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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.

How to sample training/validation data is an important question for machine learning models, especially when the dataset is heterogeneous and skewed. In this paper, we propose a data sampling method that robustly selects training/validation data. We formulate the training/validation data sampling process as a two-player game: a trainer aims to sample training data so as to minimize the test error, while a validator adversarially samples validation data that can increase the test error. Robust sampling is achieved at the game equilibrium. To accelerate the searching process, we adopt reinforcement learning aided Monte Carlo trees search (MCTS). We apply our method to a car-following modeling problem, a complicated scenario with heterogeneous and random human driving behavior. Real-world data, the Next Generation SIMulation (NGSIM), is used to validate this method, and experiment results demonstrate the sampling robustness and thereby the model out-of-sample performance.

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.

Trajectory prediction aims to forecast future trajectories of agents (such as vehicles, pedestrians) based on their historical values. It is a fundamental step for advancing transportation management and control, directly impacting the safety and efficiency of modern transportation systems. In this research domain, deep learning-based methods have been widely adopted, achieving impressive performance. However, these methods have several drawbacks. First, they require substantial amounts of data. Second, they are prone to randomness inherent in real-world data. Third, complex interactions among transportation agents impose high demands on deep learning models.This dissertation seeks to address these challenges through physics-informed deep learning (PIDL), a promising approach that integrates physics-based prior knowledge into data-driven models. The dissertation is organized into three parts, focusing on different aspects of applying PIDL for trajectory prediction. First, we formulate the problem of single-agent trajectory prediction using PIDL. Second, we enhance PIDL by incorporating uncertainty quantification, accounting for uncertainties in both data and model parameters, and predicting future trajectories with confidence intervals. Third, we extend the single-agent trajectory prediction problem to a multi-agent setting, employing graph neural networks to model complex spatial interactions and NeuralODE to capture long-term dependencies.Through evaluations on both numerical and real-world datasets, our proposed methods demonstrate improved performance compared to state-of-the-art approaches. Moreover, leveraging physics-based prior knowledge makes our methods particularly robust in scenarios where deep learning models struggle, such as data-scarce environments and long-term predictions.

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.

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.

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.

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.

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.

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.