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

Diaz, Alejandro Nicolas; McQuarrie, Shane Alexander; Tencer, John Thomas; Blonigan, Patrick Joseph

doi:10.1016/j.cma.2026.118734

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

Journal Article · Tue Jan 20 00:00:00 EST 2026 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2026.118734· OSTI ID:3018786

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Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Brigham Young Univ., Provo, UT (United States); Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

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. In conclusion, the approach is demonstrated in several numerical experiments that include comparisons to operator inference using both proper orthogonal decomposition and quadratic manifold dimension reduction.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: NA0003525

OSTI ID:: 3018786

Report Number(s):: SAND--2026-16617J; 1780351

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Journal Issue: Part A Vol. 452; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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

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