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 Heiß, 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…
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…