CERAMATHS - DMATHS seminar : presentations by Yousri Slaoui and Clément Cancès

The CERAMATHS Mathematics Department seminar will welcome at 2:00 pm Yousri Slaoui (University of Poitiers) for the following talk:

Recursive estimation in the framework of functional data: predictions, classifications and applications

In the context of big data, we are very often required to deal with a large set of data.
In the first part, we use stochastic algorithms, in order to build recursive estimators. The major interest of these recursive approaches is that they allow a fast update of the estimators when the data are observed sequentially without being obliged to store in memory all the past observations. In the second part, we focus on the problem of recursive estimation of a regression function in the case of functional data, we present some results concerning the asymptotic behavior of the proposed non-parametric estimator, we subsequently automate the smoothing parameter and we compare the proposed method to existing methods using simulated data and then real data.
In the third part, we address the problem of supervised curve classification, we highlight the gain of using recursive approaches using simulated data and then real data.
In the fourth part, we consider the problem of unsupervised classification using an application example from the field of Psychology more precisely in electroencephalography (EEG) which highlights the practical interest of the method and we compare our approach to a parametric approach based on stochastic block models (SBM).

And at 3:15 pm Clément Cancès (INRIA Lille - Nord Europe) for the following talk:

Towards thermodynamically compatible models for steel corrosion

In the context of deep underground storage of nuclear waste, the solution chosen by France, long-lived waste is collected in steel containers and stored in an aqueous medium. A fine modeling of the corrosion of the steel is then necessary, both to anticipate its degradation, and especially to anticipate the production of dihydrogen from the chemical reaction.
In this presentation, we focus on the corrosion of the steel. In this presentation, we are interested in the evolution of the oxide layer (magnetite) on the surface of a steel block immersed in an aqueous medium.
Charge carriers (ferric cations, electrons and oxygen vacancies) move in the crystalline structure of the oxide and exchange with the solution and the metal, making the geometry of the oxide layer and its composition evolve in time.
We propose a one-dimensional Nernst-Planck-Poisson type model to model the evolution of the oxide layer over time, taking care that the model encodes the second principle of thermodynamics, contrary to the state-of-the-art reference model.
In the simplified case where we neglect the displacement of hydrogen vacancies (and thus the geometrical evolution of the oxide layer), we show the existence of a solution to our model. The analysis is based on the decay of the free energy with time, as well as on uniform bounds obtained by Moser iterations.