Difference between revisions of "Sensitivity Analysis"
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;Analysis title | ;Analysis title | ||
| − | :Sensitivity Analysis | + | :[[File:Differential-algebraic-equations-Sensitivity-Analysis-icon.png]] Sensitivity Analysis |
;Provider | ;Provider | ||
:[[Institute of Systems Biology]] | :[[Institute of Systems Biology]] | ||
| + | ;Class | ||
| + | :{{Class|biouml.plugins.modelreduction.SensitivityAnalysis}} | ||
| + | ;Plugin | ||
| + | :[[Biouml.plugins.modelreduction (plugin)|biouml.plugins.modelreduction (Model reduction plug-in)]] | ||
==== Description ==== | ==== Description ==== | ||
The method calculates sensitivities associated with the steady state of the purely temporal system | The method calculates sensitivities associated with the steady state of the purely temporal system | ||
| − | :: [[File: | + | :: [[File:Differential-algebraic-equations-Sensitivity-Analysis-sa1.png]] |
where ''c'' is the ''n''-vector of species concentrations, ''α'' is the ''m''-vector of systems parameters (which can include the initial conditions ''c''<sup>0</sup>), and ''t'' (time) is the variable of integration. | where ''c'' is the ''n''-vector of species concentrations, ''α'' is the ''m''-vector of systems parameters (which can include the initial conditions ''c''<sup>0</sup>), and ''t'' (time) is the variable of integration. | ||
| − | The local sensitivities ∂''c''/∂''α<sub>j</sub>'' are calculated via finite difference approximations | + | The local unscaled sensitivities ∂''c''/∂''α<sub>j</sub>'' are calculated via finite difference approximations |
| − | :: [[File: | + | :: [[File:Differential-algebraic-equations-Sensitivity-Analysis-sa2.png]] |
where ''c<sub>ss</sub>''(''α<sub>j</sub>'') and ''c<sub>ss</sub>''(''α<sub>j</sub>''+Δ''α<sub>j</sub>'') correspond to the solutions of the algebraic systems ''f''(''c'', ''α<sub>j</sub>'') = 0 and ''f''(''c'', ''α<sub>j</sub>''+Δ''α<sub>j</sub>'') = 0 respectively. | where ''c<sub>ss</sub>''(''α<sub>j</sub>'') and ''c<sub>ss</sub>''(''α<sub>j</sub>''+Δ''α<sub>j</sub>'') correspond to the solutions of the algebraic systems ''f''(''c'', ''α<sub>j</sub>'') = 0 and ''f''(''c'', ''α<sub>j</sub>''+Δ''α<sub>j</sub>'') = 0 respectively. | ||
| + | |||
| + | The scaled sensitivities is calculated by multiplying each component ∂''c<sup>k</sup>''/∂''α<sub>j</sub>'' of the vector ∂''c''/∂''α<sub>j</sub>'' by the normalization factor ''α<sub>j</sub>''/''c<sup>k</sup><sub>ss</sub>''(''α<sub>j</sub>''). | ||
| + | |||
==== References ==== | ==== References ==== | ||
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[[Category:Analyses]] | [[Category:Analyses]] | ||
| − | [[Category: | + | [[Category:Differential algebraic equations (analyses group)]] |
[[Category:ISB analyses]] | [[Category:ISB analyses]] | ||
[[Category:Autogenerated pages]] | [[Category:Autogenerated pages]] | ||
Latest revision as of 18:14, 9 December 2020
- Analysis title
Sensitivity Analysis
- Provider
- Institute of Systems Biology
- Class
SensitivityAnalysis- Plugin
- biouml.plugins.modelreduction (Model reduction plug-in)
[edit] Description
The method calculates sensitivities associated with the steady state of the purely temporal system
where c is the n-vector of species concentrations, α is the m-vector of systems parameters (which can include the initial conditions c0), and t (time) is the variable of integration.
The local unscaled sensitivities ∂c/∂αj are calculated via finite difference approximations
where css(αj) and css(αj+Δαj) correspond to the solutions of the algebraic systems f(c, αj) = 0 and f(c, αj+Δαj) = 0 respectively.
The scaled sensitivities is calculated by multiplying each component ∂ck/∂αj of the vector ∂c/∂αj by the normalization factor αj/ckss(αj).
[edit] References
- H Rabitz, M Kramer, D Dacol, "Sensitivity analysis in chemical kinetics". Annu. Rev. of Phys. Chem., 34:419-461.
