2 citations · 4 across the 5 of their papers we have counts for
6 papers · 1 filter
Multilevel Sparse Tensor Approximation for High-Dimensional Parametric PDEs
Martin Eigel, Philipp Trunschke, Dana Wrischnig
In this paper the efficiency of multilevel sparse tensor approximation methods for high-dimensional affine parametric diffusion equations is investigated. Methodologically, the rec…
Optimal sampling for least squares approximation with general dictionaries
Philipp Trunschke, Anthony Nouy
We consider the problem of approximating an unknown function from point evaluations. This problem is a crucial subproblem in many modern (nonlinear) approximation schemes. When obt…
Sample-based almost-sure quasi-optimal approximation in reproducing kernel Hilbert spaces
Nando Hegemann, Anthony Nouy, Philipp Trunschke
This paper addresses the problem of approximating an unknown function from point evaluations. When obtaining these point evaluations is costly, minimising the required sample size…
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…
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…
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…