B1556
Title: The SPDE approach for spatio-temporal datasets with advection and diffusion: A matrix-free approach
Authors: Lucia Clarotto - Mines Paris, PSL University (France) [presenting]
Denis Allard - INRAE (France)
Thomas Romary - Mines Paris PSL University (France)
Nicolas Desassis - Mines Paris PSL University (France)
Abstract: In the task of predicting spatio-temporal fields in environmental science, introducing models inspired by the physics of the underlying phenomena that are numerically efficient is of growing interest in spatial statistics. The size of space-time datasets calls for new numerical methods to process them efficiently. The SPDE (Stochastic Partial Differential Equation) approach has proven to be effective for the estimation and prediction in a spatial context. We present the advection-diffusion SPDE with first-order derivative in time to enlarge the SPDE family to the space-time context. By varying the coefficients of the differential operators, the approach allows us to define a large class of non-separable spatio-temporal models. A Gaussian Markov random field approximation of the solution of the SPDE is built by discretizing the temporal derivative with a finite difference method (implicit Euler) and by solving the purely spatial SPDE with a finite element method (continuous Galerkin) at each time step. The Streamline Diffusion stabilization technique is introduced when the advection term dominates the diffusion term. Computationally efficient methods are proposed to estimate the parameters of the SPDE and to predict the spatio-temporal field by kriging. The approach is applied to a solar radiation dataset.
