Abstract
A new approach for calculating effective models for nonlinear dynamical
systems is presented. This is accomplished by combining the Density Matrix
Renormalisation Group(DMRG), a numerical precision method in the field
of strongly correlated quantum systems, and the Proper Orthogonal
Decomposition(POD), a widely used method in the numerics of Partial
Differential Equations(PDEs).
Our method allows to find a reduction without ever performing a
calculation on the full system.
We apply our method to several nonlinear PDEs.
An analysis of the errors and a comparison to existing model reduction
methods is made. Also the stability of the algorithm will be discussed.
The results of our approach are comparable or even superior to
standard POD. This holds for both, accuracy and computational costs.
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