Approximation Bounds for Model Reduction on Polynomially Mapped Manifolds

• DOI: 10.5802/crmath.632
• Publication Date: 2024-12-03T14:03:40Z
• Authors: Patrick Buchfink; Silke Glas; Bernard Haasdonk
• Keywords: polynomial mappings; QA1-939; FOS: Mathematics; polynomial $(n,p)$-widths; Model Order Reduction; Mathematics - Numerical Analysis; Numerical Analysis (math.NA); 41A45, 41A46, 41A65, 65L70, 65M15, 65N15; nonlinear manifolds; Mathematics

For projection-based linear-subspace model order reduction (MOR), it is well known that the Kolmogorov n-width describes best-possible error for a reduced (ROM) of size n. In this paper, we provide approximation bounds ROMs on polynomially mapped manifolds. particular, show depend polynomial degree p mapping function as linear underlying problem. This results in (n,p)-width, which lower bound ROM manifolds and