19 citations · 46 across the 9 of their papers we have counts for
5 papers · 1 filter
Robust Deep FOSLS for Transmission Problems
Alejandro Duque, Paulina Sepúlveda, Carlos Uriarte +2
This work presents a robust, energy-based deep learning framework for solving transmission problems in heterogeneous media, including cases with discontinuous material scenarios. W…
An -adaptive finite element method using neural networks for parametric self-adjoint elliptic problem
Danilo Aballay, Federico Fuentes, Vicente Iligaray +5
This work proposes an -adaptive finite element method (FEM) using neural networks (NNs). The method employs the Ritz energy functional as the loss function, currently limiting i…
A Least-Squares-Based Neural Network (LS-Net) for Solving Linear Parametric PDEs
Shima Baharlouei, Jamie M. Taylor, Carlos Uriarte +1
Developing efficient methods for solving parametric partial differential equations is crucial for addressing inverse problems. This work introduces a Least-Squares-based Neural Net…
Optimizing Variational Physics-Informed Neural Networks Using Least Squares
Carlos Uriarte, Manuela Bastidas, David Pardo +2
Variational Physics-Informed Neural Networks often suffer from poor convergence when using stochastic gradient-descent-based optimizers. By introducing a Least Squares solver for t…
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…