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For projection-based linear-subspace model order reduction (MOR), it is wellknown that the Kolmogorov n-width describes the best-possible error for areduced order model (ROM) of size n. In this paper, we provide approximationbounds for ROMs on polynomially mapped manifolds. In particular, we show thatthe approximation bounds depend on the polynomial degree p of the mappingfunction as well as on the linear Kolmogorov n-width for the underlyingproblem. This results in a Kolmogorov (n, p)-width, which describes a lowerbound for the best-possible error for a ROM on polynomially mapped manifolds ofpolynomial degree p and reduced size n.

Approximation Bounds for Model Reduction on Polynomially Mapped Manifolds