42 citations · 124 across the 12 of their papers we have counts for
13 papers
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…
Adaptive Deep Learning Method for Solving Partial Differential Equations
Ángel J. Omella, David Pardo
We introduce an adaptive algorithm to solve Partial Differential Equations using a Deep Neural Network. The proposed method restricts to tensor product meshes and optimizes the…
On quadrature rules for solving Partial Differential Equations using Neural Networks
Jon A. Rivera, Jamie M. Taylor, Ángel J. Omella +1
Neural Networks have been widely used to solve Partial Differential Equations. These methods require to approximate definite integrals using quadrature rules. Here, we illustrate v…
Refined isogeometric analysis for generalized Hermitian eigenproblems
Ali Hashemian, David Pardo, Victor M. Calo
We use the refined isogeometric analysis (rIGA) to solve generalized Hermitian eigenproblems . The rIGA framework conserves the desirable properties of maximum-continui…
Goal-oriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin norm
Sergio Rojas, David Pardo, Pouria Behnoudfar +1
We propose a goal-oriented mesh-adaptive algorithm for a finite element method stabilized via residual minimization on dual discontinuous-Galerkin norms. By solving a saddle-point…
Error Control and Loss Functions for the Deep Learning Inversion of Borehole Resistivity Measurements
M. Shahriari, D. Pardo, J. A. Rivera +5
Deep learning (DL) is a numerical method that approximates functions. Recently, its use has become attractive for the simulation and inversion of multiple problems in computational…