11 citations · 28 across the 12 of their papers we have counts for
3 papers · 1 filter
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…