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NN function approximation: What's wrong with my code?

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Ande Mandoyi on 8 Sep 2020
Commented: Ande Mandoyi on 8 Sep 2020
I have just started learning neural networks and have been stuck on a homework question for quite a while. the question is as follows:
Design a feed forward multi-layer neural network to approximate the function y=sin(x1)+cos(x2). Here, -5<x1<5 and 0<x2<5. Please use x1 = (rand(1,50)-0.5)*10; x2 = rand(1,50)*5; to get the samples to train the neural network. Finally, please draw the prediction error series y - ynet for the inputs x1=-5:0.1:5 and x2=0:0.05:5.
Here's my code:
x1 = (rand(1,50)-0.5)*10; %training sample one
x2 = rand(1,50)*5; %training sample two
x = [x1;x2];
y=sin(x1)+cos(x2); %targeted output
net = newff(minmax(x),[20 1],{'tansig','purelin'},'trainlm');
net.trainparam.epochs = 10000;
net.trainparam.goal = 1e-25;
net.trainparam.lr = 0.01;
net = train(net,x,y);
input1 = -5:0.1:5;
input2 = 0:0.05:5;
input = [input1;input2];
y=sin(input1)+cos(input2);
ynet = net(input);
plot(y-ynet)
grid
The prediction error I get is very high.
Thanks in advance
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Accepted Answer

Walter Roberson on 8 Sep 2020
If you sort your y and ynet based upon input1, then you can see that the error is especially bad towards the right hand side (input1 close to 5). If you sort based upon input2, then there are multiple not-good places but especially towards input2 close to 5.
If you scatter(x1, x2), then at least for the run I did, the number of random samples close to x1 = 5 or x2 = 5 is not high.
I think you need more training data.
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Ande Mandoyi on 8 Sep 2020
Those were my initial thoughts as well, more data is required. Thanks for the insight.

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