Xuan Di

Xuan Di, Rongye Shi, Zhaobin Mo et al. · cmu

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 (DNN), 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 physics are encoded into DNNs and how the physics and data components are represented. In this paper, we provide 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.

Kuang Huang, Xuan Di, Qiang Du et al.

This paper proposes an efficient computational framework for longitudinal velocity control of a large number of autonomous vehicles (AVs) and develops a traffic flow theory for AVs. Instead of hypothesizing explicitly how AVs drive, our goal is to design future AVs as rational, utility-optimizing agents that continuously select optimal velocity over a period of planning horizon. With a large number of interacting AVs, this design problem can become computationally intractable. This paper aims to tackle such a challenge by employing mean field approximation and deriving a mean field game (MFG) as the limiting differential game with an infinite number of agents. The proposed micro-macro model allows one to define individuals on a microscopic level as utility-optimizing agents while translating rich microscopic behaviors to macroscopic models. Different from existing studies on the application of MFG to traffic flow models, the present study offers a systematic framework to apply MFG to autonomous vehicle velocity control. The MFG-based AV controller is shown to mitigate traffic jam faster than the LWR-based controller. MFG also embodies classical traffic flow models with behavioral interpretation, thereby providing a new traffic flow theory for AVs.

Chenyu Zhang, Xu Chen, Xuan Di · mit

Mean field games (MFGs) model interactions in large-population multi-agent systems through population distributions. Traditional learning methods for MFGs are based on fixed-point iteration (FPI), where policy updates and induced population distributions are computed separately and sequentially. However, FPI-type methods may suffer from inefficiency and instability due to potential oscillations caused by this forward-backward procedure. In this work, we propose a novel perspective that treats the policy and population as a unified parameter controlling the game dynamics. By applying stochastic parameter approximation to this unified parameter, we develop SemiSGD, a simple stochastic gradient descent (SGD)-type method, where an agent updates its policy and population estimates simultaneously and fully asynchronously. Building on this perspective, we further apply linear function approximation (LFA) to the unified parameter, resulting in the first population-aware LFA (PA-LFA) for learning MFGs on continuous state-action spaces. A comprehensive finite-time convergence analysis is provided for SemiSGD with PA-LFA, including its convergence to the equilibrium for linear MFGs -- a class of MFGs with a linear structure concerning the population -- under the standard contractivity condition, and to a neighborhood of the equilibrium under a more practical condition. We also characterize the approximation error for non-linear MFGs. We validate our theoretical findings with six experiments on three MFGs.

Zhaobin Mo, Yongjie Fu, Daran Xu et al.

This paper proposes the TrafficFlowGAN, a physics-informed flow based generative adversarial network (GAN), for uncertainty quantification (UQ) of dynamical systems. TrafficFlowGAN adopts a normalizing flow model as the generator to explicitly estimate the data likelihood. This flow model is trained to maximize the data likelihood and to generate synthetic data that can fool a convolutional discriminator. We further regularize this training process using prior physics information, so-called physics-informed deep learning (PIDL). To the best of our knowledge, we are the first to propose an integration of flow, GAN and PIDL for the UQ problems. We take the traffic state estimation (TSE), which aims to estimate the traffic variables (e.g. traffic density and velocity) using partially observed data, as an example to demonstrate the performance of our proposed model. We conduct numerical experiments where the proposed model is applied to learn the solutions of stochastic differential equations. The results demonstrate the robustness and accuracy of the proposed model, together with the ability to learn a machine learning surrogate model. We also test it on a real-world dataset, the Next Generation SIMulation (NGSIM), to show that the proposed TrafficFlowGAN can outperform the baselines, including the pure flow model, the physics-informed flow model, and the flow based GAN model.

Zhaobin Mo, Yongjie Fu, Xuan Di

This paper aims to quantify uncertainty in traffic state estimation (TSE) using the generative adversarial network based physics-informed deep learning (PIDL). The uncertainty of the focus arises from fundamental diagrams, in other words, the mapping from traffic density to velocity. To quantify uncertainty for the TSE problem is to characterize the robustness of predicted traffic states. Since its inception, generative adversarial networks (GAN) have become a popular probabilistic machine learning framework. In this paper, we will inform the GAN based predictions using stochastic traffic flow models and develop a GAN based PIDL framework for TSE, named ``PhysGAN-TSE". By conducting experiments on a real-world dataset, the Next Generation SIMulation (NGSIM) dataset, this method is shown to be more robust for uncertainty quantification than the pure GAN model or pure traffic flow models. Two physics models, the Lighthill-Whitham-Richards (LWR) and the Aw-Rascle-Zhang (ARZ) models, are compared as the physics components for the PhysGAN, and results show that the ARZ-based PhysGAN achieves a better performance than the LWR-based one.

Rui Xu, Shanyin Tong, Xuan Di

Existing macroscopic traffic control methods often struggle to strictly regulate rare, safety-critical extreme events under stochastic disturbances. In this paper, we develop a rare chance-constrained optimal control framework for autonomous traffic management. To efficiently enforce these probabilistic safety specifications, we exploit a large deviation theory (LDT) based approximation method, which converts the original highly non-convex, sampling-heavy optimization problem into a tractable deterministic nonlinear programming problem. In addition, the proposed LDT-based reformulation exhibits superior computational scalability, as it maintains a constant computational burden regardless of the target violation probability level, effectively bypassing the extreme scaling bottlenecks of traditional sampling-based methods. The effectiveness of the proposed framework in achieving precise near-target probability control and superior computational efficiency over risk-averse baselines is illustrated through extensive numerical simulations across diverse traffic risk measures.

Yongjie Fu, Anmol Jain, Xuan Di et al.

The advancement of autonomous driving technologies necessitates increasingly sophisticated methods for understanding and predicting real-world scenarios. Vision language models (VLMs) are emerging as revolutionary tools with significant potential to influence autonomous driving. In this paper, we propose the DriveGenVLM framework to generate driving videos and use VLMs to understand them. To achieve this, we employ a video generation framework grounded in denoising diffusion probabilistic models (DDPM) aimed at predicting real-world video sequences. We then explore the adequacy of our generated videos for use in VLMs by employing a pre-trained model known as Efficient In-context Learning on Egocentric Videos (EILEV). The diffusion model is trained with the Waymo open dataset and evaluated using the Fréchet Video Distance (FVD) score to ensure the quality and realism of the generated videos. Corresponding narrations are provided by EILEV for these generated videos, which may be beneficial in the autonomous driving domain. These narrations can enhance traffic scene understanding, aid in navigation, and improve planning capabilities. The integration of video generation with VLMs in the DriveGenVLM framework represents a significant step forward in leveraging advanced AI models to address complex challenges in autonomous driving.

Boxuan Wang, Haonan Duan, Yanhao Feng et al.

Social norm is defined as a shared standard of acceptable behavior in a society. The emergence of social norms fosters coordination among agents without any hard-coded rules, which is crucial for the large-scale deployment of AVs in an intelligent transportation system. This paper explores the application of LLMs in understanding and modeling social norms in autonomous driving games. We introduce LLMs into autonomous driving games as intelligent agents who make decisions according to text prompts. These agents are referred to as LLM-based agents. Our framework involves LLM-based agents playing Markov games in a multi-agent system (MAS), allowing us to investigate the emergence of social norms among individual agents. We aim to identify social norms by designing prompts and utilizing LLMs on textual information related to the environment setup and the observations of LLM-based agents. Using the OpenAI Chat API powered by GPT-4.0, we conduct experiments to simulate interactions and evaluate the performance of LLM-based agents in two driving scenarios: unsignalized intersection and highway platoon. The results show that LLM-based agents can handle dynamically changing environments in Markov games, and social norms evolve among LLM-based agents in both scenarios. In the intersection game, LLM-based agents tend to adopt a conservative driving policy when facing a potential car crash. The advantage of LLM-based agents in games lies in their strong operability and analyzability, which facilitate experimental design.

Yuping Wang, Shuo Xing, Cui Can et al.

Generative Artificial Intelligence (GenAI) constitutes a transformative technological wave that reconfigures industries through its unparalleled capabilities for content creation, reasoning, planning, and multimodal understanding. This revolutionary force offers the most promising path yet toward solving one of engineering's grandest challenges: achieving reliable, fully autonomous driving, particularly the pursuit of Level 5 autonomy. This survey delivers a comprehensive and critical synthesis of the emerging role of GenAI across the autonomous driving stack. We begin by distilling the principles and trade-offs of modern generative modeling, encompassing VAEs, GANs, Diffusion Models, and Large Language Models (LLMs). We then map their frontier applications in image, LiDAR, trajectory, occupancy, video generation as well as LLM-guided reasoning and decision making. We categorize practical applications, such as synthetic data workflows, end-to-end driving strategies, high-fidelity digital twin systems, smart transportation networks, and cross-domain transfer to embodied AI. We identify key obstacles and possibilities such as comprehensive generalization across rare cases, evaluation and safety checks, budget-limited implementation, regulatory compliance, ethical concerns, and environmental effects, while proposing research plans across theoretical assurances, trust metrics, transport integration, and socio-technical influence. By unifying these threads, the survey provides a forward-looking reference for researchers, engineers, and policymakers navigating the convergence of generative AI and advanced autonomous mobility. An actively maintained repository of cited works is available at https://github.com/taco-group/GenAI4AD.

Yongjie Fu, Yunlong Li, Xuan Di

Autonomous driving training requires a diverse range of datasets encompassing various traffic conditions, weather scenarios, and road types. Traditional data augmentation methods often struggle to generate datasets that represent rare occurrences. To address this challenge, we propose GenDDS, a novel approach for generating driving scenarios generation by leveraging the capabilities of Stable Diffusion XL (SDXL), an advanced latent diffusion model. Our methodology involves the use of descriptive prompts to guide the synthesis process, aimed at producing realistic and diverse driving scenarios. With the power of the latest computer vision techniques, such as ControlNet and Hotshot-XL, we have built a complete pipeline for video generation together with SDXL. We employ the KITTI dataset, which includes real-world driving videos, to train the model. Through a series of experiments, we demonstrate that our model can generate high-quality driving videos that closely replicate the complexity and variability of real-world driving scenarios. This research contributes to the development of sophisticated training data for autonomous driving systems and opens new avenues for creating virtual environments for simulation and validation purposes.

Yongjie Fu, Qi Gao, Mahshid Ghasemi Dehkordi et al.

Digital twins (DTs) for urban transportation systems have gained increasing attention; however, their systematic evaluation in safety-critical scenarios remains limited. This paper presents a multi-pedestrian safety warning system at urban intersections enabled by a tightly coupled physical-digital twin framework. Built upon the COSMOS city-scale wireless testbed in New York City, the proposed system integrates camera and ultra-wideband (UWB), edge-cloud computing, predictive trajectory modeling, and MQTT-based communication to deliver real-time safety alerts to vulnerable road users (VRUs). The system is evaluated through both field deployment and virtual reality (VR) experiments. Results demonstrate high warning generation accuracy, localization accuracy, efficient end-to-end latency under different model configurations, and significant reductions in user response time when warnings are issued. The proposed DT framework provides a scalable, modular, and generalizable solution for real-time multi-pedestrian safety enhancement at complex urban intersections.

Baohua Yan, Jennifer Kava, Qingyuan Liu et al.

Standard diffusion models (DMs) rely on the total destruction of data into non-informative white noise, forcing the backward process to denoise from a fully unstructured noise state. While ensuring diversity, this results in a cumbersome and computationally intensive image generation task. We address this challenge by proposing new forward and backward process within a mathematically tractable spectral space. Unlike pixel-based DMs, our forward process converges towards an informative Gaussian prior N(mu_hat,Sigma_hat) rather than white noise. Our method, termed Preserving Spectral Structure and Statistics (PreSS) in diffusion models, guides spectral components toward this informative prior while ensuring that corresponding structural signals remain intact at terminal time. This provides a principled starting point for the backward process, enabling high-quality image reconstruction that builds upon preserved spectral structure while maintaining high generative diversity. Experimental results on CIFAR-10, CelebA and CelebA-HQ demonstrate significant reductions in computational complexity, improved visual diversity, less drift, and a smoother diffusion process compared to pixel-based DMs.

Bowen Fang, Ruijian Zha, Xuan Di

Predicting public transit incident duration from unstructured text alerts is a critical but challenging task. Addressing the domain sparsity of transit operations with standard Supervised Fine-Tuning (SFT) is difficult, as the task involves noisy, continuous labels and lacks reliable expert demonstrations for reasoning. While Reinforcement Learning from Verifiable Rewards (RLVR) excels at tasks with binary correctness, like mathematics, its applicability to noisy, continuous forecasting is an open question. This work, to our knowledge, is the first to bridge the gap between RLVR LLM training with the critical, real-world forecasting challenges in public transit operations. We adapt RLVR to this task by introducing a tolerance-based, shaped reward function that grants partial credit within a continuous error margin, rather than demanding a single correct answer. We systematically evaluate this framework on a curated dataset of NYC MTA service alerts. Our findings show that general-purpose, instruction-tuned LLMs significantly outperform specialized math-reasoning models, which struggle with the ambiguous, real-world text. We empirically demonstrate that the binary reward is unstable and degrades performance, whereas our shaped reward design is critical and allows our model to dominate on the most challenging metrics. While classical regressors are superior at minimizing overall MAE or MSE, our RLVR approach achieved a 35\% relative improvement in 5-minute accuracy (Acc@5) over the strongest baseline. This demonstrates that RLVR can be successfully adapted to real-world, noisy forecasting, but requires a verifier design that reflects the continuous nature of the problem.

Kangrui Ruan, Xinyang Wang, Xuan Di

Social media has become an important platform for people to express their opinions towards transportation services and infrastructure, which holds the potential for researchers to gain a deeper understanding of individuals' travel choices, for transportation operators to improve service quality, and for policymakers to regulate mobility services. A significant challenge, however, lies in the unstructured nature of social media data. In other words, textual data like social media is not labeled, and large-scale manual annotations are cost-prohibitive. In this study, we introduce a novel methodological framework utilizing Large Language Models (LLMs) to infer the mentioned travel modes from social media posts, and reason people's attitudes toward the associated travel mode, without the need for manual annotation. We compare different LLMs along with various prompting engineering methods in light of human assessment and LLM verification. We find that most social media posts manifest negative rather than positive sentiments. We thus identify the contributing factors to these negative posts and, accordingly, propose recommendations to traffic operators and policymakers.

Fuzhong Zhou, Chenyu Zhang, Xu Chen et al. · mit

We propose a discrete time graphon game formulation on continuous state and action spaces using a representative player to study stochastic games with heterogeneous interaction among agents. This formulation admits both philosophical and mathematical advantages, compared to a widely adopted formulation using a continuum of players. We prove the existence and uniqueness of the graphon equilibrium with mild assumptions, and show that this equilibrium can be used to construct an approximate solution for finite player game on networks, which is challenging to analyze and solve due to curse of dimensionality. An online oracle-free learning algorithm is developed to solve the equilibrium numerically, and sample complexity analysis is provided for its convergence.

Bowen Fang, Zixiao Yang, Xuan Di

Existing navigation systems often fail during urban disruptions, struggling to incorporate real-time events and complex user constraints, such as avoiding specific areas. We address this gap with TraveLLM, a system using Large Language Models (LLMs) for disruption-aware public transit routing. We leverage LLMs' reasoning capabilities to directly process multimodal user queries combining natural language requests (origin, destination, preferences, disruption info) with map data (e.g., subway, bus, bike-share). To evaluate this approach, we design challenging test scenarios reflecting real-world disruptions like weather events, emergencies, and dynamic service availability. We benchmark the performance of state-of-the-art LLMs, including GPT-4, Claude 3, and Gemini, on generating accurate travel plans. Our experiments demonstrate that LLMs, notably GPT-4, can effectively generate viable and context-aware navigation plans under these demanding conditions. These findings suggest a promising direction for using LLMs to build more flexible and intelligent navigation systems capable of handling dynamic disruptions and diverse user needs.

Yongjie Fu, Ruijian Zha, Pei Tian et al.

Designing diverse and safety-critical driving scenarios is essential for evaluating autonomous driving systems. In this paper, we propose a novel framework that leverages Large Language Models (LLMs) for few-shot code generation to automatically synthesize driving scenarios within the CARLA simulator, which has flexibility in scenario scripting, efficient code-based control of traffic participants, and enforcement of realistic physical dynamics. Given a few example prompts and code samples, the LLM generates safety-critical scenario scripts that specify the behavior and placement of traffic participants, with a particular focus on collision events. To bridge the gap between simulation and real-world appearance, we integrate a video generation pipeline using Cosmos-Transfer1 with ControlNet, which converts rendered scenes into realistic driving videos. Our approach enables controllable scenario generation and facilitates the creation of rare but critical edge cases, such as pedestrian crossings under occlusion or sudden vehicle cut-ins. Experimental results demonstrate the effectiveness of our method in generating a wide range of realistic, diverse, and safety-critical scenarios, offering a promising tool for simulation-based testing of autonomous vehicles.

Zhaobin Mo, Yunlong Li, Xuan Di

Safety-critical driving data is crucial for developing safe and trustworthy self-driving algorithms. Due to the scarcity of safety-critical data in naturalistic datasets, current approaches primarily utilize simulated or artificially generated images. However, there remains a gap in authenticity between these generated images and naturalistic ones. We propose a novel framework to augment the safety-critical driving data from the naturalistic dataset to address this issue. In this framework, we first detect vehicles using YOLOv5, followed by depth estimation and 3D transformation to simulate vehicle proximity and critical driving scenarios better. This allows for targeted modification of vehicle dynamics data to reflect potentially hazardous situations. Compared to the simulated or artificially generated data, our augmentation methods can generate safety-critical driving data with minimal compromise on image authenticity. Experiments using KITTI datasets demonstrate that a downstream self-driving algorithm trained on this augmented dataset performs superiorly compared to the baselines, which include SMOGN and importance sampling.

Chenyu Zhang, Xu Chen, Xuan Di · mit

Mean field games (MFGs) are a promising framework for modeling the behavior of large-population systems. However, solving MFGs can be challenging due to the coupling of forward population evolution and backward agent dynamics. Typically, obtaining mean field Nash equilibria (MFNE) involves an iterative approach where the forward and backward processes are solved alternately, known as fixed-point iteration (FPI). This method requires fully observed population propagation and agent dynamics over the entire spatial domain, which could be impractical in some real-world scenarios. To overcome this limitation, this paper introduces a novel online single-agent model-free learning scheme, which enables a single agent to learn MFNE using online samples, without prior knowledge of the state-action space, reward function, or transition dynamics. Specifically, the agent updates its policy through the value function (Q), while simultaneously evaluating the mean field state (M), using the same batch of observations. We develop two variants of this learning scheme: off-policy and on-policy QM iteration. We prove that they efficiently approximate FPI, and a sample complexity guarantee is provided. The efficacy of our methods is confirmed by numerical experiments.

Yongjie Fu, Lingyun Zhong, Zifan Li et al.

Multi-agent reinforcement learning (MARL) has shown promise for adaptive traffic signal control (ATSC), enabling multiple intersections to coordinate signal timings in real time. However, in large-scale settings, MARL faces constraints due to extensive data sharing and communication requirements. Federated learning (FL) mitigates these challenges by training shared models without directly exchanging raw data, yet traditional FL methods such as FedAvg struggle with highly heterogeneous intersections. Different intersections exhibit varying traffic patterns, demands, and road structures, so performing FedAvg across all agents is inefficient. To address this gap, we propose Hierarchical Federated Reinforcement Learning (HFRL) for ATSC. HFRL employs clustering-based or optimization-based techniques to dynamically group intersections and perform FedAvg independently within groups of intersections with similar characteristics, enabling more effective coordination and scalability than standard FedAvg. Our experiments on synthetic and real-world traffic networks demonstrate that HFRL not only outperforms both decentralized and standard federated RL approaches but also identifies suitable grouping patterns based on network structure or traffic demand, resulting in a more robust framework for distributed, heterogeneous systems.

Zhaobin Mo, Qingyuan Liu, Baohua Yan et al.

Spatiotemporal prediction over graphs (STPG) is crucial for transportation systems. In existing STPG models, an adjacency matrix is an important component that captures the relations among nodes over graphs. However, most studies calculate the adjacency matrix by directly memorizing the data, such as distance- and correlation-based matrices. These adjacency matrices do not consider potential pattern shift for the test data, and may result in suboptimal performance if the test data has a different distribution from the training one. This issue is known as the Out-of-Distribution generalization problem. To address this issue, in this paper we propose a Causal Adjacency Learning (CAL) method to discover causal relations over graphs. The learned causal adjacency matrix is evaluated on a downstream spatiotemporal prediction task using real-world graph data. Results demonstrate that our proposed adjacency matrix can capture the causal relations, and using our learned adjacency matrix can enhance prediction performance on the OOD test data, even though causal learning is not conducted in the downstream task.

Zhaobin Mo, Haotian Xiang, Xuan Di

Spatiotemporal prediction over graphs (STPG) is challenging, because real-world data suffers 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 like images, and may not generalize well to graph-structure data such as spatiotemporal graphs due to 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, or environment diversity. 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: i) data augmentation and ii) 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. The real-world experiment uses three human mobility datasets, i.e. SafeGraph, PeMS04, and PeMS08. Our proposed diffIRM outperforms baselines.

Yongjie Fu, Mehmet K. Turkcan, Mahshid Ghasemi et al.

We present methods and applications for the development of digital twins (DT) for urban traffic management. While the majority of studies on the DT focus on its ``eyes," which is the emerging sensing and perception like object detection and tracking, what really distinguishes the DT from a traditional simulator lies in its ``brain," the prediction and decision making capabilities of extracting patterns and making informed decisions from what has been seen and perceived. In order to add value to urban transportation management, DTs need to be powered by artificial intelligence and complement with low-latency high-bandwidth sensing and networking technologies, in other words, cyberphysical systems (CPS). We will first review the DT pipeline enabled by CPS and propose our DT architecture deployed on a real-world testbed in New York City. This paper can be a pointer to help researchers and practitioners identify challenges and opportunities for the development of DTs; a bridge to initiate conversations across disciplines; and a road map to exploiting potentials of DTs for diverse urban transportation applications.

Bowen Fang, Xu Chen, Xuan Di

This paper aims to develop a learning method for a special class of traveling salesman problems (TSP), namely, the pickup-and-delivery TSP (PDTSP), which finds the shortest tour along a sequence of one-to-one pickup-and-delivery nodes. One-to-one here means that the transported people or goods are associated with designated pairs of pickup and delivery nodes, in contrast to that indistinguishable goods can be delivered to any nodes. In PDTSP, precedence constraints need to be satisfied that each pickup node must be visited before its corresponding delivery node. Classic operations research (OR) algorithms for PDTSP are difficult to scale to large-sized problems. Recently, reinforcement learning (RL) has been applied to TSPs. The basic idea is to explore and evaluate visiting sequences in a solution space. However, this approach could be less computationally efficient, as it has to potentially evaluate many infeasible solutions of which precedence constraints are violated. To restrict solution search within a feasible space, we utilize operators that always map one feasible solution to another, without spending time exploring the infeasible solution space. Such operators are evaluated and selected as policies to solve PDTSPs in an RL framework. We make a comparison of our method and baselines, including classic OR algorithms and existing learning methods. Results show that our approach can find tours shorter than baselines.

Rongye Shi, Zhaobin Mo, Kuang Huang et al.

Traffic state estimation (TSE) bifurcates into two categories, model-driven and data-driven (e.g., machine learning, ML), while each suffers from either deficient physics or small data. To mitigate these limitations, recent studies introduced a hybrid paradigm, physics-informed deep learning (PIDL), which contains both model-driven and data-driven components. This paper contributes an improved version, called physics-informed deep learning with a fundamental diagram learner (PIDL+FDL), which integrates ML terms into the model-driven component to learn a functional form of a fundamental diagram (FD), i.e., a mapping from traffic density to flow or velocity. The proposed PIDL+FDL has the advantages of performing the TSE learning, model parameter identification, and FD estimation simultaneously. We demonstrate the use of PIDL+FDL to solve popular first-order and second-order traffic flow models and reconstruct the FD relation as well as model parameters that are outside the FD terms. We then evaluate the PIDL+FDL-based TSE using the Next Generation SIMulation (NGSIM) dataset. The experimental results show the superiority of the PIDL+FDL in terms of improved estimation accuracy and data efficiency over advanced baseline TSE methods, and additionally, the capacity to properly learn the unknown underlying FD relation.

Mobin Zhao, Wangzhi Li, Yongjie Fu et al.

This paper develops a decentralized reinforcement learning (RL) scheme for multi-intersection adaptive traffic signal control (TSC), called "CVLight", that leverages data collected from connected vehicles (CVs). The state and reward design facilitates coordination among agents and considers travel delays collected by CVs. A novel algorithm, Asymmetric Advantage Actor-critic (Asym-A2C), is proposed where both CV and non-CV information is used to train the critic network, while only CV information is used to execute optimal signal timing. Comprehensive experiments show the superiority of CVLight over state-of-the-art algorithms under a 2-by-2 synthetic road network with various traffic demand patterns and penetration rates. The learned policy is then visualized to further demonstrate the advantage of Asym-A2C. A pre-train technique is applied to improve the scalability of CVLight, which significantly shortens the training time and shows the advantage in performance under a 5-by-5 road network. A case study is performed on a 2-by-2 road network located in State College, Pennsylvania, USA, to further demonstrate the effectiveness of the proposed algorithm under real-world scenarios. Compared to other baseline models, the trained CVLight agent can efficiently control multiple intersections solely based on CV data and achieve the best performance, especially under low CV penetration rates.

Rongye Shi, Zhaobin Mo, Kuang Huang et al.

Traffic state estimation (TSE), which reconstructs the traffic variables (e.g., density) on road segments using partially observed data, plays an important role on efficient traffic control and operation that intelligent transportation systems (ITS) need to provide to people. Over decades, TSE approaches bifurcate into two main categories, model-driven approaches and data-driven approaches. However, each of them has limitations: the former highly relies on existing physical traffic flow models, such as Lighthill-Whitham-Richards (LWR) models, which may only capture limited dynamics of real-world traffic, resulting in low-quality estimation, while the latter requires massive data in order to perform accurate and generalizable estimation. To mitigate the limitations, this paper introduces a physics-informed deep learning (PIDL) framework to efficiently conduct high-quality TSE with small amounts of observed data. PIDL contains both model-driven and data-driven components, making possible the integration of the strong points of both approaches while overcoming the shortcomings of either. This paper focuses on highway TSE with observed data from loop detectors, using traffic density as the traffic variables. We demonstrate the use of PIDL to solve (with data from loop detectors) two popular physical traffic flow models, i.e., Greenshields-based LWR and three-parameter-based LWR, and discover the model parameters. We then evaluate the PIDL-based highway TSE using the Next Generation SIMulation (NGSIM) dataset. The experimental results show the advantages of the PIDL-based approach in terms of estimation accuracy and data efficiency over advanced baseline TSE methods.

Zhaobin Mo, Xuan Di, Rongye Shi

Car-following behavior has been extensively studied using physics-based models, such as the Intelligent Driver Model. These models successfully interpret traffic phenomena observed in the real-world but may not fully capture the complex cognitive process of driving. Deep learning models, on the other hand, have demonstrated their power in capturing observed traffic phenomena but require a large amount of driving data to train. This paper aims to develop a family of neural network based car-following models that are informed by physics-based models, which leverage the advantage of both physics-based (being data-efficient and interpretable) and deep learning based (being generalizable) models. We design physics-informed deep learning car-following (PIDL-CF) architectures encoded with two popular physics-based models - IDM and OVM, on which acceleration is predicted for four traffic regimes: acceleration, deceleration, cruising, and emergency braking. Two types of PIDL-CFM problems are studied, one to predict acceleration only and the other to jointly predict acceleration and discover model parameters. We also demonstrate the superior performance of PIDL with the Next Generation SIMulation (NGSIM) dataset over baselines, especially when the training data is sparse. The results demonstrate the superior performance of neural networks informed by physics over those without. The developed PIDL-CF framework holds the potential for system identification of driving models and for the development of driving-based controls for automated vehicles.

Zhenyu Shou, Xu Chen, Yongjie Fu et al.

This paper aims to develop a paradigm that models the learning behavior of intelligent agents (including but not limited to autonomous vehicles, connected and automated vehicles, or human-driven vehicles with intelligent navigation systems where human drivers follow the navigation instructions completely) with a utility-optimizing goal and the system's equilibrating processes in a routing game among atomic selfish agents. Such a paradigm can assist policymakers in devising optimal operational and planning countermeasures under both normal and abnormal circumstances. To this end, we develop a Markov routing game (MRG) in which each agent learns and updates her own en-route path choice policy while interacting with others in transportation networks. To efficiently solve MRG, we formulate it as multi-agent reinforcement learning (MARL) and devise a mean field multi-agent deep Q learning (MF-MA-DQL) approach that captures the competition among agents. The linkage between the classical DUE paradigm and our proposed Markov routing game (MRG) is discussed. We show that the routing behavior of intelligent agents is shown to converge to the classical notion of predictive dynamic user equilibrium (DUE) when traffic environments are simulated using dynamic loading models (DNL). In other words, the MRG depicts DUEs assuming perfect information and deterministic environments propagated by DNL models. Four examples are solved to illustrate the algorithm efficiency and consistency between DUE and the MRG equilibrium, on a simple network without and with spillback, the Ortuzar Willumsen (OW) Network, and a real-world network near Columbia University's campus in Manhattan of New York City.

Xuan Di, Rongye Shi

This paper serves as an introduction and overview of the potentially useful models and methodologies from artificial intelligence (AI) into the field of transportation engineering for autonomous vehicle (AV) control in the era of mixed autonomy. We will discuss state-of-the-art applications of AI-guided methods, identify opportunities and obstacles, raise open questions, and help suggest the building blocks and areas where AI could play a role in mixed autonomy. We divide the stage of autonomous vehicle (AV) deployment into four phases: the pure HVs, the HV-dominated, the AVdominated, and the pure AVs. This paper is primarily focused on the latter three phases. It is the first-of-its-kind survey paper to comprehensively review literature in both transportation engineering and AI for mixed traffic modeling. Models used for each phase are summarized, encompassing game theory, deep (reinforcement) learning, and imitation learning. While reviewing the methodologies, we primarily focus on the following research questions: (1) What scalable driving policies are to control a large number of AVs in mixed traffic comprised of human drivers and uncontrollable AVs? (2) How do we estimate human driver behaviors? (3) How should the driving behavior of uncontrollable AVs be modeled in the environment? (4) How are the interactions between human drivers and autonomous vehicles characterized? Hopefully this paper will not only inspire our transportation community to rethink the conventional models that are developed in the data-shortage era, but also reach out to other disciplines, in particular robotics and machine learning, to join forces towards creating a safe and efficient mixed traffic ecosystem.

Zhenyu Shou, Ziran Wang, Kyungtae Han et al.

Behavior prediction plays an essential role in both autonomous driving systems and Advanced Driver Assistance Systems (ADAS), since it enhances vehicle's awareness of the imminent hazards in the surrounding environment. Many existing lane change prediction models take as input lateral or angle information and make short-term (< 5 seconds) maneuver predictions. In this study, we propose a longer-term (5~10 seconds) prediction model without any lateral or angle information. Three prediction models are introduced, including a logistic regression model, a multilayer perceptron (MLP) model, and a recurrent neural network (RNN) model, and their performances are compared by using the real-world NGSIM dataset. To properly label the trajectory data, this study proposes a new time-window labeling scheme by adding a time gap between positive and negative samples. Two approaches are also proposed to address the unstable prediction issue, where the aggressive approach propagates each positive prediction for certain seconds, while the conservative approach adopts a roll-window average to smooth the prediction. Evaluation results show that the developed prediction model is able to capture 75% of real lane change maneuvers with an average advanced prediction time of 8.05 seconds.

Zhenyu Shou, Xuan Di

A large portion of passenger requests is reportedly unserviced, partially due to vacant for-hire drivers' cruising behavior during the passenger seeking process. This paper aims to model the multi-driver repositioning task through a mean field multi-agent reinforcement learning (MARL) approach that captures competition among multiple agents. Because the direct application of MARL to the multi-driver system under a given reward mechanism will likely yield a suboptimal equilibrium due to the selfishness of drivers, this study proposes a reward design scheme with which a more desired equilibrium can be reached. To effectively solve the bilevel optimization problem with upper level as the reward design and the lower level as a multi-agent system, a Bayesian optimization (BO) algorithm is adopted to speed up the learning process. We then apply the bilevel optimization model to two case studies, namely, e-hailing driver repositioning under service charge and multiclass taxi driver repositioning under NYC congestion pricing. In the first case study, the model is validated by the agreement between the derived optimal control from BO and that from an analytical solution. With a simple piecewise linear service charge, the objective of the e-hailing platform can be increased by 8.4%. In the second case study, an optimal toll charge of $5.1 is solved using BO, which improves the objective of city planners by 7.9%, compared to that without any toll charge. Under this optimal toll charge, the number of taxis in the NYC central business district is decreased, indicating a better traffic condition, without substantially increasing the crowdedness of the subway system.

Zhicheng Gu, Zhihao Li, Xuan Di et al.

The Waymo Open Dataset has been released recently, providing a platform to crowdsource some fundamental challenges for automated vehicles (AVs), such as 3D detection and tracking. While~the dataset provides a large amount of high-quality and multi-source driving information, people in academia are more interested in the underlying driving policy programmed in Waymo self-driving cars, which is inaccessible due to AV manufacturers' proprietary protection. Accordingly, academic researchers have to make various assumptions to implement AV components in their models or simulations, which may not represent the realistic interactions in real-world traffic. Thus, this paper introduces an approach to learn a long short-term memory (LSTM)-based model for imitating the behavior of Waymo's self-driving model. The proposed model has been evaluated based on Mean Absolute Error (MAE). The experimental results show that our model outperforms several baseline models in driving action prediction. In addition, a visualization tool is presented for verifying the performance of the model.

Xuan Di, Xu Chen, Eric Talley

Autonomous vehicles (AVs) are inevitably entering our lives with potential benefits for improved traffic safety, mobility, and accessibility. However, AVs' benefits also introduce a serious potential challenge, in the form of complex interactions with human-driven vehicles (HVs). The emergence of AVs introduces uncertainty in the behavior of human actors and in the impact of the AV manufacturer on autonomous driving design. This paper thus aims to investigate how AVs affect road safety and to design socially optimal liability rules for AVs and human drivers. A unified game is developed, including a Nash game between human drivers, a Stackelberg game between the AV manufacturer and HVs, and a Stackelberg game between the law maker and other users. We also establish the existence and uniqueness of the equilibrium of the game. The game is then simulated with numerical examples to investigate the emergence of human drivers' moral hazard, the AV manufacturer's role in traffic safety, and the law maker's role in liability design. Our findings demonstrate that human drivers could develop moral hazard if they perceive their road environment has become safer and an optimal liability rule design is crucial to improve social welfare with advanced transportation technologies. More generally, the game-theoretic model developed in this paper provides an analytical tool to assist policy-makers in AV policymaking and hopefully mitigate uncertainty in the existing regulation landscape about AV technologies.

Zhenyu Shou, Xuan Di, Jieping Ye et al.

Vacant taxi drivers' passenger seeking process in a road network generates additional vehicle miles traveled, adding congestion and pollution into the road network and the environment. This paper aims to employ a Markov Decision Process (MDP) to model idle e-hailing drivers' optimal sequential decisions in passenger-seeking. Transportation network companies (TNC) or e-hailing (e.g., Didi, Uber) drivers exhibit different behaviors from traditional taxi drivers because e-hailing drivers do not need to actually search for passengers. Instead, they reposition themselves so that the matching platform can match a passenger. Accordingly, we incorporate e-hailing drivers' new features into our MDP model. The reward function used in the MDP model is uncovered by leveraging an inverse reinforcement learning technique. We then use 44,160 Didi drivers' 3-day trajectories to train the model. To validate the effectiveness of the model, a Monte Carlo simulation is conducted to simulate the performance of drivers under the guidance of the optimal policy, which is then compared with the performance of drivers following one baseline heuristic, namely, the local hotspot strategy. The results show that our model is able to achieve a 17.5% improvement over the local hotspot strategy in terms of the rate of return. The proposed MDP model captures the supply-demand ratio considering the fact that the number of drivers in this study is sufficiently large and thus the number of unmatched orders is assumed to be negligible. To better incorporate the competition among multiple drivers into the model, we have also devised and calibrated a dynamic adjustment strategy of the order matching probability.