Speaker
Description
Solving optimal control problems for transport-dominated partial
differential equations (PDEs) can become computationally expensive,
especially when dealing with high-dimensional systems.
To overcome this challenge, we focus on developing and deriving
reduced-order models that can replace the full PDE system in solving the
optimal control problem.
Specifically, we explore the use of the shifted proper orthogonal
decomposition (POD) as a reduced-order model, which is particularly
effective for capturing high-fidelity, low-dimensional representations
of transport-dominated phenomena.
Furthermore, we propose two distinct frameworks for addressing these
problems: one where the reduced-order model is constructed first,
followed by optimization of the reduced system, and another where the
original PDE system is optimized first, with the reduced-order model
subsequently applied to the optimality system.
We consider a 1D linear advection equation problem and compare the
computational performance of the shifted POD method against conventional
methods like the standard POD when the reduced-order models are used as
surrogates within a backtracking line search.
