Design of asymptotic preserving finite volume schemes for the hyperbolic heat equation on unstructured meshes. - Christophe Buet; Bruno Després; Emmanuel Franck (Numerische Mathematik, 2012)

Asymptotic Preserving Schemes on Distorted Meshes for Friedrichs Systems with Stiff Relaxation: Application to Angular Models in Linear Transport. - Christophe Buet; Bruno Després; Emmanuel Franck (J. Sci. Comput., 2015)

Finite Volume Scheme with Local High Order Discretization of the Hydrostatic Equilibrium for the Euler Equations with External Forces. - Emmanuel Franck; Laura S. Mendoza (J. Sci. Comput., 2016)

Proof of uniform convergence for a cell-centered AP discretization of the hyperbolic heat equation on general meshes. - Christophe Buet; Bruno Després; Emmanuel Franck; Thomas Leroy (Math. Comput., 2017)

A neural network closure for the Euler-Poisson system based on kinetic simulations. - Léo Bois; Emmanuel Franck; Laurent Navoret; Vincent Vigon (CoRR, 2020)

A Low Cost Semi-implicit Low-Mach Relaxation Scheme for the Full Euler Equations. - François Bouchut; Emmanuel Franck; Laurent Navoret (J. Sci. Comput., 2020)

A robust and efficient solver based on kinetic schemes for Magnetohydrodynamics (MHD) equations. - Hubert Baty; Florence Drui; Philippe Helluy; Emmanuel Franck; Christian Klingenberg; Lukas Thanhäuser (Appl. Math. Comput., 2023)

Hamiltonian reduction using a convolutional auto-encoder coupled to an Hamiltonian neural network. - Raphaël Côte; Emmanuel Franck; Laurent Navoret; Guillaume Steimer; Vincent Vigon (CoRR, 2023)

Generalizing the SINDy approach with nested neural networks. - Camilla Fiorini; Clément Flint; Louis Fostier; Emmanuel Franck; Reyhaneh Hashemi; Victor Michel-Dansac; Wassim Tenachi (CoRR, 2024)

Volume-preserving physics-informed geometric shape optimization of the Dirichlet energy. - Amaury Bélières-Frendo; Emmanuel Franck; Victor Michel-Dansac; Yannick Privat (CoRR, 2024)

Approximately well-balanced Discontinuous Galerkin methods using bases enriched with Physics-Informed Neural Networks. - Emmanuel Franck; Victor Michel-Dansac; Laurent Navoret (J. Comput. Phys., 2024)

An Optimal Control Deep Learning Method to Design Artificial Viscosities for Discontinuous Galerkin Schemes. - Léo Bois; Emmanuel Franck; Laurent Navoret; Vincent Vigon (J. Sci. Comput., 2024)

Accelerating the convergence of Newton's method for nonlinear elliptic PDEs using Fourier neural operators. - Joubine Aghili; Emmanuel Franck; Romain Hild; Victor Michel-Dansac; Vincent Vigon (Commun. Nonlinear Sci. Numer. Simul., 2025)

Volume-preserving geometric shape optimization of the Dirichlet energy using variational neural networks. - Amaury Bélières-Frendo; Emmanuel Franck; Victor Michel-Dansac; Yannick Privat (Neural Networks, 2025)

Structural schemes for hamiltonian systems. - Stéphane Clain; Emmanuel Franck; Victor Michel-Dansac (CoRR, 2025)

Enriching continuous Lagrange finite element approximation spaces using neural networks. - Hélène Barucq; Michel Duprez; Florian Faucher; Emmanuel Franck; Frédérique Lecourtier; Vanessa Lleras; Victor Michel-Dansac; Nicolas Victorion (CoRR, 2025)

Neural semi-Lagrangian method for high-dimensional advection-diffusion problems. - Emmanuel Franck; Victor Michel-Dansac; Laurent Navoret (CoRR, 2025)

Reduced Particle in Cell method for the Vlasov-Poisson system using auto-encoder and Hamiltonian neural. - Emmanuel Franck; Laurent Navoret; Vincent Vigon; Raphaël Côte; Guillaume Steimer (CoRR, 2025)