Function Approximation with AI methodologies

5/2/13

I found out how to get the NN to display the funtion it has created. you use the sim command to simulate the results example:



x=0:0.05:2;
y=humps(x);

P=x; T=y;

plot(P,T,'x')

xlabel('time'); ylabel('output'); title('Original Function');

net = fitnet(3, 'trainlm');  %fitnet is feedforward network 'n' neurons, and training function

%default settings; 1000 iterations
 net = train(net,P,T);
     view(net); %diagram of network
     y = net(x);
     a= sim(net,P);

% Plot result and compare
plot(P,a-T,P,a, P,T); grid;
legend('error', 'NN function', 'Original');



If you inrease the number of neurons you can see the NN fuction becoming closer to the orignal, also the error line is closer to zero.

humps(x) is a demo function which is equivalent to :

y = 1 ./ ((x-.3).^2 + .01) + 1 ./ ((x-.9).^2 + .04) - 6;

Alterantively you can use the data set
[x,y] = simplefit_dataset;(no need for the x=0:0.05:2 with this)