Unable to approximate the sine function using a neural network

Question

I am trying to approximate the sine() function using a neural network I wrote myself. I have tested my neural network on a simple OCR problem already and it worked, but I am

Answer 1

When you train the network, you should normalize the target (the sin function) to the range [0,1], then you can keep the sigmoid transfer function.

sin(x) in [-1,1]  =>  0.5*(sin(x)+1) in [0,1]

Train data:
    input    target    target_normalized
    ------------------------------------
    0         0          0.5
    pi/4      0.70711    0.85355
    pi/2      1           1
    ...

Note that that we mapped the target before training. Once you train and simulate the network, you can map back the output of the net.

---

The following is a MATLAB code to illustrate:

%% input and target
input = linspace(0,4*pi,200);
target = sin(input) + 0.2*randn(size(input));

% mapping
[targetMinMax,mapping] = mapminmax(target,0,1);

%% create network (one hidden layer with 6 nodes)
net = newfit(input, targetMinMax, [6], {'tansig' 'tansig'});
net.trainParam.epochs = 50;
view(net)

%% training
net = init(net);                            % init
[net,tr] = train(net, input, targetMinMax); % train
output = sim(net, input);                   % predict

%% view prediction
plot(input, mapminmax('reverse', output, mapping), 'r', 'linewidth',2), hold on
plot(input, target, 'o')
plot(input, sin(input), 'g')
hold off
legend({'predicted' 'target' 'sin()'})