4 citations · 5 across the 7 of their papers we have counts for
7 papers
Parametrizing Convex Sets Using Sublinear Neural Networks
Eloi Martinet
We propose a neural parameterization of convex sets by learning sublinear (positively homogeneous and convex) functions. Our networks implicitly represent both the support and gaug…
Numerical exploration of the range of shape functionals using neural networks
Eloi Martinet, Ilias Ftouhi
We introduce a novel numerical framework for the exploration of Blaschke--Santaló diagrams, which are efficient tools characterizing the possible inequalities relating some given s…
Spherical caps do not always maximize Neumann eigenvalues on the sphere
Dorin Bucur, Richard S. Laugesen, Eloi Martinet +1
We prove the existence of an open set for which the first positive eigenvalue of the Laplacian with Neumann boundary condition exceeds that of the geodesic d…
Meshless Shape Optimization using Neural Networks and Partial Differential Equations on Graphs
Eloi Martinet, Leon Bungert
Shape optimization involves the minimization of a cost function defined over a set of shapes, often governed by a partial differential equation (PDE). In the absence of closed-form…
Numerical optimization of Neumann eigenvalues of domains in the sphere
Eloi Martinet
This paper deals with the numerical optimization of the first three eigenvalues of the Laplace-Beltrami operator of domain in the Euclidean sphere in with Neumann bo…
Sharp inequalities for Neumann eigenvalues on the sphere
Dorin Bucur, Eloi Martinet, Mickaël Nahon
We prove that the second nontrivial Neumann eigenvalue of the Laplace-Beltrami operator on the unit sphere is maximized by the union of tw…
Maximization of Neumann eigenvalues
Dorin Bucur, Eloi Martinet, Edouard Oudet
This paper is motivated by the maximization of the -th eigenvalue of the Laplace operator with Neumann boundary conditions among domains of with prescribed measu…