Speaker
Description
This talk presents an interpretable, non-intrusive reduced-order modeling technique for parameterized problems using regularized kernel interpolation. Parameterized reduced-order models (ROMs) enable the rapid approximation of PDE solutions corresponding to a given parameter, thus accelerating uncertainty quantification or inverse problem workflows requiring many PDE solves. Existing non-intrusive parameterized ROM approaches approximate the ROM dynamics by solving a data-driven least-squares regression problem for low-dimensional matrix operators. However, these approaches typically assume affine parametric dependence, which may not be satisfied by the underlying full-order model (FOM). To overcome this limitation, our approach leverages regularized kernel interpolation, which yields an optimal approximation of the ROM dynamics from a user-defined reproducing kernel Hilbert space and allows for arbitrary parametric dependence. We further show that our kernel-based approach can produce interpretable ROMs whose structure mirrors the parameterized FOM structure by embedding judiciously chosen feature maps into the kernel. The approach is demonstrated in several numerical experiments.