Speaker
Description
Sustainable urban development requires quantitative tools able to describe complex spatio-temporal processes characterized by spatial heterogeneity and directional structure. Classical stationary models are often inadequate for heterogeneous metropolitan areas, where mobility patterns and population density evolve under infrastructure constraints and recurrent temporal cycles.
We propose a semiparametric spatio-temporal regression model in which anisotropy and non-stationarity can be properly modeled through a partial differential equation regularization term. Specifically, this term involves a general second-order linear differential operator, allowing the model to incorporate prior physical knowledge about the phenomenon under study.
In this work, we exploit this flexibility by introducing a spatially varying diffusion term that adapts to the geometry of the domain and captures directional features of the process. From a mathematical perspective, this is achieved by constructing a non-stationary diffusion tensor. Working with tensors raises several challenges, such as preserving positive definiteness when performing operations like averaging or interpolation. To address these issues, we develop a suitable mathematical framework based on the Log-Euclidean metric. This choice preserves positive definiteness, ensures computational efficiency, and provides a meaningful interpretation of the eigenstructure of the resulting mean tensor.
The advantages of the proposed approach are illustrated through an application to the Telecom Italia dataset, which collects mobile phone activity over a fine spatio-temporal grid. We focus on the metropolitan area of Milan, where the signal is strongly influenced by the proximity of highways and major roads which induce preferential spatial directions, together with daily and weekly cycles reflecting human mobility habits in the temporal dimension. By allowing for non-stationary anisotropic behavior, the proposed model provides a flexible and interpretable framework for analyzing these dynamics, producing quantitative insights that can support sustainability-oriented strategies such as the optimization of shared electric mobility services, improved traffic management, and a more efficient allocation of public resources.