AI and the World's Hard Problems · Mathematics · arXiv · 2026-10-21
Norm-optimal model order reduction in reproducing kernel Hilbert spaces
The paper considers model order reduction (MOR) in reproducing kernel Hilbert spaces and proves generalizations of well-known necessary interpolatory conditions for norm-optimal reduced-order models. It constructs an alternative to the iterative rational Krylov (IRKA) algorithm for RKHSs with differentiable kernels, and introduces generalized Malmquist-Takenaka (GMT) functions that extend the optimality conditions and algorithms to RKHSs with non-differentiable kernels. Numerical experiments demonstrate norm-optimal MOR on machine learning models such as support vector machines and deep ReLU networks, along with applications to fitting high-degree polynomials and a FEM-like method for solving partial differential equations.