# Interpretable and flexible non-intrusive reduced-order models using reproducing kernel Hilbert spaces

arXiv: https://arxiv.org/abs/2506.10224 · HTML: https://mlsanity.com/paper/2506.10224/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2025.

## Built on by (most cited first, 2 of 2)

- [Hybrid coupling with operator inference and the overlapping Schwarz alternating method](https://mlsanity.com/paper/2511.20687/) (2025)
- [Operator Inference Aware Quadratic Manifolds with Isotropic Reduced Coordinates for Nonintrusive Model Reduction](https://mlsanity.com/paper/2507.20463/) (2025)

## Abstract (arXiv)

This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven least-squares regression problem for low-dimensional matrix operators. Our approach instead leverages regularized kernel interpolation, which yields an optimal approximation of the ROM dynamics from a user-defined reproducing kernel Hilbert space. We show that our kernel-based approach can produce interpretable ROMs whose structure mirrors full-order model structure by embedding judiciously chosen feature maps into the kernel. The approach is flexible and allows a combination of informed structure through feature maps and closure terms via more general nonlinear terms in the kernel. We also derive a computable a posteriori error bound that combines standard error estimates for intrusive projection-based ROMs and kernel interpolants. The approach is demonstrated in several numerical experiments that include comparisons to operator inference using both proper orthogonal decomposition and quadratic manifold dimension reduction.