deep learning for pdes 1hardware-efficient neural nets 1high-dimensional elliptic problems 1least-squares discretization 1quantized activations 1very weak formulation 1
From the 1 of 3 linked papers with an AI index.
3 papers
math.NA2026
Neural Very Weak Formulations enabling Hardware-Oriented deep PDE solvers
Gabriel Acosta, Francisco Bersetche
The paper demonstrates that least‑squares very weak formulations of elliptic PDEs can be discretized with low‑regularity neural networks, using simple step or one‑bit quantized act…
math.AP2026
The Fractional Korn Inequality on Uniform Domains and New Korn Inequalities for Truncated Seminorms
Gabriel Acosta, Irene Drelichman, Ricardo Durán +2
We prove the so-called second case of the fractional Korn inequality for uniform domains. We obtain this result as an application of a novel fractional Korn-type inequality formula…
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…