Inverse Learning and Intervention of Transportation Network Equilibrium

The network equilibrium analysis paradigm has been a foundational tool in transportation planning and management for over seventy years. Traditionally, calibrating network equilibrium models relies on household survey data, a process that is both time-consuming and costly. With 95 percent of new vehicles expected to be connected by 2030, the increasing availability of crowdsourced trajectory data now enables direct observation of multiday travel patterns. This dissertation leverages the growing crowdsourced trajectory data, along with cutting-edge computational tools, to establish inverse learning of user equilibrium as a novel framework for constructing context-dependent network equilibrium models. Unlike traditional parametric equilibrium models, this inverse learning framework constructs novel nonparametric and semi-parametric network equilibrium models directly from empirical data without relying on predefined behavior assumptions. This framework solves inverse optimizations to infer the network equilibrium model that best matches observed multiday travel patterns. Specifically, the nonparametric approach approximates unknown model components with neural networks and embeds them within an implicit layer to enforce user equilibrium conditions. This nonparametric approach guarantees universal approximation: with sufficiently large neural networks, it can replicate any unique, differentiable user equilibrium state that solves a well-posed variational inequality. By contrast, the semi-parametric approach parameterizes unknown model components as nonnegative linear combinations of convex bases. This semi-parametric approach simplifies the inverse learning into a multiconvex optimization solvable through a sequence of convex subproblems, prioritizing computational tractability for large-scale road networks. This dissertation also mathematically quantifies the trade-offs among goodness of fit, computational efficiency, and data availability in the inverse learning process, providing a comparative analysis of nonparametric, semi-parametric, and parametric network equilibrium models. One key advantage of the inverse learning framework is its ability to incorporate context features (e.g., day of the week or weather) into network equilibrium models. These context-dependent equilibrium models more accurately capture daily variations in travel patterns than traditional models, which predict a single yearly average pattern. The inverse learning framework uses differentiable programming to develop auto-differentiation-based parallel algorithms, enabling tractable learning of context-dependent equilibrium models. This dissertation further develops a distributionally robust network design approach that applies context-dependent equilibrium models to transportation planning, reducing the underestimation of social cost under future behavioral shifts. Empirical evaluations using one year of crowdsourced trajectory data from General Motors in Ann Arbor, Michigan, validate the parametrization flexibility, computational scalability, and decision robustness of the inverse learning framework. By replacing costly household surveys with inexpensive, readily available crowdsourced data, the inverse learning framework promises to transform current planning practice and applies to every city in the world.