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arXiv · 2412.13371

A polynomial approximation scheme for nonlinear model reduction by moment matching

Carlos Doebeli·Alessandro Astolfi·Dante Kalise·Alessio Moreschini·Giordano Scarciotti·Joel Simard
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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.

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Carlos Doebeli, Alessandro Astolfi, Dante Kalise, Alessio Moreschini, Giordano Scarciotti, Joel Simard. 2024-12-17. A polynomial approximation scheme for nonlinear model reduction by moment matching. https://arxiv.org/abs/2412.13371

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