Approximation Bounds for Model Reduction on Polynomially Mapped Manifolds

Patrick Buchfink, Silke Glas, Bernard Haasdonk

Research output: Working paperPreprintAcademic

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Abstract

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. Inparticular, we showt hat 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.
Original languageEnglish
PublisherArXiv.org
Pages1-11
Number of pages11
Publication statusPublished - 4 Dec 2023

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