Density Matrix Renormalization for Model Reduction in Nonlinear Dynamics

TL;DR

This paper introduces a DMRG-inspired model reduction technique for nonlinear dynamical systems that enhances computational efficiency over traditional POD methods, demonstrated on Burgers and Fisher equations.

Contribution

It develops a novel DMRG-based approach for nonlinear model reduction, improving computational efficiency compared to standard POD methods.

Findings

Significant reduction in computational effort achieved.

Effective application demonstrated on Burgers and Fisher equations.

Method outperforms traditional POD in efficiency.

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.