Benoît Merlet


Laboratoire Paul Painlevé (Université de Lille)

and Équipe INRIA RAPSODI   

@   benoit.merlet AT
INRIA :     +33 1 69 33 45 94    Université :   +33 1 69 33 46 46
Research interests Students Publications ToyNN Curriculum Vitæ

Research interests

PHD students

  • Thanh Nhan Nguyen (2010-2013)
  • Luca Ferrari (2015-2018)
  • Antoine Zurek (2017-2020)
  • Jules Candau-Tilh (2021-)
  • Publications

    1. M. Goldman, B.M: Set-decomposition of normal rectifiable $G$-chains via an abstract decomposition principle. preprint (2023). Preprint.
    2. C. Cancès, C. Chainais-Hillairet, B. M., F. Raimondi, J. Venel: Mathematical analysis of a thermodynamically consistent reduced model for iron corrosion. Zeitschrift für Angewandte Mathematik und Physik, 74(3) :96 (June 2023). Preprint.
    3. M. Goldman, B.M: Non-convex functionals penalizing simultaneous oscillations along two independent directions: structure of the defect measure. preprint (2023). Preprint.
    4. J. Candau-Tilh, M.Goldman, B.M: NAn exterior optimal transport problem. preprint (2023). Preprint.
    5. M. Goldman, B.M: A deformation theorem for tensor flat chains and applications preprint (2022). Preprint.
    6. M. Goldman, B.M: Tensor rectifiable G-flat chains preprint (2022). Preprint.
    7. B.M, J.Venel, A.Zurek: Analysis of a one dimensional energy dissipating free boundary model with nonlinear boundary conditions. Existence of global weak solutions. preprint (2022). Preprint.
    8. M. Pegon, M. Goldman, B.M: Uniform regularity for almost-minimizers of some nonlocal perturbations of the perimeter preprint (2022). Preprint.
    9. M. Pegon, M. Goldman, B.M, S.Serfaty: Compactness and structure of zero-states for the unoriented Aviles-Giga functional Journal of the Institute of Mathematics of Jussieu (2022). Preprint.
    10. M. Pegon, B.M: Large mass rigidity for a liquid drop model in 2D with kernels of finite moments Journal de l'Ecole polytechnique. Mathématiques (2022) Preprint.
    11. F. Alouges, A. De Bouard, B.M, Léa Nicolas: Stochastic homogenization of the Landau-Lifshitz-Gilbert equation. Stochastics and Partial Differential Equations: Analysis and Computations (2021). Preprint.
    12. M. Goldman, B.M: Recent results on non-convex functionals penalizing oblique oscillations. Rendiconti Sem. Mat. Univ. Pol. Torino Vol. 77, 2 (2020), 67 – 78 (2019). Preprint.
    13. M. Goldman, B.M: Non-convex functionals penalizing simultaneous oscillations along independent directions: rigidity estimates. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) (2021). Preprint.
    14. A. Chambolle, L. Ferrari, B.M: Strong appproximation in h-mass of rectfiable currents under homological constraints Advances in Calculus of Variations. Published online (2019). Preprint.
    15. A. Chambolle, L. Ferrari, B.M: Variational approximation of size-mass energies for k-dimensional currents. ESAIM: Control, Optimisation and Calculus of Variations (2018). Preprint.
    16. C. Chainais-Hillairet, B.M, A Zurek: Convergence of a finite volume scheme for a parabolic system with a free boundary modeling concrete carbonation. ESAIM Mathematical Modelling and Numerical Analysis (2018). Preprint.
    17. C. Chainais-Hillairet, B.M, A Zurek: Design and analysis of a finite volume scheme for a concrete carbonation model. Proceedings of FVCA8 - International Conference on Finite Volumes for Complex Applications VIII (2017). Preprint.
    18. A. Vasseur, C. Chainais-Hillairet, B.M: Positive lower bound for the Numerical Solution of a Convection-Diffusion Equation. Proceedings of FVCA8 - International Conference on Finite Volumes for Complex Applications VIII (2017). Preprint.
    19. M. Goldman, B.M., V. Millot: A Ginzburg-Landau Model with topologically induced free discontinuities. Submitted (2017). Preprint.
    20. P. F. Antonietti, B.M., M. Pierre, M. Verani: Convergence to equilibrium for a second-order time semi-discretization of the Cahn-Hilliard equations. AIMS Mathematics, 1, no. 3 (2016), 178-194. Preprint.
    21. M. Goldman, B.M.: Phase segregation for binary mixtures of Bose-Einstein Condensates. SIAM J. Math. Anal. 49 (2017), no. 3, 1947–1981. Preprint.
    22. A. Chambolle, L. Ferrari, B.M: A simple phase-field approximation of the Steiner problem in dimension two. Advances in Calculus of Variations (2017). Preprint.
    23. A. Lefebvre-Lepot, B.M., T.N. Nguyen: An accurate method to include lubrication forces in numerical simulations of dense stokesian suspensions. Journal of Fluid Mechanics, 769 (2015), 369-386. Preprint.
    24. B.M.: A highly anisotropic nonlinear elasticity model for vesicles. II. Derivation of the thin bilayer bending theory. Arch. Ration. Mech. Anal. 217 (2015), no. 2, 681–740. Preprint.
    25. B.M.: A highly anisotropic nonlinear elasticity model for vesicles. I. Eulerian formulation, rigidity estimates and vanishing energy limit. Arch. Ration. Mech. Anal. 217 (2015), no. 2, 651–680. Preprint.
    26. F. ALouges, G. DiFratta, B.M.: Liouville type results for local minimizers of the micromagnetic energy. Calc. Var. Partial Differential Equations 53 (2015), no. 3-4, 525–560. Preprint.
    27. F. Alouges, A. DeSimone, L. Heltai, A. Lefebvre, B.M.: Optimally swimming stokesian robots. DCDS B, 18 (2013) no.5, 1189-1215. Preprint.
    28. B.M., T.N. Nguyen: Convergence to equilibrium for discretizations of gradient-like flows on Riemannian manifolds. Differential Integral Equations 26 (2013) no. 5-6, 571-602. Preprint.
    29. F. Alouges, A. Augier, B. Graille, B.M.: Homogenization of a coupled problem for sound propagation in porous media. Adv. Differential Equations 17 (2012), no. 11-12, 1001–1030. Preprint.
    30. R. Ignat, B.M.: Entropy method for line-energies. Calc. Var. Partial Differential Equations 44 (2012), no. 3-4, 375–418. Preprint.
    31. Radu Ignat, B.M.: Lower bound for the energy of Bloch Walls. Arch. Rat. Mech. Anal (2011), no. 2, 369–-406. Preprint.
    32. E. Audusse, P. Dreyfuss, B.M.: Optimized Schwarz Waveform Relaxation for the Primitive Equations of the Ocean SIAM J. Sci. Comput. 32 (2010), no. 5, 2908–2936. Preprint.
    33. B.M., Morgan Pierre: Convergence to equilibrium for the Euler backward scheme and applications. CPAA. 46 (2010), no. 3, 685--702. Preprint.
    34. A. Lefebvre-Lepot, B.M.: A Stokesian submarine. ESAIM Proc. (CEMRACS 2008) 28 (2009) 150–-161 Preprint.
    35. B.M.: L-infinity and L2-Error Estimates for a Finite Volume Approximation of Linear Advection SINUM. 46 (2008), no. 1, 124–150. Preprint.
    36. B.M.: Numerical study of a new global minimizer for the Mumford-Shah functional in R^3. ESAIM Control Optim. Calc. Var. 13 (2007), no. 3, 553--569. Preprint.
    37. B.M., Julien Vovelle : Error estimate for a Finite Volume Scheme. Numer. Math. 106 (2007), no. 1, 129--155. Preprint.
    38. B.M.: Two remarks on liftings of maps with values into $S\sp 1$. C. R. Math. Acad. Sci. Paris 343 (2006), no. 7, 467--472.Preprint.
    39. B.M., Morgan Pierre: Moving mesh for the axisymmetric harmonic map flow. M2AN Math. Model. Numer. Anal. 39 (2005), no. 4, 781--796. Preprint.
    40. B.M., Lionel Paumond: An Initial-and-Boundary Value Problem for the KP-II equation on a strip and on the half plane. Differential Integral Equations 18 (2005), no. 7, 813--839. Preprint.
    41. François Alouges, B.M.: Approximate shock curves for non-conservative hyperbolic systems in one space dimension. J. Hyperbolic Differ. Equ. 1 (2004), no. 4, 769--788. Preprint.

    toynn_2023 : a pyton tool box designed to for solving toy classification problems (neural networks and stochastic gradient)

  • The python file with the classes ToyNN, ToyPb and nD_data :
  • A python notebook with a friendly description of the tool box : Introduction_to_toynn_2023.ipynb
  • A python notebook with examples of optimization : Lab0_toynn_2023.ipynb

  • Curriculum Vitæ


    Last update: October 20, 2023