Surface Fitting for a pair of coupled differential equations

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?

[Torsten]

Why not minimizing

sum_i [(R_data(i)-R_simulated(i))^2 +(S_data(i)-S_simulated(i))^2]

simultaneously ?

Best wishes

Torsten.

[Samyukta Ramnath]

This is what I have done currently, but this would not be the correct way to fit the two surfaces individually... correct?

[Torsten]

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.