Physics-Informed Deep Learning for Traffic State Estimation: Illustrations With LWR and CTM Models

We present a physics-informed deep learning (PIDL) approach to tackle the challenge of data sparsity and sensor noise in traffic state estimation (TSE). PIDL strengthens (DL) neural network with knowledge flow theory accurately estimate conditions. The ‘physics’—a priori information system—acts as regularization agent during training. illustrate implementation proposed two commonly used models representing physics: Lighthill-Whitham-Richards (LWR) model cell transmission (CTM). LWR is illustrated Greenshields’ inverse-lambda fundamental diagrams; whereas, CTM works any diagram choice. Two case studies validate by reconstructing velocity-field. Case study-I uses synthetic generated resemble trajectory connected autonomous vehicles captured roadside units. study-II employs NGSIM mimicking scant probe vehicle observations. observe that particularly better lower amount training data, illustrating capability making precise timely TSE even sparse input. E.g., With 10% CAV penetration rate 15% added-noise, relative error for was at 22.9% compared 30.8% DL.