A polynomial approximation scheme for nonlinear model reduction by moment matching
| Autor: | Doebeli, Carlos, Astolfi, Alessandro, Kalise, Dante, Moreschini, Alessio, Scarciotti, Giordano, Simard, Joel |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 a system's steady-state behaviour for linear and nonlinear signal generators with system dynamics up to $n=1000$ dimensions. Comment: 26 pages, 3 figures, submitted to SIAM Journal on Scientific Computing |
| Databáze: | arXiv |
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