Density Matrix Renormalization for Model Reduction in Nonlinear Dynamics

Thorsten Bogner

doi:10.1103/physreve.76.056707

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arXiv · 0707.4384

Density Matrix Renormalization for Model Reduction in Nonlinear Dynamics

Thorsten Bogner

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Abstract

We present a novel approach for model reduction of nonlinear dynamical systems based on proper orthogonal decomposition (POD). Our method, derived from Density Matrix Renormalization Group (DMRG), provides a significant reduction in computational effort for the calculation of the reduced system, compared to a POD. The efficiency of the algorithm is tested on the one dimensional Burgers equations and a one dimensional equation of the Fisher type as nonlinear model systems.

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Thorsten Bogner. 2007-08-29. Density Matrix Renormalization for Model Reduction in Nonlinear Dynamics. https://doi.org/10.1103/physreve.76.056707

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