Neural Network (FFW, BP) - function approximation

Question

is it possible to train NN to approximate this function:

If I tun approximation for x^2 or sin or something simple, it works fine, but for this sort of function i got only constant valued line. My NN has 2 inputs (x, f(x)), one hidden layer (10 neurons), 1 output (f(x)) For training I am using BP, activation functions sigmoid -> tanh

My goal is to get "smooth" function without noise, that catch function on image above.

Or is there any other way with NN or genetic algorithm, how to approximate this ?

Answer 1

You're gping to have major problems because the input (x, f(x)) is discontinuous (not exactly, but sort of).

Therefore, your NN will have to literally memorize the x-f(x) mapping given the large discontinuities.

One approach is to use a four-layer NN which can address the discontinuities.

But really, you may simply want to look at other smoothening methods rather than NN for thos problem.

You have a periodic function so first of all, only use one period, or you will memorize and not generalize.