5 papers
Neural Very Weak Formulations enabling Hardware-Oriented deep PDE solvers
Gabriel Acosta, Francisco Bersetche
We show, as a proof of concept, that least-squares very weak formulations of elliptic problems can be effectively discretized by neural networks possessing low regularity, provided…
A nonlocal coupled system: analysis and discretization
Francisco Bersetche, Enrique Otarola, Daniel Quero
We analyze a nonlocal coupled system arising as the Euler--Lagrange equations of an energy functional involving regional fractional Laplacians of orders and ($ 0 < s_1,…
A deep first-order system least squares method for the obstacle problem
Gabriel Acosta, Eugenia Belén, Francisco M. Bersetche +1
We propose a deep learning approach to the obstacle problem inspired by the first-order system least-squares (FOSLS) framework. This method reformulates the problem as a convex min…
Local and nonlocal energy-based coupling models
Gabriel Acosta, Francisco M. Bersetche, Julio D. Rossi
In this paper we study two different ways of coupling a local operator with a nonlocal one in such a way that the resulting equation is related to an energy functional. In the firs…
Numerical approximations for a fully fractional Allen-Cahn equation
Gabriel Acosta, Francisco Bersetche
A finite element scheme for an entirely fractional Allen-Cahn equation with non-smooth initial data is introduced and analyzed. In the proposed nonlocal model, the Caputo fractiona…