Volume 2, Issue 5
Comparison of Invariant Manifolds for Model Reduction in Chemical Kinetics

E. Chiavazzo, A. N. Gorban & I. V. Karlin

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Commun. Comput. Phys., 2 (2007), pp. 964-992.

Published online: 2007-02

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  • Abstract

A modern approach to model reduction in chemical kinetics is often based on the notion of slow invariant manifold. The goal of this paper is to give a comparison of various methods of construction of slow invariant manifolds using a simple Michaelis-Menten catalytic reaction. We explore a recently introduced Method of Invariant Grids (MIG) for iteratively solving the invariance equation. Various initial approximations for the grid are considered such as Quasi Equilibrium Manifold, Spectral Quasi Equilibrium Manifold, Intrinsic Low Dimensional Manifold and Symmetric Entropic Intrinsic Low Dimensional Manifold. Slow invariant manifold was also computed using the Computational Singular Perturbation (CSP) method. A comparison between MIG and CSP is also reported. 

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@Article{CiCP-2-964, author = {}, title = {Comparison of Invariant Manifolds for Model Reduction in Chemical Kinetics}, journal = {Communications in Computational Physics}, year = {2007}, volume = {2}, number = {5}, pages = {964--992}, abstract = {

A modern approach to model reduction in chemical kinetics is often based on the notion of slow invariant manifold. The goal of this paper is to give a comparison of various methods of construction of slow invariant manifolds using a simple Michaelis-Menten catalytic reaction. We explore a recently introduced Method of Invariant Grids (MIG) for iteratively solving the invariance equation. Various initial approximations for the grid are considered such as Quasi Equilibrium Manifold, Spectral Quasi Equilibrium Manifold, Intrinsic Low Dimensional Manifold and Symmetric Entropic Intrinsic Low Dimensional Manifold. Slow invariant manifold was also computed using the Computational Singular Perturbation (CSP) method. A comparison between MIG and CSP is also reported. 

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7934.html} }
TY - JOUR T1 - Comparison of Invariant Manifolds for Model Reduction in Chemical Kinetics JO - Communications in Computational Physics VL - 5 SP - 964 EP - 992 PY - 2007 DA - 2007/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7934.html KW - AB -

A modern approach to model reduction in chemical kinetics is often based on the notion of slow invariant manifold. The goal of this paper is to give a comparison of various methods of construction of slow invariant manifolds using a simple Michaelis-Menten catalytic reaction. We explore a recently introduced Method of Invariant Grids (MIG) for iteratively solving the invariance equation. Various initial approximations for the grid are considered such as Quasi Equilibrium Manifold, Spectral Quasi Equilibrium Manifold, Intrinsic Low Dimensional Manifold and Symmetric Entropic Intrinsic Low Dimensional Manifold. Slow invariant manifold was also computed using the Computational Singular Perturbation (CSP) method. A comparison between MIG and CSP is also reported. 

E. Chiavazzo, A. N. Gorban & I. V. Karlin. (2020). Comparison of Invariant Manifolds for Model Reduction in Chemical Kinetics. Communications in Computational Physics. 2 (5). 964-992. doi:
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