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…
Modeling extra-deep electromagnetic logs using a deep neural network
Sergey Alyaev, Mostafa Shahriari, David Pardo +4
Modern geosteering is heavily dependent on real-time interpretation of deep electromagnetic (EM) measurements. We present a methodology to construct a deep neural network (DNN) mod…
A Deep Learning Approach to the Inversion of Borehole Resistivity Measurements
M. Shahriari, D. Pardo, A. Picón +3
We use borehole resistivity measurements to map the electrical properties of the subsurface and to increase the productivity of a reservoir. When used for geosteering purposes, it…
Variational Formulations for Explicit Runge-Kutta Methods
Judit Muñoz-Matute, David Pardo, Victor M. Calo +1
Variational space-time formulations for Partial Differential Equations have been of great interest in the last decades. While it is known that implicit time marching schemes have v…
Fourier finite element modeling of light emission in waveguides: 2.5-dimensional FEM approach
Yangxin Ou, David Pardo, Yuntian Chen
We present a Fourier finite element modeling of light emission of dipolar emitters coupled to infinitely long waveguides. Due to the translational symmetry, the three-dimensional (…
A direct solver with reutilization of previously-computed LU factorizations for h-adaptive finite element grids with point singularities
Maciej Paszynski, Victor Calo, David Pardo
This paper describes a direct solver algorithm for a sequence of finite element meshes that are h-refined towards one or several point singularities. For such a sequence of grids,…
The cost of continuity: performance of iterative solvers on isogeometric finite elements
Nathan Collier, Lisandro Dalcin, David Pardo +1
In this paper we study how the use of a more continuous set of basis functions affects the cost of solving systems of linear equations resulting from a discretized Galerkin weak fo…
Computational complexity and memory usage for multi-frontal direct solvers in structured mesh finite elements
Nathan Collier, David Pardo, Maciej Paszynski +1
The multi-frontal direct solver is the state-of-the-art algorithm for the direct solution of sparse linear systems. This paper provides computational complexity and memory usage es…