How to find a function that can approximate another blackbox function programmaticly?

Question

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https://stackoverflow.com/questions/21758016/how-to-find-a-function-that-can-approximate-another-blackbox-function-programmat

I was suggested to post it here.

I have two functions

m1 = f1(w, s)
m2 = f2(w, s)

f1() and f2() are all blackboxs. Given w and s, I can get m1 and m2.

Now, I need to design or find a function g, such that

 m2' = g(m1)

 Also, the difference between m2 and m2' must be minimized.

The w and s are all stochastic process.

How can I find such a function g()? What knowledge domain does this belong to ?