Statistical modeling of spatiotemporal data distributed on surfaces

For over 25 years, Andra has been conducting research for the Cigéo project, the French industrial geological storage centre designed to store highly active and long-lived radioactive waste. The project, located 500 metres below ground in the Callovo-Oxfordian (COX) argillites, aims to accommodate waste from current French nuclear facilities and from the processing of spent fuel from nuclear power plants. The facility's monitoring strategy includes comparing in situ data with predictive numerical simulations to ensure that the repository remains within the expected operating range.

The design of the Cigéo underground facility is based on guiding principles, including that of remote monitoring of control structures to trace the overall operation of other similar structures. These control structures, representative of the conditions of evolution of similar structures, are equipped with numerous monitoring devices. The aim of this post-doctorate is to estimate the temperature and deformation field on the lining of 24 cells from data from sensors. Using measurements from the cell studied such as temperature, deformation, or other relevant parameters, the scientific challenge is to develop processing algorithms capable of reliably and in detail reconstructing the thermal and mechanical conditions at all points of the cell lining and over time.

The aim of the project is thus to develop statistical methods for interpolation and prediction of spatio-temporal data distributed on surfaces. Starting from a geostatistical approach to the problem, a starting point identified for the project is the SPDE approach, according to which the observed data are modeled as samples of a Gaussian field defined as the solution of a stochastic partial differential equation. This approach has allowed the development of efficient methods for inferring non-stationary Gaussian fields, defined on surfaces and even spatio-temporal. One of the objectives of the project is therefore to adapt these methods to the case of modeling spatio-temporal fields defined on open surfaces.