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.

翻译：对于基于投影的线性子空间模型降阶（MOR），众所周知，Kolmogorov n-宽度描述了规模为n的降阶模型（ROM）所能达到的最佳误差。本文给出了多项式映射流形上ROM的逼近界。特别地，我们证明逼近界依赖于映射函数的多项式次数p以及底层问题的线性Kolmogorov n-宽度。由此得到Kolmogorov (n, p)-宽度，该量描述了多项式次数为p且约化规模为n的多项式映射流形上ROM所能达到最佳误差的下界。