data fitting with multiple independent variables

Question

Daniele Sonaglioni 2024-1-9

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https://ww2.mathworks.cn/matlabcentral/answers/2068146-data-fitting-with-multiple-independent-variables

回答： the cyclist 2024-1-9

Hi all,

I am trying to fit my experimental data with the socalled double well model. To be concise, i have several intensity profiles as a function of the distance from the detector for several temperatures and i want to fit all of them at the same time. Even though the double well model has only 5 independent parameters, by adopting this procedure I end with more than 100 fitting parameters.

I have tried to use GlobalSearch but I am not satisfied of the result: can anyone suggest me a more powerful algorithm?

Thanks to everyone.

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Matt J 2024-1-9

编辑：Matt J 2024-1-9

@Daniele Sonaglioni Your post is too exclusively text. We need to see a mathematical description of your fitting problem to understand why you think it is more difficult than standard fitting scenarios.

Torsten 2024-1-9

编辑：Torsten 2024-1-9

you are right, I forgot to say, but two of the five parameters are in common, whereas the other are temperature specific. Hence, I have two global parameter and three parameters are temperature dependent.

You should think about a new model that accounts for temperature-dependence, i.e. a model in which the variable T for temperature explicitly appears . It is against all modelling principles that for each temperature, you have three free parameters. What would be the purpose of such a model if new fitting is necessary once you have measurements for a new temperature ?

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Answer 1

William Rose 2024-1-9

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https://ww2.mathworks.cn/matlabcentral/answers/2068146-data-fitting-with-multiple-independent-variables#answer_1386476

编辑：William Rose 2024-1-9

@Daniele Sonaglioni,

[edit: correct spelling error]

Your model includes two global parameters (p1, p2) and three parameters that depend on temperature (p3, p4, p5). If you have collected data at 40 different termperatures (and I assume you know the temperatures), then you may feel the need to estimate 2+3*40 parameters, which is too many.

Assume that p3, p4, p5 are functions of temperature. Maybe you have a theoretical relationship of each parameter to temperature. If not, then assume something, such as a linear or polynomial relationship. Then you only have to fit the parameters of those three functions. For example:

p3 = a3 + b3*T

p4 = a4 + b4*T

p5 = a5 + b5*T

Then you only have to fit 8 parameters (p1, p2, a3, b3, a4, b4, a5, b5), not 122 parameters, because you know the temperatures at which you collected the data. I have used this approach for published work.