Reconstructing Physics-Informed Machine Learning for Traffic Flow Modeling: a Multi-Gradient Descent and Pareto Learning Approach
This work addresses the challenge of efficiently balancing data-driven and physics-based losses in traffic flow modeling, offering a novel optimization approach that could improve accuracy in complex scenarios, though it appears incremental in the broader ML context.
The paper tackled the limitations of linear scalarization in physics-informed machine learning for traffic flow modeling by reformulating training as a multi-objective optimization problem, using multi-gradient descent algorithms; in microscopic traffic flow models, these methods significantly outperformed traditional approaches, with notable performance gains.
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.