I am currently a postdoctoral fellow in uncertainty quantification an optimal transport for Earth Observation at CNES (Centre National des Etudes Spatiales), since December 2024. My aim is to develop mathematical methods to optimally combine satellite data from various sources while still being able to precisely quantify the associated incertitude on relevant variables.

A short bio:
I have obtained my PhD in September 2024. It took place at CMAP (applied mathematics lab in École polytechnique), under the supervision of François Alouges and Aline Lefebvre-Lepot. The manuscript is available here.
In 2019-2020, I was invited at Politecnico di Torino by Fabio Freschi , who is a full professor in the DENERG department.
I am a former student at Ecole Normale Supérieure Paris-Saclay, France.


Research

I now focus on three ongoing projects with applications to satellite data processing, using mathematical modeling, inverse problems and variational data assimilation for river bathymetry estimates, or euclidean random assignment problems to track the dynamics of identical agents in a system observed at various time stamps. I also have an interest in uncertainty propagation when predicting a quantity of interest (e.g. bathymetry estimate, water volume...), along with exploring and understanding machine learning techniques that are currently in-use in the Earth observation community.

During my PhD, I studied partial differential equations and numerical methods, and I also focused on optimizing numerical simulations, applied to swimming at the microscopic scale. The aim was to understand and model both micro-swimmers, and the even more microscopic mechanisms enabling them to swim. I have an interest in various types of micro-swimmers, ranging from living ones such as bacteria, algae or spermatozoa, to mathematical toy-models. More broadly, I like learning more about optimizing and controlling these systems, in particular linked to creating micro-robots with medical applications.
When it comes to the numerical aspect, I perform and optimize computationally expensive simulations on larger-scale problems applied to physics as well, such as wireless power transfer for electric vehicles. Moreover, the methods used in this last aspect of my work are also widely applicable to fluid-structure simulations for micro-swimmers.

Publications

Articles

  • J. Levillain, F. Alouges, A. DeSimone, A. Choudhary, S. Nambiar, I. Bochert. A bi-directional low-Reynolds-number swimmer with passive elastic arms, accepted for publication in ESAIM: Proceedings and Surveys, 2024 [Preprint].
  • F. Alouges, A. Lefebvre-Lepot, J. Levillain. A limiting model for a low Reynolds number swimmer with N passive elastic arms , May 2023. [PDF]

Preprints

  • F. Alouges, A. Lefebvre-Lepot, J. Levillain, C. Moreau. The N-link model for slender rods in a viscous fluid: well-posedness and convergence to classical elastohydrodynamics equations, submitted, 2025 [Preprint].
  • F. Alouges, I. Anello, A. DeSimone, A. Lefebvre-Lepot, J. Levillain. Some mathematical models for flagellar activation mechanisms, submitted, 2024 [Preprint].

Report

  • J. Levillain. Hierarchical matrices and Adaptive Cross-Approximation, DENERG, Politecnico di Torino (Report, pre-doctoral research year), 2020. [PDF]

Communications

2025

  • 12/03/2025: Séminaire Analyse, Phénomènes Stochastiques et Applications, LMBA, Université de Bretagne Occidentale, Brest, France.

2024

  • 22/10/2024: Workshop "Bio- and bio-inspired locomotion of elongated bodies across scales and fields", LS2N, Ecole Centrale Nantes, Nantes, France.
  • 09/11/2024: Conférence des 50 ans du CMAP, poster presentation, École polytechnique, Palaiseau, France.
  • 05/30/2024: CANUM 2024, mini-symposium organizer and talk on low-Reynolds-number swimming, Le Bois-Plage-en-Ré, Île de Ré, France.
  • 04/15/2024: Séminaire de l'équipe CALISTO, INRIA Université Côte D'Azur, Sophia Antipolis, France.
  • 03/20/2024: Séminaire des doctorants du LAMFA, LAMFA, Amiens, France.
  • 01/17/2024: Journée Maths en herbe (seminar for undergraduates), FMJH, talk Introduction to micro-swimming. IHES, Bures-sur-Yvette, France.

2023

  • 09/25/2023: Le Congrès des Jeunes Chercheurs en Mathématiques et Applications 2023, talk Bi-directional low-Reynolds-number swimmer models. CentraleSupéléc, Gif-sur-Yvette, France.
  • 08/30/2023: Talk at [ RIMS Fluid Dynamics Workshop ], Kyoto, Japan.
  • 08/22/2023: ICIAM 2023, mini-symposium on "Low-Reynolds-number swimming: modelling, analysis and applications", Tokyo, Japan. Talk and co-organization of MS with C. Moreau.
  • 07/05/2023: XX Jacques-Louis Lions Spanish-French School on Numerical Simulations in Physics & Engineering, poster presentation, Barcelona, Spain.
  • 06/16/2023: AJS Seminars, SISSA, Trieste, Italy. [Abstract]
  • 01/25/2023: Séminaire des doctorants du CMAP et du CMLS, École polytechnique, Palaiseau, France.

2022

  • 10/26/2022: RIMS Fluid Dynamics Group seminar, Kyoto University, Japan.
  • 10/18/2022: Microscale Ocean Biophysics online seminar.
  • 09/21-23/2022: Le Congrès des Jeunes Chercheurs en Mathématiques et Applications 2022, Calais, France. A mathematical model of flagellar activation mechanisms.
  • 06/13-17/2022: CANUM 2020+2, Flagellar Locomotion of Micro-organisms, invited by L. Giraldi and P. Lissy (Mini-symposium). [PDF]

Teaching

2021 -2024: École polytechnique

  • MAP350: Preparatory mathematics course, 1st year of Ingénieur Polytechnicien Program
  • Numerical Analysis 2: Linear Algebra and Optimization (MAA251, Bachelor of Science, 2nd year)
  • Computational mathematics (MAA106, Bachelor of Science, 1st year)
  • Supervision of various Bachelor Thesis (internships, Bachelor of Science, 3rd year): "Introduction to image denoising: on BM3D", "On the Perron-Frobenius theorem: discovering Google's PageRank algorithm".

    • Previous teaching experiences

    Miscellaneous

    Administrative work

    • PhD student representative at CMAP lab council (2022-2024).

    Climbing