Not sure what the question is.

If you mean "can we somehow guarantee we will have the right formula, the one the devs use" the answer is no.

If you mean "can we get a formula that will fit the data perfectly" the answer is yes.

In reality, there is no difference between the two as long as we can test for the accuracy of inter/extrapolation.

Its sort of how you can get the taylor expansion of any function, there is a polynomial approximation with some error.

You want less error, you put in more terms (in our case, perhaps more hidden layers, and more data to train).