Solving High-Dimensional Optimal Control Problems with Empirical Tensor Train Approximation

Explore a comprehensive lecture on solving high-dimensional optimal control problems using empirical tensor train approximation. Delve into two approaches: solving the Bellman equation numerically with the Policy Iteration algorithm and introducing a semiglobal optimal control problem using open loop methods on a feedback level. Discover how tensor trains and multi-polynomials, combined with high-dimensional quadrature rules like Monte-Carlo, overcome computational infeasibility. Examine numerical evidence through controlling a destabilized version of viscous Burgers and a diffusion equation with unstable reaction term. Gain insights from Mathias Oster of RWTH Aachen University in this 47-minute presentation from IPAM's Tensor Networks Workshop.