PhD opportunities

Spatio-temporal prediction by stochastic partial differential equations

Thesis proposal

Area of expertiseGeoscience and Geoengineering
Doctoral SchoolGRNE - Gosciences, Ressources Naturelles et Environnement
SupervisorM. Denis ALLARD
Co-supervisorM. Thomas ROMARY
Research unitGeosciences
ContactROMARY Thomas
Starting dateOctober 1st 2020
Keywordsspation temporal modeling, statistics, stochastic partiel differential equations , numerical analysis
AbstractIn a context of ecological transition, it is crucial to have tools for analyzing and predicting the evolution of natural environments and climatic variables for decision-making and the management of mitigation or adaptation measures. Many areas of environmental science seek to predict in space-time a variable of interest from observations at certain points in a field of study (spatio-temporal) and explanatory variables (called covariates) known exhaustively . In addition, the IT explosion and technological progress in measuring instruments have taken us from managing the scarcity of data to managing their abundance. Numerical methods need to be redesigned to efficiently process these very large datasets.
Spatio-temporal statistics have long been limited to the hypothesis of a stationary structure in space-time. The challenges of the thesis are therefore to take advantage of the richness of current data sets, which helps to relax this assumption of stationarity and thus improve the quality of the predictions of geostatistical methods. In a non-stationary framework, many approaches have been developed to model the spatial variations in structure, cf. Fouedjio (2017) or Schmidt (2020) for a review. The SPDE approach (Stochastic partial differential equations, Lindgren et al., 2011) allows these non-stationary factors to be easily incorporated by varying the coefficients of a differential operator in space and over time. It is on this SPDE approach that we propose to rely to arrive at effective spatio-temporal prediction methods in a non-stationary framework. The work undertaken in the Geostatistics team, some of which in collaboration with BioSP, is at the forefront in the field.
In the spatial framework, major mathematical and algorithmic advances (Carrizo et al, 2018; Pereira & Desassis, 2018; Pereira & Desassis, 2019) have been made, making it possible to efficiently process very large data sets. In addition, Ricardo Carrizo-Vergara's thesis (2018) made it possible to define new spatio-temporal models in this context, incorporating the physical processes linked to the studied phenomena (convection, diffusion, ...). We currently know how to simulate these models but the problems related to inference and conditioning by the observed data remain intact. The objective of this thesis project is therefore to propose efficient methods for inference and prediction in a spatio-temporal, non-stationary framework, based on the SPDE approach.
This type of approach can be applied in a large number of domains of the geosciences, for example the climate, the prediction of air quality in urban areas or that of groundwater, the quantification of water resources, monitoring of soil data, in particular the evolution of organic carbon stocks in the soil.
ProfileGood knowledge of probability, statistics and numerical analysis is required, as well as a strong interest in applications in environmental sciences. A taste for digital programming is required, and in particular a good knowledge of C, R and / or Python languages. Fluency in English is also required.
A motivation letter, a description of the Master 2 internship work, the results of the Master 1 and 2 exams, as well as two letters of recommendation or two referees will constitute the documents to bring to the application.
FundingFinancement d'un Etablissement d'enseignement suprieur