Low-rank tensor representations can provide highly compressed approximations of
functions. These concepts, which essentially amount to generalizations of classical …

Controlling systems of ordinary differential equations is ubiquitous in science and
engineering. For finding an optimal feedback controller, the value function and associated …

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 …

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 for the …

In this paper, we present an approach based on the spectral analysis of the Koopman
operator for the approximate solution of the Hamilton Jacobi equation that arises while …

The numerical approximation of partial differential equations (PDEs) poses formidable
challenges in high dimensions since classical grid-based methods suffer from the so-called …

A self-learning approach for optimal feedback gains for finite-horizon nonlinear continuous
time control systems is proposed and analysed. It relies on parameter dependent …

We present a novel method to approximate optimal feedback laws for nonlinear optimal
control based on low‐rank tensor train (TT) decompositions. The approach is based on the …

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

We consider high-dimensional, non-linear functional equations. These functional equations
are mostly the Bellman equation known from optimal control or related fields. Within this …