19 citations · 63 across the 14 of their papers we have counts for
14 papers
Robust Variational Physics-Informed Neural Networks
Sergio Rojas, Paweł Maczuga, Judit Muñoz-Matute +2
We introduce a Robust version of the Variational Physics-Informed Neural Networks method (RVPINNs). As in VPINNs, we define the quadratic loss functional in terms of a Petrov-Galer…
Physics Informed Neural Networks with strong and weak residuals for advection-dominated diffusion problems
Maciej Sikora, Patryk Krukowski, Anna Paszynska +1
This paper deals with the following important research questions. Is it possible to solve challenging advection-dominated diffusion problems in one and two dimensions using Physics…
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…
Quasi-optimal -finite element refinements towards singularities via deep neural network prediction
Tomasz Sluzalec, Rafal Grzeszczuk, Sergio Rojas +2
We show how to construct the deep neural network (DNN) expert to predict quasi-optimal -refinements for a given computational problem. The main idea is to train the DNN expert…
Complexity of direct and iterative solvers on space-time formulations versus time--marching schemes for h-refined grids towards singularities
Marcin Skotniczny, Anna Paszynska, Sergio Rojas +1
We study computational complexity aspects for Finite Element formulations considering hypercubic space--time full and time--marching discretization schemes for --refined grids t…
Isogeometric Residual Minimization Method (iGRM) with Direction Splitting for Non-Stationary Advection-Diffusion Problems
Marcin Los, Judit Munoz-Matute, Ignacio Muga +1
In this paper, we propose a novel computational implicit method, which we call Isogeometric Residual Minimization (iGRM) with direction splitting. The method mixes the benefits res…