Approximation Bounds for Model Reduction on Polynomially Mapped Manifolds
For projection-based linear-subspace model order reduction (MOR), it is well known that the Kolmogorov $n$-width describes the best-possible error for a reduced order model (ROM) of size $n$. In this paper, we provide approximation bounds for ROMs on polynomially mapped manifolds. In particular, we...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2024-12-01
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| Series: | Comptes Rendus. Mathématique |
| Subjects: | |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.632/ |
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| Summary: | For projection-based linear-subspace model order reduction (MOR), it is well known that the Kolmogorov $n$-width describes the best-possible error for a reduced order model (ROM) of size $n$. In this paper, we provide approximation bounds for ROMs on polynomially mapped manifolds. In particular, we show that the approximation bounds depend on the polynomial degree $p$ of the mapping function as well as on the linear Kolmogorov $n$-width for the underlying problem. This results in a Kolmogorov $(n,p)$-width, which describes a lower bound for the best-possible error for a ROM on polynomially mapped manifolds of polynomial degree $p$ and reduced size $n$. |
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| ISSN: | 1778-3569 |