Modeling Stochastic Microscopic Traffic Behaviors: a Physics Regularized Gaussian Process Approach

2020/07/17 by Yun Yuan, Qinzheng Wang, Yuan, Yun +4 · 10 citations
Computer Science · Engineering · Mathematics · #Algorithm #Artificial intelligence #Autonomous Vehicle Technology and Safety #Bayesian inference #Bayesian probability #Computer science #Data mining #FOS: Computer and information sciences #FOS: Electrical engineering #Gaussian #Gaussian process #Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine learning #Mathematics #Physics #Randomness #Signal Processing (eess.SP) #Statistics #Stochastic process #Traffic control and management #Vehicle emissions and performance #cs.LG #eess.SP #electronic engineering #information engineering #stat.ML

paper · pdf · doi:10.48550/arxiv.2007.10109

published in arXiv (Cornell University) (Cornell University) · 31 pages, 10 figures. arXiv admin note: text overlap with arXiv:2002.02374

arxiv created 2020/07/17 · openalex publication_date 2020/07/17 · arxiv updated 2020/07/21 · openalex created_date 2020/07/23 · openalex updated_date 2026/07/28

Abstract

Modeling stochastic traffic behaviors at the microscopic level, such as car-following and lane-changing, is a crucial task to understand the interactions between individual vehicles in traffic streams. Leveraging a recently developed theory named physics regularized Gaussian process (PRGP), this study presents a stochastic microscopic traffic model that can capture the randomness and measure errors in the real world. Physical knowledge from classical car-following models is converted as physics regularizers, in the form of shadow Gaussian process (GP), of a multivariate PRGP for improving the modeling accuracy. More specifically, a Bayesian inference algorithm is developed to estimate the mean and kernel of GPs, and an enhanced latent force model is formulated to encode physical knowledge into stochastic processes. Also, based on the posterior regularization inference framework, an efficient stochastic optimization algorithm is developed to maximize the evidence lower-bound of the system likelihood. To evaluate the performance of the proposed models, this study conducts empirical studies on real-world vehicle trajectories from the NGSIM dataset. Since one unique feature of the proposed framework is the capability of capturing both car-following and lane-changing behaviors with one single model, numerical tests are carried out with two separated datasets, one contains lane-changing maneuvers and the other doesn't. The results show the proposed method outperforms the previous influential methods in estimation precision.

Citations

• Adam: A Method for Stochastic Optimization
• Congested Traffic States in Empirical Observations and Microscopic Simulations
• Dynamical model of traffic congestion and numerical simulation
• Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations
• Learning unknown ODE models with Gaussian processes
• Physics Guided Recurrent Neural Networks For Modeling Dynamical Systems: Application to Monitoring Water Temperature And Quality In Lakes
• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Physics-Guided Machine Learning for Scientific Discovery: An Application in Simulating Lake Temperature Profiles

Cited by

• Twenty-Five Years of the Intelligent Driver Model: Foundations, Extensions, Applications, and Future Directions
• Reconstructing Physics-Informed Machine Learning for Traffic Flow Modeling: a Multi-Gradient Descent and Pareto Learning Approach

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