  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.
