Difference between revisions of "Sensitivity Analysis"

From BioUML platform
Jump to: navigation, search
(Automatic synchronization with BioUML)
(Automatic synchronization with BioUML)
 
(5 intermediate revisions by one user not shown)
Line 1: Line 1:
 
;Analysis title
 
;Analysis title
:[[File:Sensitivity-Analysis-icon.png]] 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
 
;Plugin
 
:[[Biouml.plugins.modelreduction (plugin)|biouml.plugins.modelreduction (Model reduction plug-in)]]
 
:[[Biouml.plugins.modelreduction (plugin)|biouml.plugins.modelreduction (Model reduction plug-in)]]
Line 9: Line 11:
 
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:DAE-models-Sensitivity-Analysis-sa1.png]]
+
:: [[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:DAE-models-Sensitivity-Analysis-sa2.png]]
+
:: [[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 ====
  
Line 23: Line 28:
  
 
[[Category:Analyses]]
 
[[Category:Analyses]]
[[Category:DAE models (analyses group)]]
+
[[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
Differential-algebraic-equations-Sensitivity-Analysis-icon.png 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

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 c0), and t (time) is the variable of integration.

The local unscaled sensitivities ∂c/∂αj are calculated via finite difference approximations

Differential-algebraic-equations-Sensitivity-Analysis-sa2.png

where css(αj) and css(αjαj) correspond to the solutions of the algebraic systems f(c, αj) = 0 and f(c, αjαj) = 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

  1. H Rabitz, M Kramer, D Dacol, "Sensitivity analysis in chemical kinetics". Annu. Rev. of Phys. Chem., 34:419-461.
Personal tools
Namespaces

Variants
Actions
BioUML platform
Community
Modelling
Analysis & Workflows
Collaborative research
Development
Virtual biology
Wiki
Toolbox