35 citations · 209 across the 19 of their papers we have counts for
5 papers · 1 filter
Automatic stabilization of finite-element simulations using neural networks and hierarchical matrices
Tomasz Sluzalec, Mateusz Dobija, Anna Paszynska +2
Petrov-Galerkin formulations with optimal test functions allow for the stabilization of finite element simulations. In particular, given a discrete trial space, the optimal test sp…
A Deep Double Ritz Method (DRM) for solving Partial Differential Equations using Neural Networks
Carlos Uriarte, David Pardo, Ignacio Muga +1
Residual minimization is a widely used technique for solving Partial Differential Equations in variational form. It minimizes the dual norm of the residual, which naturally yields…
A Deep Fourier Residual Method for solving PDEs using Neural Networks
Jamie M. Taylor, David Pardo, Ignacio Muga
When using Neural Networks as trial functions to numerically solve PDEs, a key choice to be made is the loss function to be minimised, which should ideally correspond to a norm of…
An adaptive superconvergent finite element method based on local residual minimization
Ignacio Muga, Sergio Rojas, Patrick Vega
We introduce an adaptive superconvergent finite element method for a class of mixed formulations to solve partial differential equations involving a diffusion term. It combines a s…
Neural Control of Discrete Weak Formulations: Galerkin, Least-Squares and Minimal-Residual Methods with Quasi-Optimal Weights
Ignacio Brevis, Ignacio Muga, Kristoffer G. van der Zee
There is tremendous potential in using neural networks to optimize numerical methods. In this paper, we introduce and analyse a framework for the neural optimization of discrete we…