deep Learning Method for Long-Sequence Car-Following Trajectory Predictioncited by 3
  11. 2023Physics-informed Machine Learning for Calibrating Macroscopic Traffic Flow Modelscited by 3
  12. 2023Perimeter Control with Heterogeneous Metering Rates for Cordon Signals: A Physics-Regularized Multi-Agent Reinforcement Learning Approachcited by 2
13 more
  1. 2024Efficient and Robust Freeway Traffic Speed Estimation under Oblique Grid using Vehicle Trajectory Datacited by 2
  2. 2025MoGERNN: An Inductive Traffic Predictor for Unobserved Locationscited by 2
  3. 2022A Hybrid Physics Machine Learning Approach for Macroscopic Traffic State Estimationcited by 1
  4. 2022A hybrid data driven-physics constrained Gaussian process regression framework with deep kernel for uncertainty quantificationcited by 1
  5. 2023Inverting the Fundamental Diagram and Forecasting Boundary Conditions: How Machine Learning Can Improve Macroscopic Models for Traffic Flowcited by 1
  6. 2025Potential failures of physics-informed machine learning in traffic flow modeling: theoretical and experimental analysiscited by 1
  7. 2025Learning to Learn the Macroscopic Fundamental Diagram using Physics-Informed and meta Machine Learning techniquescited by 1
  8. 2025PMA-Diffusion: A Physics-guided Mask-Aware Diffusion Framework for TSE from Sparse Observationscited by 1
  9. 2021Physics-Informed Deep Learning for Traffic State Estimationcited by 0
  10. 2021Estimating Traffic Speeds using Probe Data: A Deep Neural Network Approachcited by 0
  11. 2025Closed-Loop Neural Operator-Based Observer of Traffic Densitycited by 0
  12. 2025Reconstructing Physics-Informed Machine Learning for Traffic Flow Modeling: a Multi-Gradient Descent and Pareto Learning Approachcited by 0
  13. 2025Theory Foundation of Physics-Enhanced Residual Learningcited by 0