Short academic biography

I started as a permanent researcher at INRAE Montpellier in 2023. I am an Applied Mathematician and Physicist. My latest research interests focus on statistical models e.g. Hidden Markov Models, Deep Learning to tackle environmental, and climate (change) problems. I also work on practical Robust statistics.

I am a Julia enthusiast, and I am working on a few packages (see my GitHub profile.)

I was a Postdoctoral researcher at the Centre de Mathématiques Appliquées (CMAP) of the École Polytechnique from September 2020 to 2022. I worked with Emmanuel Gobet on the resilience to climate change of the French nuclear and renewable production system. I am funded by the La chaire Énergies durables (Sustainable Energy chair). I had teaching duties in Probability and Statistics.

Previously, I was a Postdoctoral fellow at the Los Alamos National Laboratory (2017-2020). There, I was part of the Advanced Network Science Initiative (ANSI) team under Marc Vuffray and Michael (Misha) Chertkov supervision.

I did my Physics Ph.D. from October 2014 to September 2017 at the Laboratoire Dieudonné, Université Côte d'Azur. My thesis advisor was Julien Barré. You can find my PhD thesis here.

Keywords flowchart of my research interests

Research projects

Some description of my present and past research projects.

Stochastic Weather Generator

Longest dry spell

Nuclear Power plants are threatened by climate change: the neighboring rivers could in the next decades become too hot or dry to cool them. In our project, we work with EDF managing the nuclear power plants. Our first goal is to build a Stochastic Weather Generator for precipitations over France, that can reproduce spatial and temporal features e.g., like very long drought (dry spell).

To build our Stochastic Weather Generator, we use Hidden Markov Models. Paper in preparation. Two packages I developed and use for this work are SmoothPeriodicStatsModels.jl, StochasticWeatherGenerator.jl, PeriodicHiddenMarkovModels.jl for using and fitting periodic Hidden Markov Chains (unfinished) and ExpectationMaximization.jl for simple but very generic (and quite fast) mixture fitting.

Robust Quasi Monte Carlo

Say you want to estimate a difficult integral μ\mu (or the expectation of the random variable XX)

μ=[0,1]df(u)du=E(f(U))=E(X) \mu = \int_{[0,1]^d} f(u)\,\mathrm{d}u = \mathbb{E}(f(U)) = \mathbb{E}(X)

where UU is uniformly distributed, UU([0,1]d)U\sim \mathcal{U}([0,1]^d). One can use Monte Carlo methods to estimate μ\mu as

μ^N=i=1Nf(Ui). \hat{\mu}_N = \sum_{i = 1}^N f(U_i).

In our recent work, we propose using some variance reduction techniques (Randomized Quasi Monte Carlo) combined with robust mean estimators, e.g., Median of Mean, to obtain "optimal" non-asymptotic confidence interval for the estimations of μ\mu.

The tools used in this work are conveniently gathered in two independent Julia packages I developed RandomizedQuasiMonteCarlo.jl and RobustMeans.jl. The former package is now deprecated in favor of collaborative QuasiMonteCarlo.jl package where I mostly contributed to the randomization methods.

Uncertainty Quantification in Power Systems

How does uncertainty propagate through a complex system and affects the outputs (quantities of interest)? In general, for nonlinear processes, no analytical relation between the inputs and outputs can be found and one needs to use Uncertainty Quantification techniques. In this project, the complex system is an electrical network governed by the AC power flow equations, i.e., the Kirchhoff law. In the deterministic case, when there is no source of uncertainty, one can find the optimal (most cost-efficient to operate) solution of the AC power flow equations respecting the safety bounds by solving one nonlinear nonconvex constrained optimization problem, the AC-OPF problem. The generalization to the stochastic case is the goal of this work.

In the stochastic version of AC-OPF, we add to this problem uncertainty. The question becomes: “Can we guarantee a reliable and optimal operation for our electrical network with uncertainty?”. In mathematical terms, we want to solve the stochastic version of a nonlinear, nonconvex large-scale optimization problem with both equality and inequality constraints.

Mean Field Control of Electrical Oscillators

PhD Bifurcation in Vlasov and Kuramoto systems (and Magneto Optical Trap)

Lieb-Robinson bound

CC BY-SA 4.0 David Métivier. Last modified: June 13, 2024. Website built with Franklin.jl and the Julia programming language.