A new MOX Report entitled “Modeling group heterogeneity in spatio-temporal data via physics-informed regression” by De Sanctis, M.F.; Arnone, E.; Ieva, F.; Sangalli, L.M. has appeared in the MOX Report Collection.
Check it out here: https://www.mate.polimi.it/biblioteca/add/qmox/65-2026.pdf
Abstract: We propose a physics-informed semiparametric framework for modeling spatiotemporal data with group structure. The approach extends classical mixed effects regression by incorporating a nonparametric space–time component, regularized through a partial differential equation to encode the underlying physical dynamics, while random effects capture group-specific variability. Estimation is carried out via a two-step procedure based on a functional extension of the Iteratively Reweighted Least Squares algorithm. We establish asymptotic properties of both fixed and random effect estimators and we assess the performance of the method through simulation studies against state-of-the-art alternatives. The proposed framework is applied to hourly nitrogen dioxide data over Lombardy (Italy), where random effects account for measurement heterogeneity across monitoring stations with different sensor technologies, demonstrating its effectiveness in cap! turing bo th physical dynamics and group heterogeneity.
