Despite the wide implementation of machine learning (ML) technique in traffic flow modeling recently, those data-driven approaches often fall short of accuracy in the cases with a small or noisy training 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 physics models) into the ML architecture and to regularize the ML training process. More specifically, leveraging the Gaussian process (GP) as the base model, 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 physics 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 the stochastic process. Based on the posterior regularization inference framework, an efficient stochastic optimization algorithm is then developed to maximize the evidence lowerbound of the system likelihood. For model evaluations, 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 traffic flow models and pure machine learning methods, in estimation precision and is more robust to the noisy training dataset.

尽管最近在交通流建模中广泛采用了机器学习（ML）技术，但在训练数据集很小或嘈杂的情况下，这些数据驱动的方法通常仍缺乏准确性。为了解决这个问题，本研究提出了一个新的建模框架，称为物理正则化机器学习（PRML），用于将经典交通流模型（称为物理模型）编码到ML架构中，并规范化ML训练过程。更具体地说，利用高斯过程（GP）作为基本模型，开发了随机物理正则化高斯过程（PRGP）模型，并使用贝叶斯推理算法来估计PRGP的均值和内核。基于宏观交通流模型的物理正则化器，还开发了通过阴影GP来增加估计量的“随机数”，并使用增强的潜力模型将物理知识编码到随机过程中。基于后验正则推理框架，然后开发了一种有效的随机优化算法，以最大化系统可能性的证据下界。为了进行模型评估，本文对从犹他州I-15高速公路延伸段收集的真实数据集进行了实证研究。结果表明，新的PRGP模型可以在估计精度方面胜过以前的兼容方法，例如校准的交通流模型和纯机器学习方法，并且对嘈杂的训练数据集更健壮。然后开发一种有效的随机优化算法，以最大程度地降低系统可能性的证据下限。为了进行模型评估，本文对从犹他州I-15高速公路延伸段收集的真实数据集进行了实证研究。结果表明，新的PRGP模型可以在估计精度方面胜过以前的兼容方法，例如校准的交通流模型和纯机器学习方法，并且对嘈杂的训练数据集更健壮。然后开发一种有效的随机优化算法，以最大程度地降低系统可能性的证据下限。为了进行模型评估，本文对从犹他州I-15高速公路延伸段收集的真实数据集进行了实证研究。结果表明，新的PRGP模型可以在估计精度方面胜过以前的兼容方法，例如校准的交通流模型和纯机器学习方法，并且对嘈杂的训练数据集更健壮。