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20212026
most citedA priori and a posteriori error estimates for the Deep Ritz method applied to the Laplace and Stokes problem

20 citations · 30 across the 9 of their papers we have counts for

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2 papers · 1 filter

math.NA2023★ 2 cited

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★ 6 cited

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…