11 citations · 26 across the 9 of their papers we have counts for
9 papers
A neural delta- particle-in-cell method: evolving the background with learned backward flows
Victor Fournet, Martin Campos Pinto, Emmanuel Franck +1
We present a novel δf particle-in-cell (PIC) method for the kinetic simulation of electrostatic plasmas in which the bulk density, acting as a control variate, is evolved using sym…
Neural network-driven domain decomposition for efficient solutions to the Helmholtz equation
Victorita Dolean, Daria Hrebenshchykova, Stéphane Lanteri +1
Accurately simulating wave propagation is crucial in fields such as acoustics, electromagnetism, and seismic analysis. Traditional numerical methods, like finite difference and fin…
Neural semi-Lagrangian method for high-dimensional advection-diffusion problems
Emmanuel Franck, Victor Michel-Dansac, Laurent Navoret +1
This work is devoted to the numerical approximation of high-dimensional advection-diffusion equations. It is well-known that classical methods, such as the finite volume method, su…
Enriching continuous Lagrange finite element approximation spaces using neural networks
Hélène Barucq, Michel Duprez, Florian Faucher +5
In this work, we present a study combining two approaches in the context of solving PDEs: the continuous finite element method (FEM) and more recent techniques based on neural netw…
Structural schemes for hamiltonian systems
Stéphane Clain, Emmanuel Franck, Victor Michel-Dansac
We present an adaptation of the so-called structural method \cite{CMM23} for Hamiltonian systems, and redesign the method for this specific context, which involves two coupled diff…
Volume-preserving geometric shape optimization of the Dirichlet energy using variational neural networks
Amaury Bélières--Frendo, Emmanuel Franck, Victor Michel-Dansac +1
In this work, we explore the numerical solution of geometric shape optimization problems using neural network-based approaches. This involves minimizing a numerical criterion that…
Generalizing the SINDy approach with nested neural networks
Camilla Fiorini, Clément Flint, Louis Fostier +4
Symbolic Regression (SR) is a widely studied field of research that aims to infer symbolic expressions from data. A popular approach for SR is the Sparse Identification of Nonlinea…
Accelerating the convergence of Newton's method for nonlinear elliptic PDEs using Fourier neural operators
Joubine Aghili, Emmanuel Franck, Romain Hild +2
It is well known that Newton's method can have trouble converging if the initial guess is too far from the solution. Such a problem particularly occurs when this method is used to…
Approximately well-balanced Discontinuous Galerkin methods using bases enriched with Physics-Informed Neural Networks
Emmanuel Franck, Victor Michel-Dansac, Laurent Navoret
This work concerns the enrichment of Discontinuous Galerkin (DG) bases, so that the resulting scheme provides a much better approximation of steady solutions to hyperbolic systems…