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math.NA2026
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…
math.NA2025
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…
math.NA2019
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…