1 citations · 2 across the 2 of their papers we have counts for
3 papers
Collocation-based Robust Variational Physics-Informed Neural Networks (CRVPINN)
Marcin Łoś, Tomasz Służalec, Paweł Maczuga +3
Physics-Informed Neural Networks (PINNs) have been successfully applied to solve Partial Differential Equations (PDEs). Their loss function is founded on a strong residual minimiza…
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…