Régis Santet

PhD Student

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

Publications

  • T. Lelièvre, R. Santet, G. Stoltz, Unbiasing Hamiltonian Monte Carlo algorithms for a general Hamiltonian function, Foundations of Computational Mathematics (2024) DOI - arXiv - HAL - Code

Preprints

  • 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
  • T. Lelièvre, R. Santet, G. Stoltz, Improving sampling by modifying the effective diffusion (2024) arXiv

Presented courses and tutorials

Conferences and workshops

Posters

General scientific communication

  • Ma Thèse en 180 secondes: 3 minutes to introduce my subject for the whole world to see - Champs-sur-Marne, March 2023 - Finale Paris-Est Sup 2023 - Video (in French)
  • 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

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

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

  • Helping pupils and students with their homeworks with Mosaïc, 2023 - Present.
  • PhD representative of the MSTIC doctoral school, 2023. Administrative meetings.
  • PhD representative of the CERMICS laboratory, 2022 - 2023. 3 days seminar organization, administrative meetings.
  • Member of the Running Vincennes Association, 2021 - 2024.
  • 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.

Régis Santet -