Multi-Scale Equilibrium under Variable Indicator Dimensionality: Faithful Reduction of Dynamic Attractors in Urban Mobility Systems

2026-07-16

AI Summary

Urban transportation systems face significant challenges under disturbances due to high-dimensional performance metrics and strong data heterogeneity, hindering the development of a unified and reliable resilience assessment framework. This work proposes a dynamic multi-layer equilibrium attractor model that distinguishes between a fast-performance layer and a slow-strategic layer, integrating statistical decision rules to enable antifragility classification. It formally characterizes, for the first time, the conditions under which multi-scale equilibrium attractors can be faithfully preserved under low-dimensional projections, proving that dimensionality reduction leads only to a unidirectional underestimation of recovery time. Theoretical guarantees are provided for preserving both Fisher information and decision-making capability. Simulation experiments across three representative urban configurations demonstrate that, within an admissible set of indicators, only two observation channels are sufficient to effectively support antifragility classification.

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.

Problem

• urban mobility
• equilibrium attractor
• indicator dimensionality
• faithful reduction
• data availability

Innovation

• multi-layer equilibrium attractor
• faithful dimensionality reduction
• urban mobility systems
• Fisher information preservation
• antifragility classification