4 papers
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…