Macroscopic Traffic Flow Modeling with Physics Regularized Gaussian Process: Generalized Formulations

• URL: http://arxiv.org/abs/2007.07762v2
• Date: Sat, 19 Mar 2022 01:04:48 GMT
• Title: Macroscopic Traffic Flow Modeling with Physics Regularized Gaussian Process: Generalized Formulations
• Authors: Yun Yuan, Zhao Zhang, Xianfeng Terry Yang
• Abstract summary: This study presents a new modeling framework, named physics regularized Gaussian process (PRGP) This novel approach can encode physics models, i.e., classical traffic flow models, into the Gaussian process architecture and so as to regularize the Machine Learning training process. To prove the effectiveness of the proposed model, this paper conducts empirical studies on a real-world dataset that is collected from a stretch of I-15 freeway, Utah.
• Score: 5.827236278192557
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Despite the success of classical traffic flow (e.g., second-order macroscopic) models and data-driven (e.g., Machine Learning - ML) approaches in traffic state estimation, those approaches either require great efforts for parameter calibrations or lack theoretical interpretation. To fill this research gap, this study presents a new modeling framework, named physics regularized Gaussian process (PRGP). This novel approach can encode physics models, i.e., classical traffic flow models, into the Gaussian process architecture and so as to regularize the ML training process. Particularly, this study aims to discuss how to develop a PRGP model when the original physics model is with discrete formulations. Then based on the posterior regularization inference framework, an efficient stochastic optimization algorithm is 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 that 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 physics models and pure machine learning methods, in estimation precision and input robustness.

Related papers

• Understanding Reinforcement Learning-Based Fine-Tuning of Diffusion Models: A Tutorial and Review [63.31328039424469]
  This tutorial provides a comprehensive survey of methods for fine-tuning diffusion models to optimize downstream reward functions. We explain the application of various RL algorithms, including PPO, differentiable optimization, reward-weighted MLE, value-weighted sampling, and path consistency learning.
  arXiv  Detail & Related papers  (2024-07-18T17:35:32Z)
• Towards Learning Stochastic Population Models by Gradient Descent [0.0]
  We show that simultaneous estimation of parameters and structure poses major challenges for optimization procedures. We demonstrate accurate estimation of models but find that enforcing the inference of parsimonious, interpretable models drastically increases the difficulty.
  arXiv  Detail & Related papers  (2024-04-10T14:38:58Z)
• Fusion of Gaussian Processes Predictions with Monte Carlo Sampling [61.31380086717422]
  In science and engineering, we often work with models designed for accurate prediction of variables of interest. Recognizing that these models are approximations of reality, it becomes desirable to apply multiple models to the same data and integrate their outcomes.
  arXiv  Detail & Related papers  (2024-03-03T04:21:21Z)
• Replication Study: Enhancing Hydrological Modeling with Physics-Guided Machine Learning [0.0]
  Current hydrological modeling methods combine data-driven Machine Learning algorithms and traditional physics-based models. Despite the accuracy of ML in outcome prediction, the integration of scientific knowledge is crucial for reliable predictions. This study introduces a Physics Informed Machine Learning model, which merges the process understanding of conceptual hydrological models with the predictive efficiency of ML algorithms.
  arXiv  Detail & Related papers  (2024-02-21T16:26:59Z)
• Online Variational Sequential Monte Carlo [49.97673761305336]
  We build upon the variational sequential Monte Carlo (VSMC) method, which provides computationally efficient and accurate model parameter estimation and Bayesian latent-state inference. Online VSMC is capable of performing efficiently, entirely on-the-fly, both parameter estimation and particle proposal adaptation.
  arXiv  Detail & Related papers  (2023-12-19T21:45:38Z)
• When to Update Your Model: Constrained Model-based Reinforcement Learning [50.74369835934703]
  We propose a novel and general theoretical scheme for a non-decreasing performance guarantee of model-based RL (MBRL) Our follow-up derived bounds reveal the relationship between model shifts and performance improvement. A further example demonstrates that learning models from a dynamically-varying number of explorations benefit the eventual returns.
  arXiv  Detail & Related papers  (2022-10-15T17:57:43Z)
• Learning continuous models for continuous physics [94.42705784823997]
  We develop a test based on numerical analysis theory to validate machine learning models for science and engineering applications. Our results illustrate how principled numerical analysis methods can be coupled with existing ML training/testing methodologies to validate models for science and engineering applications.
  arXiv  Detail & Related papers  (2022-02-17T07:56:46Z)
• Prediction of liquid fuel properties using machine learning models with Gaussian processes and probabilistic conditional generative learning [56.67751936864119]
  The present work aims to construct cheap-to-compute machine learning (ML) models to act as closure equations for predicting the physical properties of alternative fuels. Those models can be trained using the database from MD simulations and/or experimental measurements in a data-fusion-fidelity approach. The results show that ML models can predict accurately the fuel properties of a wide range of pressure and temperature conditions.
  arXiv  Detail & Related papers  (2021-10-18T14:43:50Z)
• Enhancing predictive skills in physically-consistent way: Physics Informed Machine Learning for Hydrological Processes [1.0635248457021496]
  We develop a Physics Informed Machine Learning (PIML) model that combines the process understanding of conceptual hydrological model with predictive abilities of state-of-the-art ML models. We apply the proposed model to predict the monthly time series of the target (streamflow) and intermediate variables (actual evapotranspiration) in the Narmada river basin in India.
  arXiv  Detail & Related papers  (2021-04-22T12:13:42Z)
• Modeling Stochastic Microscopic Traffic Behaviors: a Physics Regularized Gaussian Process Approach [1.6242924916178285]
  This study presents a microscopic traffic model that can capture randomness and measure errors in the real world. 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.
  arXiv  Detail & Related papers  (2020-07-17T06:03:32Z)
• Macroscopic Traffic Flow Modeling with Physics Regularized Gaussian Process: A New Insight into Machine Learning Applications [14.164058812512371]
  This study presents a new modeling framework, named physics regularized machine learning (PRML), to encode classical traffic flow models into the machine learning architecture. 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.
  arXiv  Detail & Related papers  (2020-02-06T17:22:20Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.