4 papers · 1 filter
Recurrent Neural Networks as Optimal Mesh Refinement Strategies
Jan Bohn, Michael Feischl
We show that an optimal finite element mesh refinement algorithm for a prototypical elliptic PDE can be learned by a recurrent neural network with a fixed number of trainable param…
Higher-order linearly implicit full discretization of the Landau--Lifshitz--Gilbert equation
Georgios Akrivis, Michael Feischl, Balázs Kovács +1
For the Landau--Lifshitz--Gilbert (LLG) equation of micromagnetics we study linearly implicit backward difference formula (BDF) time discretizations up to order combined with h…
Sparse Compression of Expected Solution Operators
Michael Feischl, Daniel Peterseim
We show that the expected solution operator of prototypical linear elliptic partial differential operators with random coefficients is well approximated by a computable sparse matr…
Improved Efficiency of a Multi-Index FEM for Computational Uncertainty Quantification
Josef Dick, Michael Feischl, Christoph Schwab
We propose a multi-index algorithm for the Monte Carlo (MC) discretization of a linear, elliptic PDE with affine-parametric input. We prove an error vs. work analysis which allows…