4 papers · 1 filter
Multi-level Neural Networks for high-dimensional parametric obstacle problems
Martin Eigel, Cosmas HeiÃ, Janina E. Schütte
A new method to solve computationally challenging (random) parametric obstacle problems is developed and analyzed, where the parameters can influence the related partial differenti…
Sampling from Boltzmann densities with physics informed low-rank formats
Paul Hagemann, Janina Schütte, David Sommer +2
Our method proposes the efficient generation of samples from an unnormalized Boltzmann density by solving the underlying continuity equation in the low-rank tensor train (TT) forma…
Approximating Langevin Monte Carlo with ResNet-like Neural Network architectures
Charles Miranda, Janina Schütte, David Sommer +1
We sample from a given target distribution by constructing a neural network which maps samples from a simple reference, e.g. the standard normal distribution, to samples from the t…
Multilevel CNNs for Parametric PDEs based on Adaptive Finite Elements
Janina Enrica Schütte, Martin Eigel
A neural network architecture is presented that exploits the multilevel properties of high-dimensional parameter-dependent partial differential equations, enabling an efficient app…