arXiv subjects

Xianfeng Terry Yang

Publications and source records attributed to Xianfeng Terry Yang.

11 recordsLinked to original sources

arXiv2026

Potential failures of physics-informed machine learning in traffic flow modeling: theoretical and experimental analysis

This study investigates why physics-informed machine learning (PIML) can fail in macroscopic traffic flow modeling. We define failure as cases where a PIML model underperforms both purely data-driven and purely physics-based baselines by a given threshold. Unlike in other fields, physics residuals themselves do not hinder optimization in this setting. Instead, effective updates require both data and physics gradients to form acute angles with the true gradient, a condition difficult to satisfy with low-resolution loop data. In such cases, neural networks cannot accurately approximate density and speed, and the constructed physics residuals, already degraded by discrete sampling and temporal averaging, lose their ability to capture PDE dynamics, which directly leads to PIML failure. Theoretically, although LWR and ARZ solutions are weak solutions, for piecewise $C^k$ initial data they remain $C^k$ off the shock set under mild conditions, which has Lebesgue measure zero. Thus, almost all detector or collocation points lie in smooth regions where residuals are valid, and the MLP's inability to exactly represent discontinuities is immaterial. Finally, we establish MSE lower bounds of physics residuals: higher-order models such as ARZ have strictly larger consistency error bounds than LWR under mild conditions. This explains why LWR-based PIML can outperform ARZ-based PIML even with high-resolution data, with the gap shrinking as resolution increases, consistent with prior empirical findings.

cs.LG↗

arXiv2026

A Scalable Min-Max Multi-Gradient Descent Method for Multi-Objective Transportation Problems

This paper develops a scalable min-max multi-gradient descent framework for multi-objective transportation problems with competing objectives and high-dimensional constraints. Unlike linear scalarization, which may conceal trade-offs behind pre-specified weights, and evolutionary heuristics, which can be inefficient in highly constrained feasible regions, the proposed method directly uses gradient information to construct a balanced common descent direction. At each iteration, it solves a constrained min-max problem that minimizes the worst directional derivative across all objectives, thereby prioritizing the least-improved objective and promoting robust progress. With linear constraints, the direction-finding problem reduces to a linear program. We prove the existence of the proposed direction, establish its relationship with Pareto criticality, and analyze convergence for a fixed-step update. Under a dense worst-case interior-point model, the linear-programming formulation has the same asymptotic complexity order as classical quadratic-programming-based steepest descent, while providing a distinct and more balanced direction-selection mechanism. Experiments on two transportation applications demonstrate its effectiveness. For a physics-informed car-following model, the method removes the need for manually fixed loss weights, achieves the best average predictive accuracy, reduces average RMSE by approximately /(5.81/%/) relative to the baseline, and substantially lowers variability across random seeds. For a multi-criteria traffic assignment problem balancing user equilibrium and system optimum, it produces stable common descent directions and performs favorably on large networks. Overall, the framework provides a robust, scalable, and theoretically grounded gradient-based approach to multi-objective transportation optimization.

math.OC↗

arXiv2026

Improving Feasibility in Quantum Approximate Optimization Algorithm for Vehicle Routing via Constraint-Aware Initialization and Hybrid XY-X Mixing

The Quantum Approximate Optimization Algorithm (QAOA) is a leading framework for quantum combinatorial optimization. The Vehicle Routing Problem (VRP), a core problem in logistics and transportation, is a natural application target, but it poses a major feasibility challenge for standard QAOA because feasible solutions occupy only a tiny fraction of the search space, and the conventional Pauli-$X$ mixer can disrupt partial solution structures that satisfy key local constraints. To address this issue, we propose a constraint-aware QAOA framework with two complementary components. First, we design a lightweight initialization strategy that encodes a selected subset of simple yet informative local one-hot constraints into the initial state, thereby reducing the initial superposition space and increasing the probability mass on states with important local structure. Second, we introduce a hybrid XY-$X$ mixer that preserves the constraint structure imposed at initialization while retaining exploratory flexibility over the remaining unconstrained degrees of freedom during QAOA evolution. We evaluate the proposed framework against standard QAOA under three progressively more realistic regimes: ideal statevector simulation, finite-shot sampling, and noisy finite-shot sampling. Across all regimes, the proposed method consistently achieves lower average energy and higher feasible-solution ratios than standard QAOA, indicating more effective guidance toward structurally valid, lower-cost VRP solutions. However, the performance gap narrows in the noisy regime. Because this setting adopts a hardware-inspired error model based on near-best-reported laboratory-level qubit gate and readout fidelities, the observed attenuation suggests that the practical advantage of the more structured mixer is likely to grow as quantum hardware improves and error rates decline.

cs.ET↗

arXiv2026

INSIGHT: Enhancing Autonomous Driving Safety through Vision-Language Models on Context-Aware Hazard Detection and Edge Case Evaluation

Autonomous driving systems face significant challenges in handling unpredictable edge-case scenarios, such as adversarial pedestrian movements, dangerous vehicle maneuvers, and sudden environmental changes. Current end-to-end driving models struggle with generalization to these rare events due to limitations in traditional detection and prediction approaches. To address this, we propose INSIGHT (Integration of Semantic and Visual Inputs for Generalized Hazard Tracking), a hierarchical vision-language model (VLM) framework designed to enhance hazard detection and edge-case evaluation. By using multimodal data fusion, our approach integrates semantic and visual representations, enabling precise interpretation of driving scenarios and accurate forecasting of potential dangers. Through supervised fine-tuning of VLMs, we optimize spatial hazard localization using attention-based mechanisms and coordinate regression techniques. Experimental results on the BDD100K dataset demonstrate a substantial improvement in hazard prediction straightforwardness and accuracy over existing models, achieving a notable increase in generalization performance. This advancement enhances the robustness and safety of autonomous driving systems, ensuring improved situational awareness and potential decision-making in complex real-world scenarios.

cs.CV↗

arXiv2025

Reconstructing Physics-Informed Machine Learning for Traffic Flow Modeling: a Multi-Gradient Descent and Pareto Learning Approach

Physics-informed machine learning (PIML) is crucial in modern traffic flow modeling because it combines the benefits of both physics-based and data-driven approaches. In conventional PIML, physical information is typically incorporated by constructing a hybrid loss function that combines data-driven loss and physics loss through linear scalarization. The goal is to find a trade-off between these two objectives to improve the accuracy of model predictions. However, from a mathematical perspective, linear scalarization is limited to identifying only the convex region of the Pareto front, as it treats data-driven and physics losses as separate objectives. Given that most PIML loss functions are non-convex, linear scalarization restricts the achievable trade-off solutions. Moreover, tuning the weighting coefficients for the two loss components can be both time-consuming and computationally challenging. To address these limitations, this paper introduces a paradigm shift in PIML by reformulating the training process as a multi-objective optimization problem, treating data-driven loss and physics loss independently. We apply several multi-gradient descent algorithms (MGDAs), including traditional multi-gradient descent (TMGD) and dual cone gradient descent (DCGD), to explore the Pareto front in this multi-objective setting. These methods are evaluated on both macroscopic and microscopic traffic flow models. In the macroscopic case, MGDAs achieved comparable performance to traditional linear scalarization methods. Notably, in the microscopic case, MGDAs significantly outperformed their scalarization-based counterparts, demonstrating the advantages of a multi-objective optimization approach in complex PIML scenarios.

cs.LG↗

arXiv2024

An optimization-free approximation Framework for Connected and Automated Vehicles Eco-Trajectory Planning Under limited computing capacity

The trajectory planning problem (TPP) has become increasingly crucial in the research of next-generation transportation systems, but it presents challenges due to the non-linearity of its constraints. One specific case within TPP, namely the Eco-trajectory Planning Problem (EPP), poses even greater computational difficulties due to its nonlinear, high-order, and non-convex objective function. This paper proposes an optimization-free framework to address the eco-trajectory planning problem of connected and automated vehicles (CAVs) in the straight-driving scenario. The framework consists of an offline module and an online module. In the offline module, an optimal eco-trajectory batch is constructed by solving a sequence of simplified optimization problems to minimize fuel consumption, considering various initial and terminal system states. Each candidate trajectory in the batch yields the lowest fuel consumption subject to a specific travel time from the vehicle entry to the departure from the intersection. In the online module, dynamic trajectory planning algorithms based on different scenarios are provided. Both algorithms greatly improve the computational efficiency of planning and only suffer from a limited extent of optimality losses through a batch-based selection process because optimization and calculation are pre-computed in the offline module. The latter algorithm can also handle possible emergencies and prediction errors. Numerical tests are presented and discussed to evaluate the computational quality and efficiency of the optimization-free approximation framework under a mixed-traffic flow environment that incorporates human-driving vehicles (HDV) and connected and automated vehicles (CAV) with different market penetration rates (MPR).

math.OC↗

arXiv2024

Unraveling stochastic fundamental diagrams considering empirical knowledge: modeling, limitation and further discussion

Traffic flow modeling relies heavily on fundamental diagrams. However, deterministic fundamental diagrams, such as single or multi-regime models, cannot capture the uncertainty pattern that underlies traffic flow. To address this limitation, a sparse non-parametric regression model is proposed in this paper to formulate the stochastic fundamental diagram. Unlike parametric stochastic fundamental diagram models, a non-parametric model is insensitive to parameters, flexible, and applicable. The computation complexity and the huge memory required for training in the Gaussian process regression have been reduced by introducing the sparse Gaussian process regression. The paper also discusses how empirical knowledge influences the modeling process. The paper analyzes the influence of modeling empirical knowledge in the prior of the stochastic fundamental diagram model and whether empirical knowledge can improve the robustness and accuracy of the proposed model. By introducing several well-known single-regime fundamental diagram models as the prior and testing the model's robustness and accuracy with different sampling methods given real-world data, the authors find that empirical knowledge can only benefit the model under small inducing samples given a relatively clean and large dataset. A pure data-driven approach is sufficient to estimate and describe the pattern of the density-speed relationship.

stat.AP↗

arXiv2023

A Hybrid Physics Machine Learning Approach for Macroscopic Traffic State Estimation

Full-field traffic state information (i.e., flow, speed, and density) is critical for the successful operation of Intelligent Transportation Systems (ITS) on freeways. However, incomplete traffic information tends to be directly collected from traffic detectors that are insufficiently installed in most areas, which is a major obstacle to the popularization of ITS. To tackle this issue, this paper introduces an innovative traffic state estimation (TSE) framework that hybrid regression machine learning techniques (e.g., artificial neural network (ANN), random forest (RF), and support vector machine (SVM)) with a traffic physics model (e.g., second-order macroscopic traffic flow model) using limited information from traffic sensors as inputs to construct accurate and full-field estimated traffic state for freeway systems. To examine the effectiveness of the proposed TSE framework, this paper conducted empirical studies on a real-world data set collected from a stretch of I-15 freeway in Salt Lake City, Utah. Experimental results show that the proposed method has been proved to estimate full-field traffic information accurately. Hence, the proposed method could provide accurate and full-field traffic information, thus providing the basis for the popularization of ITS.

cs.LG↗

arXiv2022

Macroscopic Traffic Flow Modeling with Physics Regularized Gaussian Process: Generalized Formulations

Despite the success of classical traffic flow (e.g., second-order macroscopic) models and data-driven (e.g., Machine Learning - ML) approaches in traffic state estimation, those approaches either require great efforts for parameter calibrations or lack theoretical interpretation. To fill this research gap, this study presents a new modeling framework, named physics regularized Gaussian process (PRGP). This novel approach can encode physics models, i.e., classical traffic flow models, into the Gaussian process architecture and so as to regularize the ML training process. Particularly, this study aims to discuss how to develop a PRGP model when the original physics model is with discrete formulations. Then based on the posterior regularization inference framework, an efficient stochastic optimization algorithm is developed to maximize the evidence lowerbound of the system likelihood. To prove the effectiveness of the proposed model, this paper conducts empirical studies on a real-world dataset that is collected from a stretch of I-15 freeway, Utah. Results show the new PRGP model can outperform the previous compatible methods, such as calibrated physics models and pure machine learning methods, in estimation precision and input robustness.

stat.ML↗

arXiv2020

Modeling Stochastic Microscopic Traffic Behaviors: a Physics Regularized Gaussian Process Approach

Modeling stochastic traffic behaviors at the microscopic level, such as car-following and lane-changing, is a crucial task to understand the interactions between individual vehicles in traffic streams. Leveraging a recently developed theory named physics regularized Gaussian process (PRGP), this study presents a stochastic microscopic traffic model that can capture the randomness and measure errors in the real world. Physical knowledge from classical car-following models is converted as physics regularizers, in the form of shadow Gaussian process (GP), of a multivariate PRGP for improving the modeling accuracy. More specifically, a Bayesian inference algorithm is developed to estimate the mean and kernel of GPs, and an enhanced latent force model is formulated to encode physical knowledge into stochastic processes. Also, based on the posterior regularization inference framework, an efficient stochastic optimization algorithm is developed to maximize the evidence lower-bound of the system likelihood. To evaluate the performance of the proposed models, this study conducts empirical studies on real-world vehicle trajectories from the NGSIM dataset. Since one unique feature of the proposed framework is the capability of capturing both car-following and lane-changing behaviors with one single model, numerical tests are carried out with two separated datasets, one contains lane-changing maneuvers and the other doesn't. The results show the proposed method outperforms the previous influential methods in estimation precision.

stat.ML↗

arXiv2020

Macroscopic Traffic Flow Modeling with Physics Regularized Gaussian Process: A New Insight into Machine Learning Applications

Despite the wide implementation of machine learning (ML) techniques in traffic flow modeling recently, those data-driven approaches often fall short of accuracy in the cases with a small or noisy dataset. To address this issue, this study presents a new modeling framework, named physics regularized machine learning (PRML), to encode classical traffic flow models (referred as physical models) into the ML architecture and to regularize the ML training process. More specifically, a stochastic physics regularized Gaussian process (PRGP) model is developed and a Bayesian inference algorithm is used to estimate the mean and kernel of the PRGP. A physical regularizer based on macroscopic traffic flow models is also developed to augment the estimation via a shadow GP and an enhanced latent force model is used to encode physical knowledge into stochastic processes. Based on the posterior regularization inference framework, an efficient stochastic optimization algorithm is also developed to maximize the evidence lowerbound of the system likelihood. To prove the effectiveness of the proposed model, this paper conducts empirical studies on a real-world dataset which is collected from a stretch of I-15 freeway, Utah. Results show the new PRGP model can outperform the previous compatible methods, such as calibrated pure physical models and pure machine learning methods, in estimation precision and input robustness.

stat.ML↗