Prediction using narx Network
%Neural network to create a Fibinocci series
u=[1 2 3 4 5 6 7 8 9 10]; %Input Series
y=[1 2 3 5 8 13 21 34 55 89]; % Target series
[u,us] = mapminmax(u);
[y,ys] = mapminmax(y);
y = con2seq(y);
u = con2seq(u); d1 = [1:2];
d2 = [1:2];
narx_net = narxnet(d1,d2,10);
narx_net.divideFcn = ‘’;
narx_net.trainParam.epochs = 1000;
narx_net.trainParam.min_grad = 1e-10;
[p,Pi,Ai,t] = preparets(narx_net,u,{},y);
% Train the Network-Open Loop
narx_net = train(narx_net,p,t,Pi);
% Simulate the Network-Open Loop
yp = sim(narx_net,p,Pi);
y_again=mapminmax(‘reverse’,yp,ys)
%view(narx_net); %error_OL = cell2mat(yp)-cell2mat(y(3:end));
%Close narx net for future prediction
narx_net_closed = closeloop(narx_net);
[p1,Pi1,Ai1,t1] = preparets(narx_net_closed,u,{},y);
% Train the Network-Closed Loop
% narx_net_closed = train(narx_net_closed,p1,t1,Pi1);
% Simulate the Network-Closed Loop
yp1 = narx_net_closed(p1,Pi1,Ai1);
yp1_again=mapminmax(‘reverse’,yp1,ys)
Please answer the following questions:
1. How can I make one step prediction without closing loop?
2. How can I get the next 5 numbers in the series? please provide the code if possible. I went through all your posts but could not solve it.
3. When I close the narx net, I get the same results as of open loop without training.
4. If I train the close loop, the outputs deviate from the target. How can I reduce this error?
ANSWER
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The Fibonacci series does not result from an input/output relationship. It is autoregressive
Either y(1:2) = [ 0 1 ] or y(1:2) = [ 1 1 ] and then
y(n+1) = y(n) + y(n-1)Obviously this can be implemented with a NARNET WITH NO HIDDEN NODES.
