Suppose I have only three independent features
(x, y, z) as the input to some machine learning routine (e.g. neural network). From some domain knowledge, I know that the output
o(x, y, z) must have the specific functional form
o(x, y, z) = f(x)*g(y)*g(z)
g(.) are the same function. The details of
g(.) are not known beforehand (except that
f(.) is a decaying function with respect to
x). Given that there is no upper limit on the sample size, is it possible to incorporate such a functional form (or in general, any specific functional form) into the machine learning routine?