4 papers
A tensor network formalism for neuro-symbolic AI
Alex Goessmann, Janina Schütte, Maximilian Fröhlich +1
The unification of neural and symbolic approaches to artificial intelligence remains a central open challenge. In this work, we introduce a tensor network formalism, which captures…
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…