A polynomial approximation scheme for nonlinear model reduction by moment matching
Abstract
We propose a procedure for the numerical approximation of invariance equations arising in the moment matching technique associated with reduced-order modeling of high-dimensional dynamical systems. The Galerkin residual method is employed to find an approximate solution to the invariance equation using a Newton iteration on the coefficients of a monomial basis expansion of the solution. These solutions to the invariance equations can then be used to construct reduced-order models. We assess the ability of the method to solve the invariance PDE system as well as to achieve moment matching and recover the steady-state behaviour of nonlinear systems with state dimension of order 1000 driven by linear and nonlinear signal generators.
Cite
@article{arxiv.2412.13371,
title = {A polynomial approximation scheme for nonlinear model reduction by moment matching},
author = {Carlos Doebeli and Alessandro Astolfi and Dante Kalise and Alessio Moreschini and Giordano Scarciotti and Joel Simard},
journal= {arXiv preprint arXiv:2412.13371},
year = {2026}
}
Comments
21 pages, 4 figures, submitted to SIAM Journal on Scientific Computing