Model reduction by empirical spectral methods via sampling of chaotic orbits

Proper Orthogonal Decomposition (POD) coupled with Galerkin method is applied to the one-dimensional model of a tubular reactor with an external heat recycle for energy recovery, which exhibits complex oscillatory – periodic and chaotic – solutions. Particularly, the effect of the cooling medium temperature onto system dynamics is considered. The issue of the optimal construction of the POD basis is addressed by sampling of the chaotic orbits, with the aim of constructing a global basis for a reduced order model (ROM). To demonstrate that such orbits are the most appropriate – because they incorporate the maximum amount of information about the system behavior – the information entropy of the orbit is calculated. Sampling of the chaotic solutions allows for the determination of the POD basis which, when employed in the POD/Galerkin method, delivers accurate solutions, even for values of the parameter for which the model behavior is far from chaotic, i.e. periodic orbits or fixed points.