### About Me

I am a PhD student in computational statistical physics under the direction of Gabriel Stoltz and Tony Lelièvre at CERMICS (École des Ponts) and MATHERIALS (INRIA Paris). Relevant topics include:

- sampling of probability measures in high dimensions using MCMC methods (Metropolis-Hastings, Generalized Hamiltonian Monte Carlo)
- overdamped/underdamped Langevin dynamics
- numerical analysis
- numerical integration

Mail: r……@enpc.fr

### Preprints

- T. Lelièvre, R. Santet, G. Stoltz,
*Unbiasing Hamiltonian Monte Carlo algorithms for a general Hamiltonian function*. (2023) arXiv - HAL - Code - T. Lelièvre, G. A. Pavliotis, G. Robin, R. Santet, G. Stoltz,
*Optimizing the diffusion coefficient of overdamped Langevin dynamics*. (2024) arXiv - HAL - Python/Julia Code

### Conferences

- June 2024 - 4th Italian Meeting on Probability and Mathematical Statistics.
*Optimizing the diffusion of overdamped Langevin dynamics*(Slides) - May 2024 - Labex Bézout PhD Day 2024.
*Computational Statistical Physics : a numerical microscope*(Slides) - January 2024 - Mostly Monte Carlo.
*Optimizing the diffusion of overdamped Langevin dynamics*(Slides) - October 2023 - d² reading group.
*Computing free energy differences using non-equilibrium dynamics*(Slides) - September 2023 - ANR SINEQ SUMMER SCHOOL 2023 - Sampling high-dimensional probability measures: applications in (non)equilibrium molceular dynamics and statistics.
*Discretization of Langevin dynamics and its Metropolization*(Notebook, GitHub repository) - June 2023 - MCM 2023.
*Unbiasing HMC for General Hamiltonian Functions*(Slides) - May 2023 - GAMM 2023 - Section 26: Modeling, analysis and simulation of molecular systems.
*Optimizing the diffusion of overdamped Langevin dynamics*(Slides) - May 2023 - Birmingham Workshop: (Non)equilibrium Molecular Dynamics: Algorithms, Analysis, and Applications.
*Optimizing the diffusion of overdamped Langevin dynamics*(Slides) - April 2023 - Mascot-Num 2023.
*Optimizing the diffusion of overdamped Langevin dynamics*(Poster, Blitz Slide) - March 2023 - Ma Thèse en 180 secondes. 3 minutes to introduce my subject for the whole world to see. Finale Paris-Est Sup 2023 - Video (in French)
- December 2022 - ANR SINEQ Meeting.
*Optimizing the diffusion for equilibrium and nonequilibrium dynamics*(Slides) - November 2022 - CERMICS JSJC 2022.
*Presenting MCMC methods in the molecular dynamics framework*(Notebook) - July 2022 - MCQMC 2022.
*Ensuring unbiased sampling of HMC schemes for non separable Hamiltonian systems*(Slides) - April 2022 - CECAM - Mixed-gen Season 2 – Session 7: Simulating non-equilibrium phenomena and rare events.
*Genuinely unbiased Metropolis schemes for Langevin-like dynamics*(Slides, Talk) - April 2022 - CECAM - Numerical Techniques for Nonequilibrium Steady States.
*Unbiased sampling of HMC schemes for non separable Hamiltonian systems*(Poster) - March 2022 - CERMICS - Young Researchers Seminar.
*Discretizing Langevin dynamics with multiplicative noise for sampling high-dimensional probability measures*(Slides)

### Teaching

- Mathematics in Action: practical sessions on scientific programming (integral computations, ODEs integration). 25 students.
**École Nationale des Ponts et Chaussées, September 2023** - Introduction to mathematical epidemiology (SIR/SIS/SIER models, control methods, demographic variations, R0 computation, local and asymptotic stability of endemic equilibrium). Supervising a group project (4 students).
**École Nationale des Ponts et Chaussées, January - March 2022** - PDE course: Sobolev spaces, elliptic PDEs (Poisson like PDEs with Dirichlet/Neumann/Robin boundary conditions on bounded spaces), Lax-Milgram theorem, Poincare inequalities, calculus of variations (energetic viewpoint). Application to linear elasticity and obstacle problems. 25 students.
**École Nationale des Ponts et Chaussées, April - May 2022, March-June 2023, April - June 2024** - Analysis course: Measure theory and integration, Hilbert spaces, Lebesgue spaces, Fourier series, Distribution theory, Partial differential equations, Finite difference methods, Fourier transform. Flipped classroom, 25 student.
**École Nationale des Ponts et Chaussées, September - December 2022** - Project about the use of a nonconstant diffusion coefficient to produce a proposal move for a Metropolis-like algorithm based on the integration of the overdamped Langevin dynamics. Introduction to Markov chains, Markov chain Monte Carlo algorithms, Finite Elements method, optimization tools. Supervising a group project (4 students).
**École Nationale des Ponts et Chaussées, February - June 2023**

I transcribed in LaTeX some mathematics exercices (and answers) that I prepared during my studies (L2 or CPGE MP* level in France). Everything is in French (and there are definitely typos here and there). Content: abstract algebra, differential calculus, matrix calculus, linear differential equations, euclidean spaces, normed vector spaces, functions of a real variable, integration, inner product spaces, probabilities, matrix reduction, series, power series, sequences and series of functions. GitHub repository

An ongoing project is also to transcribe in LaTeX the physics course I followed the same year (L2 or CPGE MP* level in France). Everything is in French (and there are definitely typos here and there, again). Content (for now):

- Mechanics: non-inertial reference frames, friction between two solids
- Electromagnetism: electromagnetic field, electrostatics, magnetostatics, electric dipoles, Maxwell equations, electromagnetic energy, waves in a vacuum, dispersion and attenuation of waves
- Thermodynamics: open systems, heat transfers

GitHub repository

### Distinction

- Pasquet’s Prize - Valedictorian of École Nationale des Ponts et Chaussées (2022)
- Bourse d’Excellence via the Chaire Saint-Gobain - École des Ponts ParisTech

### Experience

- Recognized student @ Department of Statistics (Oxford University), Michaelmas term (September - December 2023), under the supervision of George Deligiannidis. Computing free energy differences using diffusion models techniques. Relevant topics include Jarzynski-Crooks’ equality, annealed importance sampling, diffusion models, Schrödinger Bridge. Languages: Python.
- PhD student @ CERMICS (École des Ponts) and MATHERIALS (INRIA Paris), October 2021 - Ongoing, under the supervision of Tony Lelièvre and Gabriel Stoltz.
- Research Intern @ Green Shield Technology, April - August 2021, under the supervision of Renaud Dessalles. Mathematical epidemiology applied to the spread of beetroots diseases. Relevant topics include mathematical epidemiology, scientific computing, simulation. Languages: Python.
- Data Scientist & Customer Success officer @ FieldBox.ai, January - July 2020. Machine Learning challenges and IT support to customers (both front-end and back-end). Relevant topics include machine learning, IT systems, front-end and back-end development. Languages: Python, Bash, JavaScript, Erlang.
- Research Intern @ CEA DAM/DIF, June - November 2019, under the supervision of Jean-Bernard Maillet. Applying mathematics to molecular dynamics. Relevant topics include statistical physics, machine learning, scientific computing. Languages: C++ (LAMMPS interfaced with PLUMED2), Python.

### Education

**Sorbonne Université**, Master’s Degree, 2020 - 2021.*Master de la Modélisation*(Master of Modelisation), specializing in the*Analyse Numérique et Équations aux Dérivées Partielles*(Numerical Analysis and Partial Differential Equations) branch. Relevant topics include functional analysis, stochastic processes, numerical analysis, hyperbolic equations, multiscale systems, elliptic equations, Lorentzian differential geometry. Languages: Python, Julia.**École Nationale des Ponts et Chaussées**, Engineering Degree, 2017 - 2021. Specialization in the*Modélisation, Analyse, Simulation*(Modelisation, Analysis, Simulation) Master. Relevant topics include functional analysis, stochastic processes, Fourier analysis, numerical analysis, scientific computing, probabilities, statistics, optimal control, operational research, artificial intelligence, quantum mechanics, economics. Languages: C++, Python, Julia, Git, LaTeX.

### (Past) Projects

- Implementation in Julia of the multivariate effective sample size (multiESS) estimator, July 2023. Code.
- Data reduction in the context of cartography, February - May 2019, ENPC project with Be-Bound. State of the art on data reduction for maps for a mobile app development. Languages: JavaScript, Python, Bash, Git.
- Stochastic dynamics of a population using the Wright-Fisher model, October - December 2018, ENPC project. Research on random walks, Brownian motion and continuous martingales. Application to an allele population subject to mutations and selections. Languages: Julia, Git. Code - Poster
- Implementation of the arcade game “Paratroopers”, October - December 2018, ENPC project. Implementation of the video game in the context of a course on good habits for programming. Languages: C++, Git. Code
- Rare event probability estimation using the Adaptative Multilevel Splitting algorithm, September 2018, ENPC project. Implementatino of the AMS algorithm and application to molecular dynamics. Languages: Python, Git. Code
- Data reduction applied to pollutants transport, March - June 2018, ENPC project. Application of the SVD algorithm to model the evolution of a pollutant using the advection equation. Languages: Python, Git. Code
- Modeling defaults in a crystal, January - March 2018, ENPC project. Learning Hartree-Fock theory and the effect of a perturbation on Schrödinger’s equation. Language: Python.
- Entropy coding, January - June 2017, CPGE Project. Learning Shannon’s information theory and implementation of two lossless compression algorithms. Language: Python.
- Using quaternions in video games, January - June 2016, CPGE Project. Using quaternions and Bézier’s curves instead of Euler angles to implement 3D rotations in video games. Langage: Python.

### Community Involvement

- PhD representative of the MSTIC doctoral school, 2023. Administrative meetings.
- PhD representative of the CERMICS laboratory, 2022 - 2023. 3 days seminar organization, administrative meetings.
- Active runner of the Running Vincennes Association, 2021 - Present.
- Member of a sustainable development association Dévelop’Ponts, 2018 - 2019. Sustainable development projects, distribution of veggie baskets to students and administratives, website update (that has now been completely remodelled). Langages: PHP, HTML, Git.
- Member of the ENPC IT club KIClubInfo, 2018 - 2019. In charge of the club’s finances. Organization of LaTeX formations for ENPC students. Langages: LaTeX, Git.
- Co-founder of the ENPC chess club, Pions & Chaussées, 2018 - 2019. Organization of chess tournaments, and introduction to the game to ENPC students. Co-founder of the ENPC Lichess team.