sensitivity analysis on ODE model
0
$begingroup$
I have a model equation of a kind:
$frac{db}{dz} = alpha bw$
$frac{dw}{dz} = w^2 g $
$frac{dg}{dz} = g b^2$
I have a MATLAB model that can compute the solution. Now I would like to do the sensitivity analysis with regard to the input parameters and alpha. I really don't know how to begin. I have tried to read some articles but couldn't able to get how and where to begin of writing the codes.
ordinary-differential-equations
asked Jan 17 at 13:11
DerejeDereje
44
$endgroup$
add a comment |
0
$begingroup$
I have a model equation of a kind:
$frac{db}{dz} = alpha bw$
$frac{dw}{dz} = w^2 g $
$frac{dg}{dz} = g b^2$
I have a MATLAB model that can compute the solution. Now I would like to do the sensitivity analysis with regard to the input parameters and alpha. I really don't know how to begin. I have tried to read some articles but couldn't able to get how and where to begin of writing the codes.
ordinary-differential-equations
asked Jan 17 at 13:11
DerejeDereje
44
$endgroup$
$begingroup$
There are many types of sensitivity analysis. Probably you should start by trying to be more precise about what exactly you want to do.
$endgroup$
– dbx
Jan 17 at 14:36
$begingroup$
For example, how the solution affected by using different initial conditions and also how alpha affects the result.
$endgroup$
– Dereje
Jan 17 at 21:45
$begingroup$
Here are some keywords to get you started: Global analysis, Local analysis, Variance-Based Sensitivity, One-At-A-Time Analysis... have a look at: en.wikipedia.org/wiki/Sensitivity_analysis. There are lots of ways to do this so the answer to your question will depend on which method you want to use.
$endgroup$
– dbx
Jan 18 at 2:27
$begingroup$
for my case I chose external numerical differentiation method which is by varying the initial values y0 by a "small" amount lets say delta and calculate the difference of the results. So the sensitivity is the quotient becomes: (y(end) - y_varied(end)) ./ delta
$endgroup$
– Dereje
Jan 18 at 11:38
add a comment |
0
0
0
$begingroup$
I have a model equation of a kind:
$frac{db}{dz} = alpha bw$
$frac{dw}{dz} = w^2 g $
$frac{dg}{dz} = g b^2$
I have a MATLAB model that can compute the solution. Now I would like to do the sensitivity analysis with regard to the input parameters and alpha. I really don't know how to begin. I have tried to read some articles but couldn't able to get how and where to begin of writing the codes.
ordinary-differential-equations
asked Jan 17 at 13:11
DerejeDereje
44
$endgroup$
I have a model equation of a kind:
$frac{db}{dz} = alpha bw$
$frac{dw}{dz} = w^2 g $
$frac{dg}{dz} = g b^2$
I have a MATLAB model that can compute the solution. Now I would like to do the sensitivity analysis with regard to the input parameters and alpha. I really don't know how to begin. I have tried to read some articles but couldn't able to get how and where to begin of writing the codes.
ordinary-differential-equations
ordinary-differential-equations
asked Jan 17 at 13:11
DerejeDereje
44
asked Jan 17 at 13:11
DerejeDereje
44
asked Jan 17 at 13:11
DerejeDereje
44
asked Jan 17 at 13:11
DerejeDereje
44
asked Jan 17 at 13:11
DerejeDereje
44
44
$begingroup$
There are many types of sensitivity analysis. Probably you should start by trying to be more precise about what exactly you want to do.
$endgroup$
– dbx
Jan 17 at 14:36
$begingroup$
For example, how the solution affected by using different initial conditions and also how alpha affects the result.
$endgroup$
– Dereje
Jan 17 at 21:45
$begingroup$
Here are some keywords to get you started: Global analysis, Local analysis, Variance-Based Sensitivity, One-At-A-Time Analysis... have a look at: en.wikipedia.org/wiki/Sensitivity_analysis. There are lots of ways to do this so the answer to your question will depend on which method you want to use.
$endgroup$
– dbx
Jan 18 at 2:27
$begingroup$
for my case I chose external numerical differentiation method which is by varying the initial values y0 by a "small" amount lets say delta and calculate the difference of the results. So the sensitivity is the quotient becomes: (y(end) - y_varied(end)) ./ delta
$endgroup$
– Dereje
Jan 18 at 11:38
add a comment |
$begingroup$
There are many types of sensitivity analysis. Probably you should start by trying to be more precise about what exactly you want to do.
$endgroup$
– dbx
Jan 17 at 14:36
$begingroup$
For example, how the solution affected by using different initial conditions and also how alpha affects the result.
$endgroup$
– Dereje
Jan 17 at 21:45
$begingroup$
Here are some keywords to get you started: Global analysis, Local analysis, Variance-Based Sensitivity, One-At-A-Time Analysis... have a look at: en.wikipedia.org/wiki/Sensitivity_analysis. There are lots of ways to do this so the answer to your question will depend on which method you want to use.
$endgroup$
– dbx
Jan 18 at 2:27
$begingroup$
for my case I chose external numerical differentiation method which is by varying the initial values y0 by a "small" amount lets say delta and calculate the difference of the results. So the sensitivity is the quotient becomes: (y(end) - y_varied(end)) ./ delta
$endgroup$
– Dereje
Jan 18 at 11:38
$begingroup$
There are many types of sensitivity analysis. Probably you should start by trying to be more precise about what exactly you want to do.
$endgroup$
– dbx
Jan 17 at 14:36
$begingroup$
There are many types of sensitivity analysis. Probably you should start by trying to be more precise about what exactly you want to do.
$endgroup$
– dbx
Jan 17 at 14:36
$begingroup$
For example, how the solution affected by using different initial conditions and also how alpha affects the result.
$endgroup$
– Dereje
Jan 17 at 21:45
$begingroup$
For example, how the solution affected by using different initial conditions and also how alpha affects the result.
$endgroup$
– Dereje
Jan 17 at 21:45
$begingroup$
Here are some keywords to get you started: Global analysis, Local analysis, Variance-Based Sensitivity, One-At-A-Time Analysis... have a look at: en.wikipedia.org/wiki/Sensitivity_analysis. There are lots of ways to do this so the answer to your question will depend on which method you want to use.
$endgroup$
– dbx
Jan 18 at 2:27
$begingroup$
Here are some keywords to get you started: Global analysis, Local analysis, Variance-Based Sensitivity, One-At-A-Time Analysis... have a look at: en.wikipedia.org/wiki/Sensitivity_analysis. There are lots of ways to do this so the answer to your question will depend on which method you want to use.
$endgroup$
– dbx
Jan 18 at 2:27
$begingroup$
for my case I chose external numerical differentiation method which is by varying the initial values y0 by a "small" amount lets say delta and calculate the difference of the results. So the sensitivity is the quotient becomes: (y(end) - y_varied(end)) ./ delta
$endgroup$
– Dereje
Jan 18 at 11:38
$begingroup$
for my case I chose external numerical differentiation method which is by varying the initial values y0 by a "small" amount lets say delta and calculate the difference of the results. So the sensitivity is the quotient becomes: (y(end) - y_varied(end)) ./ delta
$endgroup$
– Dereje
Jan 18 at 11:38
add a comment |
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$begingroup$
There are many types of sensitivity analysis. Probably you should start by trying to be more precise about what exactly you want to do.
$endgroup$
– dbx
Jan 17 at 14:36
$begingroup$
For example, how the solution affected by using different initial conditions and also how alpha affects the result.
$endgroup$
– Dereje
Jan 17 at 21:45
$begingroup$
Here are some keywords to get you started: Global analysis, Local analysis, Variance-Based Sensitivity, One-At-A-Time Analysis... have a look at: en.wikipedia.org/wiki/Sensitivity_analysis. There are lots of ways to do this so the answer to your question will depend on which method you want to use.
$endgroup$
– dbx
Jan 18 at 2:27
$begingroup$
for my case I chose external numerical differentiation method which is by varying the initial values y0 by a "small" amount lets say delta and calculate the difference of the results. So the sensitivity is the quotient becomes: (y(end) - y_varied(end)) ./ delta
$endgroup$
– Dereje
Jan 18 at 11:38