4 papers
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 in which each iteration decouples the pointwise nonlinearity from…
Error estimates 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}^…
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…