Surface Fitting for a pair of coupled differential equations

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Samyukta Ramnath
Samyukta Ramnath 2017-5-10
评论： Torsten 2017-5-11
I a pair of coupled differential equations which solve for two variables, fe and fi. I have from a separate source, two surface plots - or quantities R_data and S_data, which I plot against fe and fi (from data).
In the differential equation for fe, there is a quantity R and in the differential equation for fi, there is a quantity S. I would like to fit the surfaces for the quantities R and S (vs. fe and fi from the differential equation) to the surfaces that I already have (R_data and S_data).
I have tried to use fminsearch for the same. However, fminsearch minimizes the error only for one surface/curve, and I have two surfaces to fit from the same set of differential equations. How would I go about solving this problem?
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Samyukta Ramnath
Samyukta Ramnath 2017-5-11
This is what I have done currently, but this would not be the correct way to fit the two surfaces individually... correct?
Torsten
Torsten 2017-5-11
If fe is a function of R alone and fi is a function of S alone, you could fit the two surfaces individually.
But you write that the differential equations for fe and fi are coupled, thus fe and fi will be functions of both R and S, I guess.
If this is the case, you will have to fit the two surfaces simultaneously by minimizing the above "combined" sum of squares
sum_i [(R_data(i)-fe(R,S,i))^2 +(S_data(i)-fi(R,S,i))^2]
Best wishes
Torsten.

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