Certified reduced-order methods for optimal treatment planning

Abstract

We study numerical methods for inverse problems arising in cancer therapy treatment under uncertainty. The interest is on efficient and reliable numerical methods that allow to determine the influence of possible unknown parameters on the treatment plan for cancer therapy. A kinetic transport equation is used to model the evolution of charged particles in tissue. A mixed variational framework is presented and existence and uniqueness of a weak solution is established. The optimality system is approximated using a low-dimensional reduced basis formulation based on a [Formula: see text]-FE discretization. We derive a posteriori bounds for the error in the reduced basis solution of the optimal control problem with respect to the solution of the [Formula: see text]-FE discretization. Numerical results in slab geometry are presented to confirm the validity of our approach.