1st year MSc internship at the BioRobotics Institute of the Scuola Superiore Sant'Anna - Pisa

May-August

Internship supervisor: Giovanni STABILE

Project ERC StG DANTE - Data Aware efficient models of the urban microclimate.

Study and implementation of an a posteriori error estimator for Reduced Order Models of Finite Volume Methods in CFD.

I used a weak formulation of Finite Volume Method (FVM) to make use of an a posteriori error estimator of Reduced Order Models (ROM) defined in the framework of Finite Element Method (FEM).

Internship Report.

I also created a research diary, longer than the report, in which I wrote all my ideas, addition material and demonstrations and our detailed methodology:

Research Diary.

1st year MSc Statistics Lecture group

February

Supervisor: Magalie FROMONT

Research project and presentation of results in a lecture format in collaboration with Rachelle RUELLE on approximation spaces for deep neural networks.

1st year MSc Analysis Lecture group

December

Supervisor: Rémi Carles

Research project and presentation of results in a lecture format in collaboration with Maxence MICHOT on general solutions of the Schrödinger equation.

Bachelor's internship at the Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS) - CNRS Saclay

May-July

Internship supervisor: Alberto ROSSO

Modeling and statistical analysis of critical branching processes such as Lévy flights and Brownian motion.

Here is my written internship report.

Here is my oral presentation support.

Supervised research project in bachelor's

January-April

Supervisor: Hugo Eulry

Research project in collaboration with Dimitry BERGEAULT on classical methods for solving partial differential equations. We gathered knowledge through reading articles and books, constructed Sobolev spaces, several representation theorems (Lax-Milgram, Riesz, ...) and solved classical equations.

Here is our written project report.

Here is our oral presentation support.

TIPE (Supervised Personal Initiative Work) : Creation of fake data by Generative Adversarial Networks for medecine

Supervisor: Pascal TONNELIER, mathematics professor at CPGE Lycée Descartes MP*

Project in collaboration with Junior ROGNON.

Partial proof of the correction of generative adversarial network (GAN) algorithms with Lebesgue Measure Theory and application to medical data of breast cancer.

Here is my written report for the ENS entrance exam.

Here is my oral presentation support used for the ENS and Mines Ponts/Centrales entrance exams.

Here is my demonstration sheet for our results and the correction of algorithms.

Here is our code for the proposed algorithms.

TIPE (Supervised Personal Initiative Work): Optimisation of a warehouse layout

Supervisors: Marie HEZARD and Pascal TONNELIER, mathematics professors at CPGE Lycée Descartes MPSI and MP*

Numerical optimization of a set of rectangles in a limited space. The goal was to calculate the best arrangement and try different methods to obtain reliable results in a short time.

Here is my oral presentation support for the Mines Ponts/Centrales entrance exam with the attached code.