3 papers
math.NA2026
Goal oriented error estimation for adaptive sampling of PINNS
Medard Govoeyi, Thomas Richter
Physics-Informed Neural Networks (PINNs) are mesh-free approaches for the numerical approximation of partial differential equations, where a neural network is trained by minimizing…
math.NA2026
Error analysis for hybrid finite element/neural network discretizations
Uladzislau Kapustsin, Utku Kaya, Johannes Pfefferer +1
We describe and analyze a hybrid finite element/neural network method for predicting solutions of partial differential equations. The methodology is designed for obtaining fine sca…
math.NA2025
An adaptive finite element multigrid solver using GPU acceleration
Manuel Liebchen, Robert Jendersie, Utku Kaya +2
Adaptive finite elements combined with geometric multigrid solvers are one of the most efficient numerical methods for problems such as the instationary Navier-Stokes equations. Ye…