The ninety-eighth UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, April 9, 2026.
2–3 PM — Lucia Clarotto (MIA Paris-Saclay, AgroParisTech - Geolearning Chair)
Prediction of spatio-temporal Gaussian processes by advection-diffusion stochastic partial differential equations
In the task of predicting spatio-temporal fields in environmental science using statistical methods, introducing statistical models inspired by the physics of the underlying phenomena that are numerically efficient is of growing interest. Large space–time datasets call for new numerical methods to efficiently process them. The Stochastic Partial Differential Equation (SPDE) approach has proven to be effective for the estimation and the prediction in a spatial context. We present here the advection–diffusion SPDE with first–order derivative in time which defines a large class of nonseparable spatio-temporal models, both on Euclidean spaces and Riemamnnian manifolds. A Gaussian Markov random field approximation of the solution to the SPDE is built by discretizing the temporal derivative with a finite difference method and by solving the spatial SPDE with a finite element method at each time step. Computationally efficient methods are proposed to estimate the parameters of the SPDE and to predict the spatio-temporal field by kriging, as well as to perform conditional simulations. The approach is applied to datasets of solar radiation and atmospheric aerosol optical depth across the Earth’s surface.
References:
- The SPDE approach for spatio-temporal datasets with advection and diffusion, Spatial Statistics, 2024
- Prediction of spatio-temporal data on meshed surfaces using advection-diffusion SPDEs, 2025
Joint work with Denis Allard (INRAE) & Nicolas Desassis & Mike Pereira & Thomas Romary (Mines PSL)
Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Vincent Chabridon (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Clément Gauchy (CEA), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Sébastien Petit (LNE), Emmanuel Vazquez (L2S), Xujia Zhu (L2S).
Coordinators: Sidonie Lefebvre (ONERA) & Xujia Zhu (L2S)
Practical details: the seminar will be held online using Microsoft Teams.
If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).
You will find the link to the seminar on the "General" UQSay channel on Teams, approximately 15 minutes before the beginning.
The technical side of things: you can use Teams either directly from your web browser or using the "fat client", which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.
