What question did this study set out to answer?

This work aims to develop a statistical model for predicting spatio-temporal data on meshed surfaces using stochastic partial differential equations.

July 12, 2026Open Access

Prediction of spatio-temporal data on meshed surfaces using advection–diffusion SPDEs

MPMike PereiraUniversité Paris Sciences et Lettres LCLucia ClarottoDépartement Mathématiques et Informatique Appliquées NDNicolas DesassisUniversité Paris Sciences et Lettres

Key Points

This work aims to develop a statistical model for predicting spatio-temporal data on meshed surfaces using stochastic partial differential equations.
Proposed a model based on advection-diffusion SPDEs on Riemannian manifolds of dimension 2.
Utilized a Galerkin approach for model discretization and simulation.
Applied the method to both simulated datasets and real-world aerosol data.
The proposed method successfully predicts Gaussian random fields demonstrating advective and diffusive characteristics.
Scalability of algorithms was established, enhancing simulation efficiency for complex datasets.

Abstract

The aim of this work is to propose a statistical model for spatio-temporal data on meshed surfaces based on the Stochastic Partial Differential Equation (SPDE) modeling approach. Specifically, we focus on a class of advection-diffusion SPDEs defined on smooth compact orientable closed Riemannian manifolds of dimension 2, and their discretization via a Galerkin approach. We demonstrate how this method enables the development of scalable algorithms for the simulation and prediction of Gaussian random fields that are solutions to the discretized SPDE. Additionally, we present recent developments in the inference of such models. The method is applied to a simulated spatio-temporal dataset exhibiting advective and diffusive behavior on the sphere, as well as to a real case study on aerosol optical depth in the atmosphere across the globe's surface.

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