5 papers · 1 filter
Non-Uniqueness of Solutions in Neural Variational Methods
Andreas Langer
Recent work has shown that strong-form physics-informed neural networks (PINNs) based on pointwise enforcement of differential operators can be ill-posed due to the combination of…
Functional Analysis and Parallel Domain Decomposition for the TV-Stokes Model
Andreas Langer, Marc Runft, Talal Rahman +2
The TV-Stokes model is a two-step variational method for image denoising that combines the estimation of a divergence-free tangent field with total variation regularization in the…
The Ill-Posed Foundations of Physics-Informed Neural Networks and Their Finite-Difference Variants
Andreas Langer
Physics-informed neural networks based on automatic differentiation (AD-PINNs) and their finite-difference counterparts (FD-PINNs) are widely used for solving partial differential…
A primal-dual adaptive finite element method for total variation minimization
Martin Alkämper, Stephan Hilb, Andreas Langer
Based on previous work we extend a primal-dual semi-smooth Newton method for minimizing a general -- functional over the space of functions of bounded variations by a…
An Adaptive Finite Difference Method for Total Variation Minimization
Thomas Jacumin, Andreas Langer
In this paper, we propose an adaptive finite difference scheme in order to numerically solve total variation type problems for image processing tasks. The automatic generation of t…