17 citations · 33 across the 17 of their papers we have counts for
19 papers
A convergent adaptive finite element stochastic Galerkin method based on multilevel expansions of random fields
Markus Bachmayr, Martin Eigel, Henrik Eisenmann +1
The subject of this work is an adaptive stochastic Galerkin finite element method for parametric or random elliptic partial differential equations, which generates sparse product p…
Generative Modelling with Tensor Train approximations of Hamilton--Jacobi--Bellman equations
David Sommer, Robert Gruhlke, Max Kirstein +2
Sampling from probability densities is a common challenge in fields such as Uncertainty Quantification (UQ) and Generative Modelling (GM). In GM in particular, the use of reverse-t…
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…
Weighted sparsity and sparse tensor networks for least squares approximation
Philipp Trunschke, Anthony Nouy, Martin Eigel
Approximation of high-dimensional functions is a problem in many scientific fields that is only feasible if advantageous structural properties, such as sparsity in a given basis, c…
Multilevel CNNs for Parametric PDEs
Cosmas Heiß, Ingo Gühring, Martin Eigel
We combine concepts from multilevel solvers for partial differential equations (PDEs) with neural network based deep learning and propose a new methodology for the efficient numeri…
On the convergence of adaptive Galerkin FEM for parametric PDEs with lognormal coefficients
Martin Eigel, Nando Hegemann
Numerically solving high-dimensional random parametric PDEs poses a challenging computational problem. It is well-known that numerical methods can greatly benefit from adaptive ref…