How can I define a gradient function that can update k values after each iteration to optimize parameters in ODEs?

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Hyukjin Jang 2021-2-26

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https://ww2.mathworks.cn/matlabcentral/answers/757244-how-can-i-define-a-gradient-function-that-can-update-k-values-after-each-iteration-to-optimize-param

回答： Star Strider 2021-2-26

I need to optimize three parameters (k1,k2,k3) by solving two ODEs.

For example,

C2' = k1*C1 - k3*C3 - k2*C2

C3' = k3*C3 - C2

C_total = C2 + C3

C_total and C1 are known data.

The only approach I can think of right now is to try different k-values using gradient method and find k-values that minimize SSE (sum(C_total_true - C_total_pred)^2) since I have C_total data avaiable.

How can I define a gradient function that can update k values after each iteration?

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Answer 1

Star Strider 2021-2-26

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https://ww2.mathworks.cn/matlabcentral/answers/757244-how-can-i-define-a-gradient-function-that-can-update-k-values-after-each-iteration-to-optimize-param#answer_634274

One option is the approach in Parameter Estimation for a System of Differential Equations. You will need to modify the ‘kinetics’ code to use your system of differential equations, and to fit the data.

The necessary data would be a time vector and as much dependent variable data as available. The ‘theta’ values would be the ‘k’ values in your system. (I have subsequently updated that code, and I can provide an update if necessary.)