Extracting nonlinear dependencies

[dmitryk]

Extracting nonlinear dependencies

Hello for all!

I am a PhD student, and my thesis is devoted to extracting nonlinear dependencies from the results of physical or technical experiments. One of the main target of the work is to extract a certain form of the dependency: if it is sinus, for example, it has to be recognized like a sinus, or, say, if it is something like y = lnx + cosAx, it has to be concluded that the dependency has a similar structure.

I have read different articles on this topic, and no one a certain approach for solution the problem has been found. There are short mentions, that the problem can be solved with neural networks, genetic programming or fuzzy computations. It?s obvious, but the fact that I have not found a specific algorithm makes me conclude that there is not a developed computational procedure for the problem.

Could anybody tell me it is right or wrong? Perhaps, I have not seen the work where such an algorithm is described. I have found a small article published in one Russian journal, where the algorithm based on genetic programming is described. But the idea to use this approach is not fresh.

So, if someone could help me, I will appreciate him sincerely
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[adnanmasood]

Dmitry

I'm not sure If I understood your question correctly but have you tried approaches such as linear / quadratic interpolations and typical numerical method implementations to evaluate and extract the dependencies?

Also, what kind (format) of data are you working with as an output of these experiments.

-Adnan