## 1 Introduction
The major advantage of physics-informed learning (PIL) is that an effective loss function can be implemented using a modest amount of data. However, there is a major limitation to using PIL: their high training costs can cause adverse effects on their performance, which is especially of concern when dealing with real-world applications. Using the domain decomposition approach, [PERSON] and [PERSON] (2020) accelerated the convergence of these models without compromising their performance by partitioning the computational domain into more than one subdomain, and then defining boundaries between these subdomains that are subject to some continuity conditions [9]. The presented numerical experiments were, however, limited to the partitioning of a single solution space, which is not representative of the network's links in a true sense. In a traffic network, the state variables are correlated with the physical characteristics of the links for example number of lanes, road geometry, etc. The existing PIL studies consider the training data from the exact solution space of the governing partial differential equation. The macroscopic traffic state variables, on the other hand, are estimated through sensors and are subject to various measurement biases and approximations. Therefore, the real or simulated traffic data does not strictly follow the traffic governing physics model. Another limitation of the existing hybrid studies for training neural networks is that they mainly consider the exact solution of the traffic flow model over a spatiotemporal space subject to relevant initial and boundary conditions. Such an approach with the exact analytical solution may lead to two potential shortcomings: (1) the analytical solution of PDE contains negative traffic state variables, which is not realistic; (2) the data generated from a continuous road segment cannot have any merging or diverging points. Such deficiency is critical for a real-world traffic network, as the traffic dynamics with and without the network consideration are significantly different. The state-of-art of the hybrid models are only applicable to one road segment or a sequence of segments without merges or divergences, which greatly limits their applications. It is therefore imperative that such studies be extended to realistic road networks. This study aims to fill the above research gaps by extending physics-informed neural network application to simulated traffic network data following the domain decomposition approach. In a domain decomposition approach, we divide the whole traffic network into individual links. Afterwards, the individual links are joined together (stitching process) cor responding to their connectivity in the network. The flow conservation condition is applied at the joints (merge/diverge sections) while stitching the link. The domain decomposition in the framework is very useful in three major aspects. First, different physical properties on different links in a traffic network can be properly modeled. Second, the decomposition of a large network into individual links may help to reduce the requirement on the structural complexity of the neural network for each link to facilitate the training. Third, given the finite number of links, a massively parallel computation can be performed. Moreover, large-scale problems can be effectively handled by such domain decomposition method. To the best of our knowledge, this is the first article to introduce PINNs for a traffic network. This study seeks to fuse traffic flow models and ML techniques in a traffic network setting with the physics-informed neural networks for network TSE. We present a novel and extensive study of the PINNs for the network TSE in this paper. The paper contributes in the following ways. First, it introduces a specific setup and training methodology to support a traffic network consisting of links. Sparse data grids within each link are unified into a regular grid. Links are processed in the neural networks and are stitched together.