End-to-End Learning of User Equilibrium: Expressivity, Generalization, and Optimization
Year: 2025
Type: article
Abstract: This paper establishes an end-to-end learning framework for constructing transportation network equilibrium models. The proposed framework directly learns supply and demand components as well as equilibrium states from multiday traffic state observations. Specifically, it parameterizes unknown model components with neural networks and embeds them in an implicit layer to enforce user equilibrium conditions. By minimizing the differences between the predicted and observed traffic states, parameters for supply and demand components are simultaneously estimated. We demonstrate that the end-to-end framework is expressive: when parameterized with sufficiently large neural networks, it can replicate any unique, differentiable equilibrium state that solves a well-posed variational inequality. Moreover, it can generalize to new, unseen data when trained with sufficient observations. For efficient training, we design an autodifferentiation-based gradient descent algorithm that handles link- and path-based user equilibrium constraints and ensures local convergence. The proposed framework is demonstrated using three synthesized data sets. History: This paper has been accepted for the Transportation Science Special Issue on Machine Learning Methods for Urban Passenger Mobility. Funding: This work described in this paper was partly supported by research grants from the USDOT Center for Connected and Automated Transportation and the National Science Foundation, Division of Civil, Mechanical and Manufacturing Innovation [Grant CMMI-2233057].
Source: Transportation Science
Authors: Zhichen Liu, Yafeng Yin
Institution: University of Michigan
Language: English
Subfield: Building and Construction
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4408406181