The fundamental importance of functional differential equations has been recognized in
many areas of mathematical physics, such as fluid dynamics (Hopf characteristic functional …

Tensor completion aims to reconstruct a high-dimensional data set where the vast majority
of entries is missing. The assumption of low-rank structure in the underlying original data …

We propose a parallel version of the cross interpolation algorithm and apply it to calculate
high-dimensional integrals motivated by Ising model in quantum physics. In contrast to …

A gradient-enhanced functional tensor train cross approximation method for the resolution of
the Hamilton–Jacobi–Bellman (HJB) equations associated with optimal feedback control of …

High-dimensional partial-differential equations (PDEs) arise in a number of fields of science
and engineering, where they are used to describe the evolution of joint probability functions …

To improve mathematical models of epidemics it is essential to move beyond the traditional
assumption of homogeneous well–mixed population and involve more precise information …

The evaluation of robustness and reliability of realistic structures in the presence of
uncertainty is numerically costly. This motivates model order reduction techniques like the …

We consider tensors in the Hierarchical Tucker format and suppose the tensor data to be
distributed among several compute nodes. We assume the compute nodes to be in a one‐to …

Scientific computations or measurements may result in huge volumes of high-dimensional
data, for instance 10 20 or 100 300 elements. Often these can be thought of representing a …

Approximation of high dimensional functions is in the focus of machine learning and data-
based scientific computing. In many applications, empirical risk minimisation techniques …