<abstract xmlns="http://www.w3.org/1999/xhtml"><p>This work develops a technique for constructing a reduced-order system that not only has low computational complexity, but also maintains the stability of the original nonlinear dynamical system. The proposed framework is designed to preserve the contractivity of the vector field in the original system, which can further guarantee stability preservation, as well as provide an error bound for the approximated equilibrium solution of the resulting reduced system. This technique employs a low-dimensional basis from proper orthogonal decomposition to optimally capture the dominant dynamics of the original system, and modifies the discrete empirical interpolation method by enforcing certain structure for the nonlinear approximation. The efficiency and accuracy of the proposed method are illustrated through numerical tests on a nonlinear reaction diffusion problem.</p></abstract>

This work develops a technique for constructing a reduced-order system that not only has low computational complexity, but also maintains the stability of the original nonlinear dynamical system. The proposed framework is designed to preserve the contractivity of the vector field in the original system, which can further guarantee stability preservation, as well as provide an error bound for the approximated equilibrium solution of the resulting reduced system. This technique employs a low-dimensional basis from proper orthogonal decomposition to optimally capture the dominant dynamics of the original system, and modifies the discrete empirical interpolation method by enforcing certain structure for the nonlinear approximation. The efficiency and accuracy of the proposed method are illustrated through numerical tests on a nonlinear reaction diffusion problem.

Stabilized model reduction for nonlinear dynamical systems through a contractivity-preserving framework

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

This work develops a technique for constructing a reduced-order system that not only has low computational complexity, but also maintains the stability of the...

Stabilized model reduction for nonlinear dynamical systems through a contractivity-preserving framework

Published Online: Dec 31, 2020

Page range: 615 - 628

Received: Apr 27, 2020

Accepted: Oct 13, 2020

DOI: https://doi.org/10.34768/amcs-2020-0045

Keywords
model order reduction, contractivity, ordinary differential equations, partial differential equations, proper orthogonal decomposition, discrete empirical interpolation method

© 2020 Saifon Chaturantabut, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Stabilized model reduction for nonlinear dynamical systems through a contractivity-preserving framework

Published Online: Dec 31, 2020

Page range: 615 - 628

Received: Apr 27, 2020

Accepted: Oct 13, 2020

DOI: https://doi.org/10.34768/amcs-2020-0045

Keywordsmodel order reduction, contractivity, ordinary differential equations, partial differential equations, proper orthogonal decomposition, discrete empirical interpolation method

© 2020 Saifon Chaturantabut, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
model order reduction, contractivity, ordinary differential equations, partial differential equations, proper orthogonal decomposition, discrete empirical interpolation method