5 papers
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 stochastic and natural gradient descent
Robert Gruhlke, Anthony Nouy, Philipp Trunschke
We consider the problem of optimising the expected value of a loss functional over a nonlinear model class of functions, assuming that we have only access to realisations of the gr…
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…
Estimating systematic errors in Bayesian inversion using transport maps
Maren Casfor, Philipp Trunschke, Sebastian Heidenreich +1
In indirect measurements, the measurand is determined by solving an inverse problem which requires a model of the measurement process. Such models are often approximations and intr…