15 citations · 15 across the 3 of their papers we have counts for
4 papers
Designing Rotationally Invariant Neural Networks from PDEs and Variational Methods
Tobias Alt, Karl Schrader, Joachim Weickert +2
Partial differential equation (PDE) models and their associated variational energy formulations are often rotationally invariant by design. This ensures that a rotation of the inpu…
Connections between Numerical Algorithms for PDEs and Neural Networks
Tobias Alt, Karl Schrader, Matthias Augustin +2
We investigate numerous structural connections between numerical algorithms for partial differential equations (PDEs) and neural architectures. Our goal is to transfer the rich set…
Sparse Inpainting with Smoothed Particle Hydrodynamics
Viktor Daropoulos, Matthias Augustin, Joachim Weickert
Digital image inpainting refers to techniques used to reconstruct a damaged or incomplete image by exploiting available image information. The main goal of this work is to perform…
Roll convection of binary fluid mixtures in porous media
Rudolf Umla, Matthias Augustin, Bjoern Huke +1
We investigate theoretically the nonlinear state of ideal straight rolls in the Rayleigh-Bénard system of a fluid layer heated from below with a porous medium using a Galerkin meth…