Learning Urban Access Costs from Origin-Destination Flows via Inverse Optimal Transport

A new computational framework recovers the hidden costs that shape how households access urban services, using school enrollment patterns in the Philippines as a test case, according to a preprint posted Friday [1]. The study, submitted to arXiv on 12 Jun 2026 by researcher Paula Joy Martinez, treats school-to-school enrollment flows as an entropic optimal transport plan [1]. The goal is to infer the latent cost function that families trade off — distance, price, and institutional access — when choosing a school, information that is not directly visible to planners [2]. The work focuses on the Philippines, where the country’s largest national education subsidy aims to shift learners from crowded public schools to participating private institutions [1]. The framework was applied to 283,016 learner trips across 23,820 observed flows in the most populated region [2]. Two complementary inverse optimal transport models were deployed: an interpretable distance-banded model incorporating a subsidy term, and a neural cost model trained through a differentiable Sinkhorn forward pass [1]. The analysis yields a metric called subsidy-equivalent distance, interpreted as the kilometers of perceived travel cost offset by the subsidy [2]. This approach sits within the broader field of spatial analysis, which uses topological, geometric, and geographic properties to study entities and is applied in fields ranging from urban design to genomics [4]. By transforming administrative origin-destination data into planning metrics, the method offers a tool for accessibility-aware subsidy design, facility siting, and urban service allocation [1]. The preprint, weighing 115 KB, demonstrates how inverse optimal transport can bridge the gap between observed mobility patterns and the economic pressures that produce them [1].