17 citations · 32 across the 14 of their papers we have counts for
5 papers · 1 filter
Adaptive non-intrusive reconstruction of solutions to high-dimensional parametric PDEs
Martin Eigel, Nando Farchmin, Sebastian Heidenreich +1
Numerical methods for random parametric PDEs can greatly benefit from adaptive refinement schemes, in particular when functional approximations are computed as in stochastic Galerk…
Convergence bounds for nonlinear least squares and applications to tensor recovery
Philipp Trunschke
We consider the problem of approximating a function in general nonlinear subsets of when only a weighted Monte Carlo estimate of the -norm can be computed. Of particular…
Efficient approximation of high-dimensional exponentials by tensornetworks
Martin Eigel, Nando Farchmin, Sebastian Heidenreich +1
In this work a general approach to compute a compressed representation of the exponential of a high-dimensional function is presented. Such exponential functions play…
A block-sparse Tensor Train Format for sample-efficient high-dimensional Polynomial Regression
Michael Götte, Reinhold Schneider, Philipp Trunschke
Low-rank tensors are an established framework for high-dimensional least-squares problems. We propose to extend this framework by including the concept of block-sparsity. In the co…
Pricing high-dimensional Bermudan options with hierarchical tensor formats
Christian Bayer, Martin Eigel, Leon Sallandt +1
An efficient compression technique based on hierarchical tensors for popular option pricing methods is presented. It is shown that the "curse of dimensionality" can be alleviated f…