We examine an adaptive learning framework for nonatomic congestion games where the players' cost functions may be subject to exogenous fluctuations (e.g., due to disturbances in the network, variations in the traffic going through a link, etc.).

Urban traffic congestion stems from the misalignment between self-interested routing decisions and socially optimal flows. Intersections, as critical bottlenecks, amplify these inefficiencies because existing control schemes often neglect drivers' strategic behavior. Autonomous intersections, enabled by vehicle-to-infrastructure communication, permit vehicle-level scheduling based on individual requests. Leveraging this fine-grained control, we propose a non-monetary mechanism that strategically adjusts request timestamps-delaying or advancing passage times-to incentivize socially efficient routing. We present a hierarchical architecture separating local scheduling by roadside units from network-wide timestamp adjustments by a central planner. We establish an experimentally validated analytical model, prove the existence and essential uniqueness of equilibrium flows and formulate the planner's problem as an offline bilevel optimization program solvable with standard tools. Experiments on the Sioux Falls network show up to a 68% reduction in the efficiency gap between equilibrium and optimal flows, demonstrating scalability and effectiveness.

Scientific data, from cellular snapshots in biology to celestial distributions in cosmology, often consists of static patterns from underlying dynamical systems. These snapshots, while lacking temporal ordering, implicitly encode the processes that preserve them. This work investigates how strongly such a distribution constrains its underlying dynamics and how to recover them. We introduce the Equilibrium flow method, a framework that learns continuous dynamics that preserve a given pattern distribution. Our method successfully identifies plausible dynamics for 2-D systems and recovers the signature chaotic behavior of the Lorenz attractor. For high-dimensional Turing patterns from the Gray-Scott model, we develop an efficient, training-free variant that achieves high fidelity to the ground truth, validated both quantitatively and qualitatively. Our analysis reveals the solution space is constrained not only by the data but also by the learning model's inductive biases. This capability extends beyond recovering known systems, enabling a new paradigm of inverse design for Artificial Life. By specifying a target pattern distribution, we can discover the local interaction rules that preserve it, leading to the spontaneous emergence of complex behaviors, such as life-like flocking, attraction, and repulsion patterns, from simple, user-defined snapshots.

Credit-based congestion pricing (CBCP) has emerged as a mechanism to alleviate the social inequity concerns of road congestion pricing - a promising strategy for traffic congestion mitigation - by providing low-income users with travel credits to offset some of their toll payments. While CBCP offers immense potential for addressing inequity issues that hamper the practical viability of congestion pricing, the deployment of CBCP in practice is nascent, and the potential efficacy and optimal design of CBCP schemes have yet to be formalized. In this work, we study the design of CBCP schemes to achieve particular societal objectives and investigate their influence on traffic patterns when routing heterogeneous users with different values of time (VoTs) in a multi-lane highway with an express lane. We introduce a new non-atomic congestion game model of a mixed-economy, wherein eligible users receive travel credits while the remaining ineligible users pay out-of-pocket to use the express lane. In this setting, we investigate the effect of CBCP schemes on traffic patterns by characterizing the properties (i.e., existence, comparative statics) of the corresponding Nash equilibria and, in the setting when eligible users have time-invariant VoTs, develop a convex program to compute these equilibria. We further present a bi-level optimization framework to design optimal CBCP schemes to achieve a central planner's societal objectives. Finally, we conduct numerical experiments based on a case study of the San Mateo 101 Express Lanes Project, one of the first North American CBCP pilots. Our results demonstrate the potential of CBCP to enable low-income travelers to avail of the travel time savings provided by congestion pricing on express lanes while having comparatively low impacts on the travel costs of other road users.