Multi-Scale Equilibrium under Variable Indicator Dimensionality: Faithful Reduction of Dynamic Attractors in Urban Mobility Systems
Authors: Ali Ghoroghi, Yacine Rezgui, Afrouz Ghaemi, Cristina De Nardi, Andrei Hodorog
Organizations: School of Engineering, Cardiff University, Cardiff, United Kingdom
Abstract
Equilibrium analysis of urban mobility systems is formulated in a high-dimensional indicator space, whilst data availability varies sharply across cities and disruption contexts. This paper gives a formal treatment of that mismatch. It presents a dynamic multi-layer equilibrium attractor for disrupted urban mobility, in which a fast performance layer relaxes towards an indicator-dependent target, a slow strategic layer supplies a joint traffic, modal and learning fixed point, and antifragility is classified through a statistical decision rule on the post-to-baseline performance ratio. It then characterises when a lower-dimensional indicator projection is faithful to this equilibrium structure, establishing four results: conditions for exact and approximate projectability of the attractor with an explicit error bound; preservation of the coupled two-layer fixed point up to a contraction boundary; the retained Fisher information and decision power of any indicator support under a measurement model on observable urban indicators; and a one-sided restoration-time bias, whereby reduced monitoring can only understate recovery duration. A simulation study on three stylised pilot-city configurations verifies each result, and shows that two observable channels suffice for the candidate classification target where the indicator catalogue permits. The framework gives city authorities a principled basis for deciding which indicators must be maintained.
Real-time urban governance depends not only on knowing where people are, but on how they move between places, directional flows that could be conventionally resolved by tracking individuals through space, i.e., expensive to sustain and built on traces that are highly unique and readily re-identifiable. Here we show that this directional structure need not be observed to be known: aggregated counts which cities already collect retain enough information to reconstruct the temporal evolution of origin-destination (OD) matrix. Using an uncertainty-aware physics-informed framework, we infer future OD flows from area-level counts alone across twelve mobility datasets from cities in the United States and China, reaching accuracy comparable to models that take historical OD matrices as input. Probabilistic modeling corrects the systematic underestimation of sparse, high-value corridors and yields calibrated predictions consistent with observed flows. Architectures that respect the generation-before-assignment logic of transport planning recover interactions more faithfully, indicating that location-level spatial heterogeneity should be preserved before pairwise interactions are reconstructed. Because inference requires only aggregated observations after training, recovering interactions this way reduces reliance on continuous individual-level tracking, pointing toward a more deployable and less exposure-heavy basis for real-time urban intelligence.
Urban public transport disruptions require rapid response strategies, yet existing studies rarely provide a decision support framework to compare alternative disruption response solutions using a common set of dynamic, passenger, operator, and environment oriented indicators. This paper proposes a KPI-driven, time-indexed framework to assess the resilience of disruption response solutions in urban transit systems. The framework combines an optimization model with a behavioral evaluation in agent-based simulation. It also underlays the secondary service degradation induced on helper lines when in-service vehicles are withdrawn to support the disrupted corridor. Rather than treating resilience as a single score, it evaluates complementary dimensions including vulnerability, adaptability, robustness, resilience loss, responsiveness, cost-based performance, emissions, and equity. The framework is implemented for the RER B transit line in the Ile-de-France (Paris) network. Results show that the coordinated strategy provides the most balanced resilience profile, combining high service continuity with lower total disruption cost than single mode alternatives, while also improving equity and maintaining competitive environmental performance. Sensitivity analysis further identifies the disruption conditions under which coordinated multimodal response is most valuable.
Accurate modeling of human mobility is critical for tackling urban planning and public health challenges. In undeveloped regions, the absence of comprehensive travel surveys necessitates reconstructing mobility networks from publicly available data. Here we develop neuroGravity, a physics-informed deep learning model that reliably reconstructs mobility flows from limited observations and transfers to unobserved cities. Using only urban facility and population distributions, we find that neuroGravity's regional representations strongly correlate with socioeconomic and livability status, offering scalable proxies for costly surveys. Furthermore, we uncover that spatial income segregation plays a key role in model transferability: mobility networks are most reliably reconstructed when target cities share similar segregation levels with the source. We design an index to quantify this segregation and accurately predict transferability. Finally, we generate mobility flow proxies for over 1,200 cities worldwide, highlighting neuroGravity's potential to mitigate critical data shortages in resource-limited, underdeveloped areas.