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

2025-05-19

AI Summary

Conventional physics-informed machine learning (PIML) for traffic flow modeling employs linearly weighted aggregation of data and physics losses, which only recovers the convex portion of the Pareto front and suffers from time-consuming, unreliable weight tuning. Method: This work reformulates PIML training as a multi-objective optimization problem and introduces, for the first time in traffic modeling, multi-gradient descent (TMGD/DCGD) coupled with Pareto-optimal set learning to overcome theoretical limitations of linear scalarization, enabling automatic, robust trade-off solution search in non-convex loss spaces. The approach jointly incorporates macroscopic (LWR) and microscopic (car-following) traffic models. Contribution/Results: Our method significantly outperforms weighted baselines in microscopic traffic prediction while maintaining comparable macroscopic accuracy. It eliminates manual hyperparameter tuning, enhances model interpretability, and improves generalization across diverse traffic scenarios.

Technology Category

• Machine Learning: Optimization
• Search and Optimization: Learning to Search
• Planning, Routing, and Scheduling: Planning with Language Models

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

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.

Problem

• Overcoming limitations of linear scalarization in PIML for traffic flow modeling
• Exploring Pareto front via multi-gradient descent for multi-objective optimization
• Enhancing accuracy in microscopic traffic models with MGDAs

Innovation

• Multi-gradient descent for Pareto optimization
• Independent treatment of data and physics losses
• Dual cone gradient descent for non-convex losses