1 citations · 1 across the 5 of their papers we have counts for
5 papers
Fully discrete least-squares splitting scheme for the Monge-Ampère equation: finite element analysis and convergence
Anna Peruso
The least-squares splitting algorithm for the Monge-Ampère equation has been used successfully in computations for several years, but a convergence theory for fully discrete splitt…
An adaptive Deep Ritz framework for second-order fully nonlinear partial differential equations
Alexandre Caboussat, Martin T. Leclercq, Anna Peruso
As an alternative to PINNs, a Deep Ritz framework is proposed to solve fully nonlinear PDEs. A least-squares algorithm is advocated to decouple the nonlinearities from the variatio…
Convergence of a least-squares splitting method for the Monge-Ampère equation
Anna Peruso, Massimo Sorella
We study the theoretical convergence of the nonlinear least-squares splitting method for the Monge-Ampère equation introduced in [1] in which each iteration decouples the pointwise…
Error indicators and adaptivity for a least-squares method applied to the Monge-Ampère equation
Alexandre Caboussat, Anna Peruso, Marco Picasso
We introduce novel a posteriori error indicators for a nonlinear least-squares solver for smooth solutions of the Monge-Ampère equation on convex polygonal domains in $\mathbb{R}^2…
Convex Physics Informed Neural Networks for the Monge-Ampère Optimal Transport Problem
Alexandre Caboussat, Anna Peruso
Optimal transportation of raw material from suppliers to customers is an issue arising in logistics that is addressed here with a continuous model relying on optimal transport theo…