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

We establish a connection between stochastic optimal control and generative models based
on stochastic differential equations (SDEs), such as recently developed diffusion …

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 …

A learning based method for obtaining feedback laws for nonlinear optimal control problems
is proposed. The learning problem is posed such that the open loop value function is its …

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

We consider the approximation of some optimal control problems for the Navier-Stokes
equation via a Dynamic Programming approach. These control problems arise in many …

Sampling from probability densities is a common challenge in fields such as Uncertainty
Quantification (UQ) and Generative Modelling (GM). In GM in particular, the use of reverse …

Numerical methods for the optimal feedback control of high-dimensional dynamical systems
typically suffer from the curse of dimensionality. In the current presentation, we devise a …

The goal of reinforcement learning is estimating a policy that maps states to actions and
maximizes the cumulative reward of a Markov Decision Process (MDP). This is oftentimes …

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 …