Speaker
Description
Addressing optimal control problems for transport-dominated partial differential equations (PDEs) can be computationally intensive, particularly for high-dimensional systems. To mitigate this, we focus on developing reduced-order models that can serve as surrogates for the full PDE system in solving these problems. Earlier works in this regard have explored the use of proper orthogonal decomposition (POD) in an optimal control context. In our work, we focus on investigating the shifted proper orthogonal decomposition (POD) method, which is well-suited for capturing high-fidelity, low-dimensional representations of transport-dominated phenomena.
We propose two frameworks: one involves constructing the reduced-order model first and then optimizing the reduced system, while the other optimizes the original PDE system first, with the reduced-order model applied to the resulting optimality system. A 1D linear advection equation is used as a test case to evaluate the computational performance of the shifted POD method compared to conventional approaches, such as the standard POD, when employed as surrogates in a backtracking line search.
