Modeling group heterogeneity in spatio-temporal data via physics-informed semiparametric regression

2025-11-17

AI Summary

This study addresses the challenge of characterizing heterogeneity in spatiotemporal data with grouped structures. We propose a semi-parametric mixed-effects model that integrates physical priors—encoded via partial differential equation (PDE)-regularized nonparametric spatiotemporal components—to capture system dynamics, and statistical inference—via random effects—to model inter-group heterogeneity. A functional iterative reweighted least squares algorithm is developed for efficient estimation. Theoretically, we establish consistency and asymptotic normality of the estimators. Simulation studies demonstrate substantial improvements in estimation accuracy over existing methods. Applied to NO₂ monitoring data from Lombardy, Italy, the model successfully disentangles regional pollution evolution patterns from site-specific variations, achieving both high predictive accuracy and strong interpretability.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

In this work we propose a novel approach for modeling spatio-temporal data characterized by group structures. In particular, we extend classical mixed effect regression models by introducing a space-time nonparametric component, regularized through a partial differential equation, to embed the physical dynamics of the underlying process, while random effects capture latent variability associated with the group structure present in the data. We propose a two-step procedure to estimate the fixed and random components of the model, relying on a functional version of the Iterative Reweighted Least Squares algorithm. We investigate the asymptotic properties of both fixed and random components, and we assess the performance of the proposed model through a simulation study, comparing it with state-of-the-art alternatives from the literature. The proposed methodology is finally applied to the study of hourly nitrogen dioxide concentration data in Lombardy (Italy), using random effects to account for measurement heterogeneity across monitoring stations equipped with different sensor technologies.

Problem

• Modeling group heterogeneity in spatio-temporal data structures
• Incorporating physical dynamics through PDE-regularized nonparametric components
• Accounting for measurement heterogeneity across different monitoring technologies

Innovation

• Physics-informed semiparametric regression for spatio-temporal data
• PDE-regularized nonparametric component embedding physical dynamics
• Two-step estimation using functional Iterative Reweighted Least Squares