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

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.