Publications

My research work mainly focuses on the development of approximation and model order reduction methods for partial differential equations using either deterministic and probabilistic approaches.

Preprints and on going work

• Billaud-Friess, M. & Heuzé, T.:Reconstruction of finite volume solution for parameter-dependent linear hyperbolic conservation laws, ArXiv e-print.

Published papers

• Aghili, J., Atokple, J., Billaud-Friess, M., Garnier, G., Mula, O. & Tognon, N.: A dynamical neural Galerkin scheme for filtering problems, ESAIM : Proceedings and surveys (2025)

• Billaud-Friess, M., Macherey, A., Nouy, A. & Prieur, C.: A probabilistic reduced basis method for parameter-dependent problems, Advances in Computational Mathematics (2024)

• Billaud-Friess, M., Macherey, A., Nouy, A. & Prieur, C.:A PAC algorithm in relative precision for bandit problem with costly sampling. Math. Methods Oper. Res., 1-25 (2022)

• Billaud-Friess, M., Falco, A. & Nouy, A.: A new splitting algorithm for dynamical low-rank approximation motivated by the fibre bundle structure of matrix manifolds Bit Numer. Math., 1–22, (2021)

• Billaud-Friess, M., Falco, A. & Nouy, A.: Principal bundle structure of matrix manifolds, MDPI, Mathematics, 9(14), 1669 (2021)

• Billaud-Friess, M., Macherey, A., Nouy, A. & Prieur, C.:Stochastic methods for solving high-dimensional partial differential equations. Springer Proceedings in Mathematics & Statistics, MCQMC 2018 (2020)

• Billaud-Friess, M. & Nouy, A.: Dynamical model reduction method for solving parameter-dependent dynamical systems. SIAM SISC 39 (4):A1766–A1792, (2017)

• Zahm, O., Billaud-Friess, M. & Nouy, A.:Projection-based model order reduction methods for the estimation of vector-valued variables of interest. SIAM SISC 39 (4), A1647-A1674 (2017)

• Billaud-Friess, M., Nouy, A. & Zahm, O.:A tensor approximation method based on ideal minimal residual formulations for the solution of high-dimensional problems. ESAIM : Mathematical Modelling and Numerical Analysis 48 (6), 1777-1806, (2014)

• Billaud-Friess, M. & Kokh, S.:Simulation of sharp interface multi-material flows involving an arbitrary number of components through an extended five-equation model J. Comput. Phys. 273, 488-519, (2014)

• Billaud-Friess, M., Breil, J., Maire, P.-H. & Shashkov, M.:A multi-material CCALE-MOF approach in cylindrical geometry. Commun. Comput. Phys. 15, 330–364 (2014)

• Billaud-Friess, M., Nouy, A. & Zahm, O.:Méthode de réduction de modèle apriori basée sur des formulations idéales en minimum de résidu. Actes CSMA (2013)

• Billaud-Friess, M. & Kokh, S. An anti-diffusive Lagrange-Remap scheme for multi-material compressible flows with an arbitrary number of components. ESAIM : Proceedings 35, 203–209 (2012)

• Billaud-Friess, M., Boutin, B., Caetano, F., Faccanoni, G., Kokh, S., Lagoutière, F. & Navoret, L. :A second order anti-diffusive Lagrange-remap scheme for two-component flows. ESAIM : Proceedings 32, 149–162 (2011)

• Billaud, M., Gallice, G. & Nkonga, B. A simple stabilized finite element method for solving two phase compressible-incompressible interface Comput. Methods Appl. Mech. Eng. 200, 1272–1290 (2011)

• Billaud, M., Gallice, G. & Nkonga, B.: Stabilized Finite Element Method for Compressible/Incompressible Diphasic Flows. Numerical Mathematics and Advanced Applications 2009, 171–179 (2010)

Theses

Habilitation Thesis defended the 21st October 2022, Nantes Université.
Title: Contributions for the approximation and model order reduction of partial differential equations

PhD Thesis defended the 27th November 2009, Université Bordeaux I.
Title: Stabilized finite element method for incompressible-compressible two-phase flows