4 papers · 1 filter
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…
Adaptive Multilevel Neural Networks for Parametric PDEs with Error Estimation
Janina E. Schütte, Martin Eigel
To solve high-dimensional parameter-dependent partial differential equations (pPDEs), a neural network architecture is presented. It is constructed to map parameters of the model d…
Functional SDE approximation inspired by a deep operator network architecture
Martin Eigel, Charles Miranda
A novel approach to approximate solutions of Stochastic Differential Equations (SDEs) by Deep Neural Networks is derived and analysed. The architecture is inspired by the notion of…