Interpretable and flexible non-intrusive reduced-order models using reproducing kernel Hilbert spaces
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915748616601600 |
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| author | Diaz, Alejandro N McQuarrie, Shane A Tencer, John T Blonigan, Patrick J |
| author_facet | Diaz, Alejandro N McQuarrie, Shane A Tencer, John T Blonigan, Patrick J |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10224 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Interpretable and flexible non-intrusive reduced-order models using reproducing kernel Hilbert spaces Diaz, Alejandro N McQuarrie, Shane A Tencer, John T Blonigan, Patrick J Computational Engineering, Finance, and Science Numerical Analysis 65D05, 46E22, 62J05 G.1.0 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. |
| title | Interpretable and flexible non-intrusive reduced-order models using reproducing kernel Hilbert spaces |
| topic | Computational Engineering, Finance, and Science Numerical Analysis 65D05, 46E22, 62J05 G.1.0 |
| url | https://arxiv.org/abs/2506.10224 |