2 papers
math.NA2023
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.NA2023
A hybrid finite element/neural network solver and its application to the Poisson problem
Uladzislau Kapustsin, Utku Kaya, Thomas Richter
We analyze a hybrid method that enriches coarse grid finite element solutions with fine scale fluctuations obtained from a neural network. The idea stems from the Deep Neural Netwo…