Clémentine Courtès

Assistant professor in mathematics

Research

Research interests :

Key words : Partial differential equations, numerical analysis, scientific computing, machine learning

Analysis of numerical schemes: [A2, A1, P2]

  • Finite difference numerical schemes, rate of convergence, error estimates
  • Applications in hydrodynamics: dispersive equations, (Airy's, Korteweg-de Vries', Benjamin-Bona-Mahony's equations), hyperbolic-dispersive systems ("abcd" system of Boussinesq)
Conception of numerical schemes: [A3, P3, P1]
  • High order methods for non linear hyperbolic PDEs, kinetic BGK schemes, Lattice-Boltzmann methods, preconditioner
  • Applications in fluid mechanics: shallow-water equations, multilayer shallow water model, Euler equations at low Mach number
Study and analysis of some localised solutions: [T1]
  • Travelling waves, solitons,
  • Applications in hydrodynamics and magnetism: Korteweg-de Vries-Kuramoto-Sivashinsky's equation, Landau-Lifshitz-Gilbert's equation
Design of reduced models by machine learning : [A4, A9]
  • Neural networks, deep learning, reinforcement learning, optimal control, structure preserving integration, neural model
  • Applications in epidemiology and in hamitonian systems
Micromagnetism modeling : [A5, A6, A7, A8]
  • Optimal control, calculus of variations, minimal time problem, Curie temperature
  • Applications in ferromagnetism : Landau-Lifshitz-Gilbert's equation

Publications :

Submitted articles :

  • [A9] Neural non-canonical Hamiltonian dynamics for long-time simulations,
    C.Courtès, E. Franck, M. Kraus, L. Navoret and L. Trémant.
    submitted, (2025). [HAL] [related code]

  • [A8] The Spear and the Ring: Emergent Structures in Magnetic Colloidal Suspensions,
    R.Côte, C.Courtès, G.Ferriere, L.Godard-Cadillac and Y.Privat.
    submitted, (2025). [HAL]

Published articles :
  • [A7] Existence and uniqueness of domain walls for notched ferromagnetic nanowires,
    R.Côte, C.Courtès, G.Ferriere, L.Godard-Cadillac and Y.Privat.
    ESAIM: Control, Optimisation and Calculus of Variations, 31(60):1-37 (2025). [article] [HAL]

  • [A6] Micromagnetic simulations of the size dependence of the Curie temperature in ferromagnetic nanowires and nanolayers,
    C.Courtès, M.Boileau, R.Côte, P.-A.Hervieux and G.Manfredi
    Journal of Magnetism and Magnetic Materials, 598:172040 (2024). [paper] [HAL] [arXiv] [related code]

  • [A5] Minimal time of magnetization switching in small ferromagnetic ellipsoidal samples,
    R.Côte, C.Courtès, G.Ferriere and Y.Privat.
    Journal de l'Ecole Polytechnique. Mathématiques, 12:147-184 (2025). [article] [HAL] [arXiv]

  • [A4] Reduced modelling and optimal control of epidemiological individual-based models with contact heterogeneity,
    C.Courtès, E.Franck, K.Lutz, L.Navoret and Y.Privat.
    Optimal Control Applications and Methods, 45(2):459-493, (2024). [paper] [HAL] [arXiv]

  • [A3] Vectorial kinetic relaxation model with central velocity. Application to implicit relaxation schemes,
    D.Coulette, C.Courtès, E.Franck and L.Navoret.
    Communications in Computational Physics, 27(4):976-1013, (2020). [paper] [HAL]

  • [A2] Error estimates of finite difference schemes for the Korteweg-de Vries equation,
    C.Courtès, F.Lagoutière and F.Rousset.
    IMA Journal of Numerical Analysis, 40(1):628–685 (2020). [paper] [HAL] [arXiv]

  • [A1] Energy estimates for some numerical schemes on the abcd system,
    C.Burtea and C.Courtès.
    Communications in Mathematical Sciences, 17(1):243-298 (2019). [paper] [HAL] [arXiv]

Peer-reviewed conference proceedings:
  • [P3] Linear stability of a vectorial kinetic relaxation scheme with a central velocity,
    C.Courtès and E.Franck.
    Hyperbolic Problems : Theory, Numerics and Application, AIMS on Applied Mathematics, 10:400-407 (2020). [paper] [HAL]

  • [P2] Convergence for PDEs with an arbitrary odd order spatial derivative term,
    C.Courtès.
    Theory, Numerics and Applications of Hyperbolic Problems I, Springer Proceedings in Mathematics and Statistics, 236:413-425 (2018). [paper] [HAL] [arXiv]

  • [P1] Study of physic-based preconditioning with high order Galerkin method discretization for hyperbolic wave problems,
    C.Courtès, E.Franck, P.Helluy and H.Oberlin.
    Esaim : Proceedings and surveys, 55:61-82 (2016). [paper] [HAL]

Research report :
  • [R1] Compressed sensing pour l'imagerie radar,
    C.Courtès, G.Dusson, R.Hatchi, R.Molina and A.Thomas.
    Semaine d'Etude Maths Entreprises, Paris (2015). [HAL]

Ph.D. :

  • [T1] Numerical analysis of hyperbolic-dispersive systems, [TEL] defended on the 11/23/2017 at Paris Sud University. The Ph.D examining committee was composed of
    • Ph.D supervisors : Frédéric Lagoutière and Frédéric Rousset
    • Referees (external examiners) : Claire Chainais-Hillairet and Pascal Noble
    • Jury president : Raphaèle Herbin
    • Examiner : Bertrand Maury

Talks and posters :

In 2025 :

  • Talk at workshop Variational methods for topological patterns arising in physics, (future) November 2025, Laboratoire Ypatia des sciences mathématiques in Rome (IRL LYSM, Italy)
  • Talk at workshop Progress in modeling and analysis for nanomagnetism and related topics, (future) October 2025, University of Pisa (Italy)
  • Scientific talk for the CNRS visit, September 2025, University of Strasbourg
  • Talk at workshop PANDA, June 2025, INRIA center at the University of Lille
  • Seminar at the EDP and Scientific computing Working Group, June 2025, LMRS, University of Rouen Normandy
  • PDEs Seminar, January 2025, LJK, Grenoble-Alpes University

In 2024 :

  • Talk at the workshop "Modeling, theory and numerics for PDEs (kinetic and hyperbolic systems)", October 2024, Aussois
  • Talk at the workshop PANDA Lille-Santiago (online), September 2024, Universidad de Chile, Santiago (Chile)
  • Talk at the workshop of ANR MOSICOF, June 2024, Sorbonne University
  • Seminar "Rencontres INRIA-LJLL en calcul scientifique", May 2024, Paris
  • Internal laboratory seminar, April 2024, University of Strasbourg
  • Optimization and nonlinear analysis seminar, April 2024, LMA, University of Avignon
  • Numerical analysis and PDEs seminar, February 2024, University of Lille
  • INRIA seminar (POEMS team), February 2024, INRIA, ENSTA, Paris
  • Talk in the TONUS/MACARON days, February 2024, INRIA, Belmont (Bas-Rhin)

In 2023 :

  • Talk for the Lebesgue Ph.D. Meeting (mentor for the 2023 edition), April 2023, University of Nantes
  • Working group on Machine Learning, March 2023, University of Strasbourg
  • Mini-course at the MasterClass of PDE's , January 2023, University of Lorraine, Nancy, lecture notes

In 2022 :

  • Scientific talk for the HCERES visit, October 2022, University of Strasbourg
  • Talk at the workshop of ANR MOSICOF, July 2022, Sorbonne University
  • Reims Mathematics Laboratory seminar, June 2022, University of Reims
  • PDEs days of Élie Cartan's Institut, March 2022, University of Lorraine
  • Analysis seminar, March 2022, University of Strasbourg
  • PDE, Modelling and Scientific computing seminar of Lyon-Saint Etienne, March 2022, Institut Camille Jordan (Lyon)

In 2021 :

  • Working group on Machine Learning (online), December 2021, University of Strasbourg
  • Working group on Machine Learning (online), November 2021, University of Strasbourg
  • Working group on Machine Learning (online), May 2021, University of Strasbourg
  • Working group on Machine Learning (online), March 2021, University of Strasbourg
  • PDEs and numerical analysis seminar (online), January 2021, University of Nice

In 2020 :

  • PDE and Applications seminar (online), December 2020, University of Poitiers
  • Mini-course, EDP seminar (online), November 2020, University of Strasbourg
  • PDEs and numerical analysis seminar, June 2020, University of Nice 1
  • PDE, Modelling and Scientific computing seminar of Lyon-Saint Etienne, May 2020, Institut Camille Jordan (Lyon) 1
  • PDEs days of Élie Cartan's Institut, March 2020, University of Lorraine 1
  • 32nd Seminar on Computational Fluid Dynamics, February 2020, CEA-SMAI/GAMNI (IHP, Paris)
  • 11th Itinerant Workshop in PDEs, January 2020, Bonn (Germany)

1. Seminars cancelled due to COVID-19 outbreak.

In 2019 :

  • Talk at the IRMA day, October 2019, University of Strasbourg
  • Poster session, Conference Numerical Methods for Multiscale Models arising in Physics and Biology, June 2019, University of Nantes
  • Conference Shark-FV 2019, May 2019, Povoa de Varzim (Portugal)
  • Poster session, Journées Jeunes EDPistes, March 2019, INSA of Rennes
  • Numerical Analysis and Scientific Computing seminar, February 2019, University of Besançon

In 2018 :
  • Talk at the "Mathematics for the Industry and Physics" day, December 2018, Toulouse Mathematics Institute
  • Scientific computing and Modeling seminar, December 2018, University of Bordeaux
  • Talk at the new entrants day, October 2018, INSA of Toulouse
  • Poster session, Conference HYP, June 2018, University Park, Pennsylvania (USA) poster
  • Conference HYP, (contributed talk), June 2018, University Park, Pennsylvania (USA)
  • CANUM, (minisymposium), May 2018, Cap d'Agde (Hérault)
  • Journées Jeunes EDPistes, March 2018, University of Lorraine, Nancy
  • INRIA seminar (ANGE team), March 2018, INRIA Paris
  • PDEs and numerical analysis seminar, March 2018, University of Nice
  • Applied mathematics seminar, February 2018, University of Nantes

In 2017 :

  • Lebesgue Ph.D. Meeting, October 2017, University of Rennes
  • Talk at the "numerical analysis and PDEs" day, October 2017, University Paris Sud (Orsay)
  • Talk in the summer school "Dispersive hydrodynamics and oceanography: from experiments to theory", August 2017, Les Houches
  • Congress SMAI, June 2017, La Tremblade (Charente-Maritime)
  • Numerical analysis and PDEs seminar, March 2017, Laboratory Paul Painlevé (Lille)
  • Poster session, Journées Jeunes EDPistes, March 2017, Autrans (Isère)
  • Ph.D.'s seminar, March 2017, Laboratory of Mathematics Jean Leray (Nantes)
  • Ph.D.'s seminar "jeunes chercheurs", February 2017, University of Lorraine

In 2016 :

  • Ph.D. students and young doctors' working group, October 2016, University Paris Descartes
  • Ph.D.'s seminar, October 2016, University Paris Est (Créteil)
  • Poster session, Conference HYP, August 2016, Aachen (Germany) poster
  • ECMI Conference, (minisymposium) June 2016, Santiago de Compostela (Spain)
  • CANUM, May 2016, Obernai (Alsace)
  • Numerical Analysis and PDEs seminar, March 2016, University Paris Sud (Orsay)

In 2015 :

  • Young researchers "Landau" seminar November 2015, University of Rennes 1
  • Young researchers seminar, November 2015, University of Reims
  • PDEs seminar, November 2015, University of Strasbourg
  • Talk at the internal meeting, ANR BoND, November 2015, University of Besançon
  • Ph.D.'s seminar, June 2015, University Paris Sud (Orsay)
  • Poster session, Congress SMAI, June 2015, Les Karellis (Savoie) poster

Schools and research projects :

  • Member of associated INRIA team PANDA : 2024-2026,
    • Research project : Study of systems of dispersive PDEs for the propagation of waves
    • Principal Investigator : A. de Laire (University of Lille)
  • Member of ANR project MOSICOF : 2021-2025,
    • Research project : Modeling and Simulation of Complex Ferromagnetic Systems
    • Principal Investigator : S. Labbé (Sorbonne University)
  • Member of ANR DFG project MILK : 2021-2024,
    • Research project : Machine learning for reduced kinetic models
    • Principal Investigator : E. Franck (INRIA Nancy-Grand Est, University of Strasbourg)
  • Principal Investigator of project "PEPS Jeunes Chercheurs" : 2019, (approx. 3500 €)
    • Research project : Study of the magnetization reversal dynamics in nanowires : influence of temperature and external magnetic field
    • Associate collaborators : R.Côte, P.-A.Hervieux, R.Ignat, G.Manfredi
  • Member of project "PEPS Jeunes Chercheurs" : 2018, (approx. 4500 €)
    • Research project : Implicit relaxation schemes for hyperbolic and parabolic systems
    • Other members : E.Franck (Principal Investigator of the project), F.Drui
  • Summer school of the ANR BoND : August 2017, Les Houches
    • Dispersive hydrodynamics and oceanography: from experiments to theory
  • CEMRACS'15 : July-August 2015, CIRM, Marseille
    • Summer school : Coupling Multi-Physics Models involving Fluids
    • Research project : Physic-Based preconditioning for hyperbolic system and Discontinuous Galerkin discretization (joint work with E.Franck, H.Oberlin and P.Helluy)
  • SEME : (Semaine d'Etude Maths Entreprises), January 2015, Paris
    • Research project proposed by Airbus : Application du compress sensing hors du cadre classique du traitement d'images (joint work with G.Dusson, R.Hatchi, R.Molina and A.Thomas) slides , report.
  • Winter school of the ANR BoND : February 2014, Les Houches
    • Nonlinear dispersive waves : theory, numerics and applications

Other conferences I have attended :