Recorded 05 February 2024. Mathias Oster of RWTH Aachen University presents "Solving High-Dimensional Optimal Control Problems with Empirical Tensor Train Approximation" at IPAM's Tensor Networks Workshop. Abstract: We display two approaches to solve finite horizon optimal control problems with Tensor Train approximation. First we solve the Bellman equation numerically by employing the Policy Iteration algorithm. Second, we introduce a semiglobal optimal con- trol problem and use open loop methods on a feedback level. To overcome computational infeasability we use tensor trains and multi-polynomials, together with high-dimensional quadrature rules, e.g. Monte-Carlo. By controlling a destabilized version of viscous Burgers and a diffusion equation with unstable reaction term numerical evidence is given. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/tensor-networks/