13 citations · 37 across the 18 of their papers we have counts for
9 papers · 1 filter
Learning the Willmore flow with a lightweight neural operator
Elie Bretin, Roland Denis, Tokuhiro Eto +1
We extend to the Willmore flow the phase-field neural operator approach proposed by Bretin, Denis, Masnou, and Terii (2022) for mean curvature motion in two and three dimensions. T…
A penalized Allen-Cahn equation for the mean curvature flow of thin structures
Elie Bretin, Chih-Kang Huang, Simon Masnou
This paper addresses the approximation of the mean curvature flow of thin structures for which classical phase field methods are not suitable. By thin structures, we mean surfaces…
A mobility-SAV approach for a Cahn-Hilliard equation with degenerate mobilities
Elie Bretin, Luca Calatroni, Simon Masnou
A novel numerical strategy is introduced for computing approximations of solutions to a Cahn-Hilliard model with degenerate mobilities. This model has recently been introduced as a…
Learning phase field mean curvature flows with neural networks
Elie Bretin, Roland Denis, Simon Masnou +1
We introduce in this paper new and very effective numerical methods based on neural networks for the approximation of the mean curvature flow of either oriented or non-orientable s…
Approximation of multiphase mean curvature flows with arbitrary nonnegative mobilities
Eric Bonnetier, Elie Bretin, Simon Masnou
This paper is devoted to the robust approximation with a variational phase field approach of multiphase mean curvature flows with possibly highly contrasted mobilities. The case of…
Stability for finite element discretization of some elliptic inverse parameter problems from internal data -- application to elastography
Elie Bretin, Pierre Millien, Laurent Seppecher
In this article, we provide stability estimates for the finite element discretization of a class of inverse parameter problems of the form $-\nabla\cdot(μS) = \g f$ in a domain …