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?

Thanks in advance Regards

[Nawras Kh]

hello,plz can u help me i need the NARX code for predict my data

Answer 1

[Greg Heath]

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.

Hope this helps.

Thank you for formally accepting my answer

Greg

[Unnikrishnan PC]

Thanks a lot Greg.

Answer 2

[Greg Heath]

% Prediction using narx :

% Sent By Unnikrishnan P.C. On:Sep 09/19/14 1:45 PM

%Neural network to create a Fibinocci series

 close all, clear all, clc, plt = 0
X   = { 1 2 3 4 5 6 7 8 9 10 };             % Input Series
T   = { 1 2 3 5 8 13 21 34 55 89 };      % Target series
d1 = [ 1:2 ]; d2 = [ 1:2 ];
net                    =  narxnet( d1, d2, [] );
net.divideFcn    =  '';

 [ Xs, Xi, Ai, Ts ] =  preparets( net, X, {}, T );
whos X T Xs Xi Ai Ts
%  Name   Size      Bytes  Class   
%   Ai        1x0             0    cell     % ==> Timedelaynet          
%   T         1x10     1200    cell               
%   Ts       1x8         960    cell      % T(3:end)           
%   X         1x10     1200    cell               
%   Xi         2x2        480    cell      %  { X(1:2)     ; T(1:2) }           
%   Xs        2x8      1920    cell       % { X(3:end) ; T(3:end)}

 xs                     = cell2mat(Xs);
xs1                   = xs(1,:);
ts                      =  cell2mat( Ts );
MSE00s            =  var( ts',1 )         %  789

% Open-Loop Training

 rng('default')
view(net)
[ net tr Ys Es Xf Af ] = train( net, Xs, Ts, Xi, Ai);
view(net)
% Ys =  net( Xs, Xi, Ai );
% Es = gsubtract(net, Ts, Ys)

 whos Xs Ts Xi Ai Ys Es Xf Af
% Name      Size           Bytes  Class    
%   Af         1x0                 0       cell               
%   Ai         1x0                 0       cell               
%   Es        1x8               960    cell               
%   Ts        1x8               960    cell               
%   Xf         2x2              480    cell               
%   Xi         2x2               480    cell               
%   Xs        2x8             1920  cell               
%   Ys        1x8               960   cell

 ys    = cell2mat( Ys );
es    = cell2mat( Es );
R2s = 1 - mse( es )/MSE00s            % 1

 IW = net.IW{:}                    % 0.023  -0.023
b   = net.b{:}                      % 1.0632
LW = net.LW{:}                  % []
[ xsn xsettings ] = mapminmax(xs);
[ tsn tsettings ] = mapminmax(ts);
ysn = tansig(b(1) +  IW*xsn);

 plt = plt+1, figure( plt )
figure( plt )
subplot( 211 )
title('Fibonacci Series Model')
hold on
plot( xs1, ts )
plot( xs1, ys, 'ro' )
legend('Fibonacci','Open Loop Model',2)
subplot(212)
plot( xs1, es, 'ko-' )
legend('Open Loop Model Error')

%Close narx net for future prediction

 [ netc Xic Aic ]    = closeloop( net, Xi, Ai );
isequalX = isequal(Xic,Xi)       % 0
isequalA = isequal(Aic,Ai)       % 0
[  Xc, Xic, Aic, Tc ] = preparets( netc, X, {}, T );
isequalT = isequal(Tc,Ts)
tc           = ts;
MSE00c = MSE00s                         %    789
Yc    = netc( Xc, Xic, Aic );
yc    = cell2mat(Yc);
R2c = 1-mse(tc-yc)/MSE00c           % 1

 IW = netc.IW{:}                    % 0.023  -0.023
b   = netc.b{:}                      % 1.0632
LW = netc.LW{:}                  % 1    1

% Train the Closed Loop Network?

 [ netc trc Yc Ec Xfc Afc ]  = train(netc, Xc, Tc, Xic, Aic);
IW = netc.IW{:}                    % 0.023  -0.023
b   = netc.b{:}                      % 1.0632
LW = netc.LW{:}                  % 1    1

% Predict Future Outputs

 Xcf = con2seq(11:20);
Ycf = netc( Xcf , Xfc, Afc );
xcf = cell2mat( Xcf );
ycf = cell2mat( Ycf );
plt=plt+1, figure(plt)
subplot(211)
hold on
plot( xs1, ts )
plot( xs1, ys, 'ro' )
subplot(212)
hold on
plot( xs1, ts )
plot( xs1, ys, 'ro' )
plot(xcf, ycf, 'r-o')
}