I am a
From September 2022 to December 2024, I was a PhD student under the supervision of Professors Julien Reygner (CERMICS, École Nationale des Ponts et Chaussées) and Philippe Moireau (Inria M3DISIM, École Polytechnique).
Research interests
My research work is focusing on the behaviour of
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Estimation and filtering . When modelling a dynamical phenomenon, a discrepancy is often measured between the model prediction and the targeted quantity; it is then natural to look for an improved version of the model that takes into account the measured error. A first example is thefiltering problem , which computes the conditional distribution of a system in real-time given a noisy measurement on it. When it comes to high-dimensional systems, famous examples are given by statistical mechanics and data analysis, like theGibbs principle and theSchrödinger bridge problem. In all physical experiments, measurements are affected by uncertainties of different natures; thus, the question ofstability comes along with the estimation problem.
Sampling and optimal transport. A fundamental question in probability and statistics is to sample from probability measures that minimise a given cost functional, possibly under additional constraints. A prominent example is theoptimal transport problem, which searches for an optimal measure on a product space with imposed marginal laws. Sampling from measures can be achieved by constructing appropriate dynamics with the desired large time behaviour, preferably satisfying the same constraints as the target. A famous example is given by thediffusion models in machine learning, which turns out to be closely connected toSchrödinger bridges . The question of stability and long-time convergence for the sampling dynamics is once again crucial.