For its robust predictive power (compared to pure physics-based models) and sample-efficient training (compared to pure deep learning models), physics-informed deep learning (PIDL), a paradigm hybridizing physics-based models and deep neural networks (DNNs), has been booming in science and engineering fields. One key challenge of applying PIDL to various domains and problems lies in the design of a computational graph that integrates physics and DNNs. In other words, how the physics is encoded into DNNs and how the physics and data components are represented. In this paper, we offer an overview of a variety of architecture designs of PIDL computational graphs and how these structures are customized to traffic state estimation (TSE), a central problem in transportation engineering. When observation data, problem type, and goal vary, we demonstrate potential architectures of PIDL computational graphs and compare these variants using the same real-world dataset.

The development of more sustainable urban transportation is prompting the need for better energy management techniques. Connected electric vehicles can take advantage of environmental information regarding the status of traffic lights. In this context, eco-approach and departure methods have been proposed in the literature. Integrating these methods with regenerative braking allows for safe, power-efficient navigation through intersections and crossroad layouts. This paper proposes rule- and fuzzy inference system-based strategies for a coupled eco-approach and departure regenerative braking system. This analysis is carried out through a numerical simulator based on a three-degree-of-freedom connected electric vehicle model. The powertrain is represented by a realistic power loss map in motoring and regenerative quadrants. The simulations aim to compare both longitudinal navigation strategies by means of relevant metrics: power, efficiency, comfort, and usage duty cycle in motor and generator modes. Numerical results show that the vehicle is able to yield safe navigation while focusing on energy regeneration through different navigation conditions.

A traffic system can be interpreted as a multiagent system, wherein vehicles choose the most efficient driving approaches guided by interconnected goals or strategies. This paper aims to develop a family of mean field games (MFG) for generic second-order traffic flow models (GSOM), in which cars control individual velocity to optimize their objective functions. GSOMs do not generally assume that cars optimize self-interested objectives, so such a game-theoretic reinterpretation offers insights into the agents’ underlying behaviors. In general, an MFG allows one to model individuals on a microscopic level as rational utility-optimizing agents while translating rich microscopic behaviors to macroscopic models. Building on the MFG framework, we devise a new class of second-order traffic flow MFGs (i.e., GSOM-MFG), which control cars’ acceleration to ensure smooth velocity change. A fixed-point algorithm with fictitious play technique is developed to solve GSOM-MFG numerically. In numerical examples, different traffic patterns are presented under different cost functions. For real-world validation, we further use an inverse reinforcement learning approach (IRL) to uncover the underlying cost function on the next-generation simulation (NGSIM) data set. We formulate the problem of inferring cost functions as a min-max game and use an apprenticeship learning algorithm to solve for cost function coefficients. The results show that our proposed GSOM-MFG is a generic framework that can accommodate various cost functions. The Aw Rascle and Zhang (ARZ) and Light-Whitham-Richards (LWR) fundamental diagrams in traffic flow models belong to our GSOM-MFG when costs are specified. History: This paper has been accepted for the Transportation Science Special Issue on ISTTT25 Conference. Funding: X. Di is supported by the National Science Foundation [CAREER Award CMMI-1943998]. E. Iacomini is partially supported by the Italian Research Center on High-Performance Computing, Big Data and Quantum Computing (ICSC) funded by MUR Missione 4-Next Generation EU (NGEU) [Spoke 1 “FutureHPC & BigData”]. C. Segala and M. Herty thank the Deutsche Forschungsgemeinschaft (DFG) for financial support [Grants 320021702/GRK2326, 333849990/IRTG-2379, B04, B05, and B06 of 442047500/SFB1481, HE5386/18-1,19-2,22-1,23-1,25-1, ERS SFDdM035; Germany’s Excellence Strategy EXC-2023 Internet of Production 390621612; and Excellence Strategy of the Federal Government and the Länder]. Support through the EU DATAHYKING is also acknowledged. This work was also funded by the DFG [TRR 154, Mathematical Modelling, Simulation and Optimization Using the Example of Gas Networks, Projects C03 and C05, Project No. 239904186]. Moreover, E. Iacomini and C. Segala are members of the Indam GNCS (Italian National Group of Scientific Calculus).

The COVID-19 pandemic has dramatically transformed human mobility patterns. Therefore, human mobility prediction for the “new normal” is crucial to infrastructure redesign, emergency management, and urban planning post the pandemic. This paper aims to predict people’s number of visits to various locations in New York City using COVID and mobility data in the past two years. To quantitatively model the impact of COVID cases on human mobility patterns and predict mobility patterns across the pandemic period, this paper develops a model CCAAT-GCN ( C ross- and C ontext- A ttention based Spatial-Temporal G raph C onvolutional N etworks). The proposed model is validated using SafeGraph data in New York City from August 2020 to April 2022. A rich set of baselines are performed to demonstrate the performance of our proposed model. Results demonstrate the superior performance of our proposed method. Also, the attention matrix learned by our model exhibits a strong alignment with the COVID-19 situation and the points of interest within the geographic region. This alignment suggests that the model effectively captures the intricate relationships between COVID-19 case rates and human mobility patterns. The developed model and findings can offer insights into the mobility pattern prediction for future disruptive events and pandemics, so as to assist with emergency preparedness for planners, decision-makers and policymakers.

Spatiotemporal prediction over graphs (STPG) is challenging because real-world data suffer from the out-of-distribution (OOD) generalization problem, where test data follow different distributions from training ones. To address this issue, invariant risk minimization (IRM) has emerged as a promising approach for learning invariant representations across different environments. However, IRM and its variants are originally designed for Euclidean data, such as images, and may not generalize well to graph-structure data, such as spatiotemporal graphs, because of spatial correlations in graphs. To overcome the challenge posed by graph-structure data, the existing graph OOD methods adhere to the principles of invariance existence (i.e., there exist invariant features that consistently relate to the label across various environments) or environment diversity (i.e., diversifying training environments increases the likelihood that test environments align with training ones). However, there is little research that combines both principles in the STPG problem. A combination of the two is crucial for efficiently distinguishing between invariant features and spurious ones. In this study, we fill in this research gap and propose a diffusion-augmented invariant risk minimization (diffIRM) framework that combines these two principles for the STPG problem. Our diffIRM contains two processes: (1) data augmentation, and (2) invariant learning. In the data augmentation process, a causal mask generator identifies causal features, and a graph-based diffusion model acts as an environment augmentor to generate augmented spatiotemporal graph data. In the invariant learning process, an invariance penalty is designed using the augmented data and then serves as a regularizer for training the spatiotemporal prediction model. We provide theoretical evidence supporting diffIRM’s ability to identify invariant features. The effectiveness of diffIRM is further demonstrated through experiments on both numerical and real-world data. The numerical data are generated from a known structural causal model (SCM), and our proposed diffIRM successfully identifies the true invariant features. The real-world experiment uses three human mobility data sets, that is, SafeGraph, PeMS04, and PeMS08. Our proposed diffIRM outperforms baselines. Furthermore, our model demonstrates interpretability by discerning invariant features while making predictions. History: This paper has been accepted for the Transportation Science Special Issue on Machine Learning Methods for Urban Passenger Mobility. Funding: This work was supported by the National Science Foundation [Grant 2218809].